RUNNING HEAD: Knowledge and Inductive Reasoning

The engine of thought is a hybrid: Roles of associative and structured knowledge in

reasoning

Aimée K. Bright

Queen Mary University of London

Aidan Feeney

Queen’s University Belfast

Author Note

Aimée K. Bright, School of Biological and Chemical Sciences, Psychology Division,

Queen Mary University of London; Aidan Feeney, Department of Psychology, Queen’s

University Belfast

This research was supported by an ESRC PhD studentship awarded to Aimée K.

Bright

Correspondence concerning this article should be addressed to Aimée K. Bright,

School of Biological and Chemical Sciences, Psychology Division, Queen Mary University

of London, E1 4NS, London, United Kingdom.

Email: a.bright@qmul.ac.uk

Word Count: 15,041

Knowledge and Inductive Reasoning

Abstract

Across a range of domains in psychology different theories assume different mental

representations of knowledge. For example, in the literature on category-based inductive

reasoning, certain theories (e.g. Rogers & McClelland, 2004; Sloutsky & Fisher, 2008)

assume that the knowledge upon which inductive inferences are based is associative whereas

others (e.g Heit & Rubinstein, 1994; Kemp & Tenenbaum, 2009; Osherson, Smith, Wilkie,

Lopez, & Shafir, 1990) assume that knowledge is structured. In this paper we investigate

whether associative and structured knowledge underlie inductive reasoning to different

degrees under different processing conditions. We develop a measure of knowledge about the

degree of association between categories and show that it dissociates from measures of

structured knowledge. In Experiment 1 participants rated the strength of inductive arguments

whose categories were either taxonomically or causally related. A measure of associative

strength predicted reasoning when people had to respond fast, whereas causal and taxonomic

knowledge explained inference strength when people responded slowly. In Experiment 2, we

also manipulated whether the causal link between the categories was predictive or diagnostic.

Participants preferred predictive to diagnostic arguments except when they responded under

cognitive load. In Experiment 3, using an open-ended induction paradigm, people generated

and evaluated their own conclusion categories. Inductive strength was predicted by

associative strength under heavy cognitive load, whereas an index of structured knowledge

was more predictive of inductive strength under minimal cognitive load. Together these

results suggest that associative and structured models of reasoning apply best under different

processing conditions, and that the application of structured knowledge in reasoning is often

effortful.

Keywords: inductive reasoning, associative, causal knowledge, categories

Introduction

Inductive reasoning has been referred to as the engine of thought because it allows us

to use what we already know to reduce our uncertainty about the way the world is. To ensure

that our inductive inferences are potent but sufficiently constrained, it is crucial that we select

the appropriate background knowledge. For example, if you eat shrimps and get ill, in future

you might avoid eating shrimps and other members of the shellfish family. However, if you

realize that the shrimps were past their expiration date, you might instead avoid eating meat,

dairy or vegetables past their expiration date, but happily eat fresh shrimps in future. As yet,

our understanding about the form taken by the knowledge that drives our inductive inferences

and how reasoners select the most appropriate knowledge with which to constrain a particular

inference is relatively poor. In this paper we will argue that the inductive engine of thought is

a hybrid, taking both associative and structured knowledge as input. Because associative

knowledge can influence the reasoning process relatively automatically and effortlessly,

whereas the influence of structured knowledge is more cognitively demanding and time-

consuming, environmental conditions are likely to determine which type of knowledge is

most important for a particular inference. In a series of experiments where processing

conditions were manipulated, we examined whether associative and structured knowledge

have dissociable effects on inductive reasoning.

In this paper we will focus on category-based inductive reasoning as it has been the

focus of much recent attention, and there are well specified models of category-based

induction which make different representational assumptions. In a category-based inductive

argument participants are asked to evaluate how strongly knowing that members of one

category possess a property supports the conclusion that members of another category do. For

example, knowing that shrimp possess property A how likely is it that mussels also possess

that property? Although early studies of category based induction (e.g. Osherson et al., 1990;

Rips, 1975) tended to use properties about which participants were unlikely to possess

background knowledge, subsequent studies showed the importance of the type of property in

the argument (see Heit & Rubenstein, 1994; Osherson, et al., 1993). More recent work

(Coley, 2012; for a review see Vasilyeva & Coley, 2010) has emphasized the different types

of knowledge made available by taxonomic (genes, cells) versus ecological properties

(infections, diseases).

Although the basic category-based inductive reasoning paradigm appears simple it

has generated quite a number of models (for a review see chapters in Feeney & Heit, 2007).

Because models of category-based reasoning appear to make contrasting representational

suppositions, which means that knowledge will be represented in only one form, there is a

pressing need for synthesis. We will consider the implications of our results for other types of

inductive reasoning and for a variety of modeling frameworks in the General Discussion. We

will begin with a review of literature highlighting the difference between associative and

structured knowledge and the role each type of knowledge plays in the reasoning process. We

then review current theories of category-based induction, broadly distinguishing them by the

contrasting emphasis they place on structured and associative knowledge. We then argue that

a process-level account can resolve the apparent dichotomy between frameworks which

emphasize different types of knowledge. This account predicts that the extent to which

associative and structured knowledge serve as input to reasoning processes will depend on

processing conditions.

Associative and Structured Knowledge

There are multiple types of knowledge that result from perception, learning and

reasoning. Here we want to focus on associative and structured knowledge. Broadly

speaking, associative knowledge develops as a result of co-occurrence, similarity or

contiguity (e.g. Kruschke, 1992; McClelland & Rumelhart, 1985; Rescorla & Wagner, 1972).

What we will refer to as structured knowledge captures the relations that exist between things

in the world. These relations can be causal, taxonomic, functional, spatial or take some other

form. Although the term “relational” is commonly used to refer to the type of knowledge we

wish to consider here (see Halford, Wilson, & Phillips, 2010), as “relational” theories of

category-based induction often posit the existence of complex structures of relations between

categories, we prefer the term “structured knowledge”. However, we mean the term

“structured” to refer to both complex (Kemp & Tenenbaum, 2009) and relatively simple

(Halford et al., 2010) relational knowledge.

There have been numerous attempts to define the characteristics of structured or

relational knowledge (see Halford et al., 2010; Markman, 1999). From our point of view,

perhaps the most important is that categories or objects are bound to a particular role by their

involvement in a particular relation (see Holyoak, 2012). Thus, in the context of induction,

the relation provides a mechanism by which the two categories involved in the relation come

to share a property. For example, we may think it likely that horses and cows share a gene

because their relative positions in the taxonomic hierarchy mean that they stand in close

relation to one another, but think it unlikely that horses and eagles will share a gene because

the taxonomic relation between them is not strong (see Osherson et al., 1990; Shafto, Kemp,

Bonawitz, Coley, & Tenenbaum, 2008). Similarly, we may think it likely that rabbits will

have a disease given that carrots have it, because their involvement in a food web (see Shafto

et al., 2008) may provide an unseen causal mechanism for disease transmission. This last

example clearly illustrates the importance of role-binding as carrots serve as the cause and

rabbits possessing the disease as the effect. These roles stay the same even when we reason

diagnostically i.e. when we consider the likelihood that carrots have a disease given that

rabbits have it (see Fernbach, Darlow, & Sloman, 2011).

Associative and structured knowledge appear to differ in a number of ways. First, the

knowledge types appear to have different developmental trajectories. Andrews, Halford and

Boyce (2012) demonstrated that children between 4 and 6 years could learn conditional

discriminations without awareness of the conditional relation. They argued that awareness of

the relation indicated relational rather than associative knowledge. Awareness of the

relational structure increased with age and was associated with a measure of fluid

intelligence. This suggests that the ability to represent and make use of structured relational

knowledge is an effortful process that develops with age.

Evidence for a second difference between the knowledge types comes from

comparative studies. Results in this area are contentious, and some authors have suggested

for example, that baboons in the wild are sensitive to hierarchical structure (Bergman,

Beehner, Cheney, & Seyfarth, 2003). However, Penn, Holyoak and Povenilli (2008) have

argued that whilst humans are not the only animals to possess associative knowledge,

possession of knowledge in the form of symbolic relational structure is unique to humans.

Furthermore, they argue that the extant evidence on animal’s sensitivity to hierarchical and

causal relations (see Bergman et al., 2003; Seed, Tebbich, Emery, & Clayton, 2006) suggests

that animals do not possess human-like sensitivity to unseen causal mechanisms or to

hierarchical relational structure (for a recent alternative view see Taylor, Miller, & Gray,

2013).

A third difference between these knowledge types is that requesting participants to

use one or other type of knowledge leads to different patterns of performance. For example,

Fenker, Waldman and Holyoak (2005) showed that there is a causal asymmetry effect in

reaction times when people evaluate the existence of causal relations between pairs of

categories (e.g. spark & flame). Reaction times were faster when the categories were

presented in a predictive (spark flame) compared to a diagnostic order (flame spark).

However, the asymmetry effect disappeared for evaluations of an association between the

same category pairs. This suggests that relations in semantic memory can be represented

either by explicitly encoded higher-order structural relations, or by simpler associations

between entities which cannot be reduced to one another. This also implies that the same

information can be encoded in different forms even if it is redundant (Sun, 1994; 2002).

In the rest of this paper we will consider whether the different types of process which

operate over associative and structured knowledge might have dissociable effects on

inductive reasoning. This possibility has not been considered before, but as we will see in the

following review, it could offer a way of synthesising apparently contradictory theoretical

frameworks for explaining category-based induction.

Associative Knowledge for Inductive Reasoning

The rationale for assuming that associative knowledge must play a central role in

inductive reasoning comes from a vast developmental literature (Colunga & Smith, 2005;

French, Mareschal, Mermillod, & Quinn, 2004; Jones & Smith, 2002; Sloutsky, Kloos, &

Fisher, 2007). These studies suggest that early induction is heavily influenced by the

statistical properties inherent in the environment such as co-occurrence and statistical

distribution of perceptual features. For example, Sloutsky and Fisher (2008) found that

associative learning mechanisms could explain young children’s flexible reasoning patterns

in the absence of higher-level, conceptual knowledge.These researchers also assume that

there is only a gradual and developmentally late transition from exclusive reliance on

associative knowledge to the use of category membership as a basis for induction (Sloutsky

& Fisher, 2008). This transition is largely seen as the product of explicit instruction and

learning about general characteristics of categories (Fisher & Sloutsky, 2005). However,

despite category representations being supplemented and expanded by top-down knowledge,

proponents of associative approaches advocate that adult induction is still heavily influenced

by similarity (Sloman, 1993, 1998) and associations in semantic memory (Rogers &

McClelland, 2004; Sloman, 1998). For example, Sloman’s (1993) Feature-Based Model

(FBM) explains generalizations in terms of the extent to which features which are associated

with different categories are simultaneously activated. The more associated features they

have in common, the more willing people should be to infer that the categories share a

property. Without reference to category membership, this neural network model can explain

several inductive reasoning phenomena. Sloman (1998) does not preclude the possibility that

assessment of similarity and inference process can at times reflect a more effortful process

which draws on knowledge about stable category hierarchies. However, he does suggest that

the default mode of category-based induction reflects a predominantly intuitive thought

process, requiring no processing effort or reference to class inclusion relations, especially

when people lack relevant knowledge, are under time pressure or have not been explicitly

instructed to carefully consider their response.

Smith and DeCoster (2000) link this associative view to underlying memory

processes. A slow-learning system gradually forms stable representations of the environment

based on the accumulation of similar experiences. When similar situations or objects are

encountered in the future, there is an automatic activation of these knowledge representations,

which deliver information and shape behaviour without the need for deliberate or effortful

thought. Thus, this kind of reasoning predominantly delivers responses which encode

statistical properties of the environment.

Smith and DeCoster’s suggestions about the nature of associative induction resonate

strongly with the characteristics of connectionist networks. A connectionist account of

category-based induction is given by Rogers and McClelland’s (2004) Parallel Distributed

Processing (PDP) model. It assumes that semantic information about an instance is stored as

an internal representation encoded by the pattern of distributed activation across processing

units. Knowledge is refined by gradually adjusting the weight of connections between

concepts (e.g. sparrows) and attributes (e.g. wings, chirp, small) for different kinds of

relations (e.g. has, can, is). This means that generalizations from one instance to another will

be strong to the extent that the activated distributed representations of the two instances

overlap via their shared attributes. Note that McClelland and colleagues (McClelland et al.,

2010) demonstrate that a structure can emerge though the gradual adjustments made to the

connections between concepts. However, this is not equivalent to having structured

knowledge about how the concepts are interrelated (Halford et al., 2010). The emergent

structures in connectionist networks represent connections between concrete concepts and

instances, that is, the nodes cannot act as abstract place holders that describe higher-order

theoretical interrelationships between concepts. Thus, theories which emphasize such higher

level theories and interrelationships would appear to stand in direct opposition to frameworks

emphasizing associative knowledge.

Structured Knowledge in Induction

Osherson et al’s (1990) Similarity-Coverage Model (SCM) was one of the earliest

models to emphasize the importance of knowledge about stable taxonomic structure when

evaluating categorical arguments. In contrast to Sloman’s (1993) feature-based

conceptualization of similarity, Osherson et al’s (1990) notion of similarity relies far more on

explicit knowledge about category relations between category instances. Thus, inductive

evaluations reflect the weighted sum of two primary parameters, similarity and coverage.

Similarity refers to the maximum average similarity between the premise and conclusion

categories. Coverage assumes that people have knowledge about stable category hierarchies

and refers to the degree to which the premise categories cover the category space of the

inclusive superordinate category.

The coverage component of the model gives rise to the diversity effect (for a

discussion see Heit, Hahn, & Feeney, 2005), whereby dissimilar premise categories act as

stronger evidence than similar premise categories. Although this phenomenon can be

explained by Sloman’s (1993) model, other evidence suggests that certain characteristics of

this effect are not explicable in terms of associative knowledge, instead requiring reference to

structured knowledge. For example, Feeney (2007) showed that only a minority of people

manifest the diversity effect when they reason about specific (e.g. rabbits) rather than general

(e.g. mammals) conclusions, and that this was related to cognitive ability. Developmental

evidence by Rhodes, Brickman and Gelman (2008) showed that even when a diverse

sampling strategy is explicitly suggested as a basis for making generalisations, children under

the age of eight years still prefer the non-diverse choice. It appears that in order to show

adult-like inductive reasoning, there must be a qualitative developmental shift in how

children use their category knowledge and acquire an appreciation of group-level properties

to make inductive inferences. For example, Lopez and colleagues (Lopez, Gelman, Gutheil,

& Smith, 1992) showed that several developmental changes seemed to depend on knowledge

about stable category hierarchies. The primary aim of these researchers was to identify

separate components which comprise the coverage parameter in Osherson et al’s (1990)

model. However, their findings are also consistent with the idea that the emergence of

computationally more complex inductive reasoning phenomena lags behind those that are

thought to rely on computationally simpler associative processes. For example, in the case of

the diversity effect for specific arguments, children first have to generate an inclusive

superordinate category before calculating coverage, a process that requires knowledge about

structured taxonomic relations between categories. Lopez et al. (1992) showed that 9-year-

old children exhibit sensitivity to diversity with general arguments, but performed at chance

levels with specific arguments.

Together these findings suggest that generating the superordinate category which

includes both the premise and conclusion category before being able to assess coverage (e.g.

having to generate the inclusive superordinate category mammal when reasoning from the

premise categories dog and sheep to the conclusion category buffalo) involves a

computationally demanding processing step that relies on knowledge about stable category

hierarchies. In contrast, this superordinate category is already available when reasoning

about general conclusions (e.g. reasoning from the premise categories dog and sheep to the

conclusion category mammal). If sensitivity to diversity was based exclusively on associative

knowledge, one would not expect differences based on cognitive ability and changing

developmental trajectories, nor should there be a dissociation between specific and general

arguments.

Accounts which draw on associative knowledge also have no straightforward means

of explaining effects that arise from considering underlying higher-order interrelationships

between categories. For example, Tenenbaum and Kemp (2009) and Shafto et al. (2008) have

demonstrated that inductive reasoning about causal disease transmission can be dissociated

from inductive inferences about physiological properties. Such dissociations suggest that the

context or property people are reasoning about prompts them to draw on different and most

relevant sources of structured knowledge. This dissociation is explained with reference to

theory-based Bayesian models, in which a domain-general Bayesian inference engine

operates over a domain-specific theoretical model. These models can represent people’s

structured knowledge about hierarchical taxonomic relations or causal links between species.

Evidence that people make extensive use of structured knowledge that might violate

similarity principles comes from cross-cultural research (e.g. Lopez, Atran, Coley, Medin &

Smith, 1997) and research on experts (e.g. Medin, Lynch, Coley & Atran, 1997; Proffitt,

Coley and Medin, 2000; Shafto & Coley, 2003). For example, Proffit and colleagues (2000)

looked at patterns of inductive inferences about tree diseases across three different types of

tree experts. Depending upon their speciality, they exhibited a variety of different reasoning

strategies, including the context-sensitive use of ecological and causal knowledge.

Knowledge structures that capture causal knowledge are especially interesting, as they

have several unique characteristics not shared by other knowledge structures. Asymmetry is

one of their most distinguishing features. That is, causes must always precede, or at least

coincide, with their effects. Causal structures can also vary in their complexity, ranging from

simple cause-effect relations such as unidirectional causal chains, to more elaborate common

cause models (Pearl, 2000). People do seem to make use of these abstract relations to

evaluate inductive arguments, as their inferences are highly sensitive to the direction of the

causal link between category features (Rehder, 2009), as well as the direction of the causal

link between species when making generalizations about novel properties (Medin, Coley,

Storms, & Hayes, 2003) and disease transmission (Shafto et al., 2008). For example, people

are more likely to endorse the argument that ‘lions have retinum’ given that ‘gazelles have

retinum’ than the diagnostic inference that ‘gazelles have retinum’ given that ‘lions have

retinum’ (Medin, et al., 2003), thus demonstrating a robust causal asymmetry effect which

can be formally derived using Bayes rule (Shafto et al., 2008). These causal asymmetry

effects have recently been generalised to children as young as five years of age (Bright &

Feeney, 2014). Again, it is hard to see how approaches relying exclusively on associative

knowledge might cogently explain such effects.

Reconciling Theories: The Importance of Processing Conditions

On the surface it appears that approaches placing divergent emphasis on different

types of knowledge are incompatible. However, there are strong arguments for the roles of

associative and structured knowledge in inductive reasoning, and there is a suggestion of

individual differences in the extent to which structured knowledge plays a role (Feeney,

2007). Particularly given its importance during development, it is likely that in adults,

associative knowledge influences category-based inductive inference with relative ease and

computational simplicity. In contrast there appear to be computational challenges involved in

drawing on structured knowledge. Thus, one way to resolve the apparent dichotomy between

theories which emphasize different kinds of knowledge is to argue that the inductive engine

of thought is a hybrid, taking different types of input depending on environmental conditions.

As we have seen, there are good reasons for ascribing different processing

characteristics to structured and associative knowledge, meaning that each is more likely to

power the inductive engine under different environmental conditions. This in turn allows us

to delineate and predict circumstances in which each type of knowledge is more likely to be

used during the inference process. For example, Rehder (2009) explicitly suggests that the

use of structured knowledge relies on an elaborate, analytical thought process, whereas

associative knowledge influences inductive reasoning fairly automatically and without much

cognitive effort. Rehder (2009) taught participants about the causal links between features of

artificial categories. In line with assumption that people draw on extensive casual knowledge,

he demonstrated various phenomena, such as a casual asymmetry effect. However, he also

found that there was a substantial minority of people whose patterns of inferences did not

adhere to those predicted by his causal-based generalization model. Instead, they seemed to

rely more on non-directional associations between category features. This suggests that

induction can either be driven by structured knowledge based on sometimes complex

relations between categories, or on associative knowledge based on temporal and/or spatial

contiguity between the categories. Whereas selecting the former type of knowledge during

the inference process might require effortful processing and availability of cognitive

resources, the latter type of knowledge may influence inductive reasoning relatively

automatically and with little processing cost.

Although ours will be the first investigation of the availability of associative and

structured knowledge to reasoning processes, there have been suggestions that some

knowledge structures may be less available to reasoning processes than others. Shafto,

Baldwin and Coley (2007) examined the processing conditions under which taxonomic and

causal knowledge impact on inductive reasoning. In general, people’s reasoning is context-

sensitive, that is, they will draw on relevant taxonomic knowledge when reasoning about

anatomical properties, but rely more heavily on causal knowledge when reasoning about

disease transmission (see also Heit & Rubinstein, 1994; Kemp & Tenenbaum, 2009; Shafto et

al. 2008). Shafto et al. (2007) showed that taxonomic knowledge predicts reasoning about

genes regardless of processing constraints whereas causal knowledge predicts reasoning

about diseases only when processing is unconstrained. Although our primary focus will be on

the contrast between structured and associative knowledge, by using Shafto et al’s paradigm

in our first experiment, we will also be able to carry out a conceptual replication of their

study of causal and taxonomic structured knowledge. Because they did not control for

associative knowledge about relations between categories, it is unclear whether their results

will hold once degree of association has been controlled for.

Our Experimental Strategy

We had four aims in the experiments to be described here. First we wanted to show

that measures of associative and structured knowledge about the relations between categories

are dissociable. Second we wished to show that both types of knowledge influence judgments

of inductive strength. Such a demonstration would be entirely novel in the context of the

literature on induction where researchers, because of their adherence to one or other model,

have assumed that only one representational form of knowledge drives inductive reasoning.

Third, we wished to examine the processing conditions under which each type of knowledge

exerts most influence on the inductive reasoning process. Showing that the type of knowledge

which is most important differs by processing condition would help to resolve conflict

between apparently contrasting models. Thus, although our experiments focus on category-

based inductive inference, our results are relevant to a number of more general questions such

as whether it is possible to dissociate the effects on reasoning of associative and structured

knowledge, whether it is possible to delineate when different representational forms of

knowledge play the biggest role in reasoning, and whether the effects of causal knowledge on

reasoning are relatively effortless and automatic or cognitively demanding. Finally, our

fourth aim was to examine whether, once degree of association between the categories in the

arguments has been controlled for, as claimed by Shafto et al. (2007), taxonomic knowledge

is more impervious to manipulations of processing resources than is causal knowledge.

Our overall experimental strategy rests on a contrast between the effects of associative

and structured knowledge on inductive reasoning. We use the term associative as it has been

used by other researchers in the literature on inductive reasoning (see Sloman, 1996; Sloutsky

& Fisher, 2008), to refer to computations that reflect temporal contiguity or similarity.

However, in the literature on priming, distinctions are made between associative and featural

overlap accounts of priming effects (see Hutchison, 2003). In that literature, the term

associative is used to refer to accounts where concepts are represented by nodes in a network

and nodes are associated with each other (see Collins & Loftus, 1975). Distributed accounts

(e.g. Masson, 1995), on the other hand, like Sloman’s (1993) and Rogers & McClelland’s

(2004) accounts of inductive reasoning, assume that concepts are represented by patterns in

the weights of connections between the features that are activated when the concept is

encountered. The simplest explanation for priming under such accounts is in terms of the

overlap between the features that are associated with the priming concept and the concept that

is primed. This explanation is very similar to the mechanism said to underlie inference in

associative models of inductive reasoning. Thus, Sloman’s (1993) and Rogers &

McClelland’s (2004) models might better be described as feature overlap rather than

associative models. However, individual categories are represented associatively in these

models, even if inferences are computed via a process of feature overlap.

As will become apparent below, we measured the associative relation between the

categories in the arguments that participants evaluated simply by asking other participants to

rate the strength of the association between the categories. It is likely that such questions are

more transparent to participants than questions referring to shared features. Feature-overlap is

often interpreted in the literature on inductive reasoning, but not the literature on priming (see

Hutchison, 2003), as a measure of similarity, so it might be argued that we should have

explicitly asked about similarity. However, as feature overlap can occur due to similarity, or

temporal contiguity, we decided to measure degree of association instead. In addition, there

are arguments (see Medin, Goldstone & Gentner, 1993) that the nature of a similarity

calculation may be time dependent; perceptual similarity, for example, may be more

automatically calculated than structural similarity. As degree of association is, by definition,

the automatic output of an associative process, it is a better concept for our present purposes.

Pretest: Dissociating types of knowledge. One problem with testing the idea that

dissociable types of knowledge can be selected in category-based inductive reasoning is how

to a) measure and b) dissociate different types of knowledge. With regards to structured

knowledge, one can simply ask participants whether or not they believe that the categories

are taxonomically, ecologically or causally related. On the face of it, indexing associative

knowledge is also simple: we can simply ask participants to rate the strength of the

association which they believe exists between pairs of categories. One obvious objection to

this method is that participants may be drawing on the same underlying knowledge to

perform both tasks. However, if they are drawing on different sources of knowledge then we

would expect the measures not to be strongly associated with each other. Moreover, because

associative knowledge can be based on co-occurrence we might expect ratings of associative

strength to correlate strongly with objective measures of co-occurrence whilst our measures

of structured knowledge should correlate much less strongly with an objective measure of co-

occurrence. Note that for co-occurring category pairs which are also visually similar, an

objective measure of co-occurrence will likely underestimate the degree of association

between the categories. This should serve to make any evidence we find for dissociation

between associative and structured knowledge more impressive.

Strength of association. To measure strength of association between category pairs,

we told 20 participants that we were interested in their beliefs about how strongly associated

two categories (e.g. “rabbits and carrots”; “salmon and herring”; “robin and grass”, etc.)

were on a scale from 1 (unrelated) to 9 (very strongly associated). They were asked to think

about all kinds of possible associations and the instructions emphasized that we wanted them

to give their first intuitive response. In total they rated the strength of association between

270 category pairs.

Conditional co-occurrence. We wanted to compare our subjective ratings to a more

objective association criterion. Thus, for all the category pairs for which we had obtained

participant association ratings, we examined their co-occurrence frequencies in natural

language. The rationale is that words which frequently co-occur in natural language should

have a stronger associative relationship (Spence & Owens, 1990). We conducted a proximity

search, specifying that the categories must co-occur in any order within a window of 6

consecutive words. We chose the search engine Exalead, which explicitly supports proximity

searches for specified distances (word 1 NEAR/ X word 2). Once we derived the co-

occurrence measure, we recorded the Exalead word frequency of each individual category.

Using Heylighen’s (2001) formula below, we calculated the conditional co-occurrence.

In this equation, represents the probability that a text contains both words

w1 and w2, represents the probability that it contains w1 on its own. To calculate the

conditional probability, one can simply count the number of times w1 and w2 co-occur and

divide this by the number of times w1 occurs by chance in the same text sample. As we were

not interested in potential asymmetries, we repeated the calculation for w2 and took the mean

conditional co-occurrence for each category pair. This was correlated with our subjective

association measures. The correlation between the subjective measure and the objective

measure was .66.

The size of this correlation suggests that our measure of associative strength is

sensitive to at least one objective measure of the strength of an association: the extent to

which the associated entities co-occur in the world. Of course, this correlation on its own

does not demonstrate that associative strength and structured knowledge are dissociated.

Thus, for each of the experiments reported in this paper we calculated, for the items used in

that experiment, the strength of the correlation between beliefs about structured relations

(collected for each experiment in a post-test, see Appendices 1 & 2), the objective measure of

co-occurrence and the measure of associative strength. These results are presented in Table 1

and will be discussed alongside the results for each experiment. To preview, the results show

that whereas the measure of association correlates strongly with the measure of co-

occurrence, our measures of structured knowledge do not correlate strongly with the measure

of associative strength nor with the measure of co-occurrence. Thus, our measures of

associative and structured knowledge are dissociated.

Experiment 1

In Experiment 1 we ran a conceptual replication of the study by Shafto et al (2007).

Shafto et al (2007) asked people to evaluate the strength of inductive inferences about cell or

disease properties in members of categories known to be taxonomically or causally related.

People were either asked to respond immediately or to delay their response. After they had

completed the inference part of the experiment, participants’ beliefs about the taxonomic and

causal relations between the categories in each argument were post-tested. In a series of

regression analyses by item, results of the post-tests were used to predict ratings of inductive

strength. Whereas beliefs about taxonomic relatedness predict argument strength regardless

of processing conditions, beliefs about causal relatedness only predicted strength judgements

for disease arguments and only in the delayed condition. Shafto et al (2007) concluded that

taxonomic knowledge was more available to reasoning processes than knowledge about

causal relations between categories. We departed from Shafto et al’s (2007) method in a

number of crucial ways. First, we chose taxonomically and causally related category pairs so

that the degree of association between the categories in the argument was controlled for.

Second, we included ratings of associative strength as a predictor in the regression analyses.

These changes allow us to address all of our aims. First, by examining correlations between

our measures of associative and structured knowledge and our objective co-occurrence

measure, we can examine whether associative and structured knowledge are dissociable.

Second, the results of the regression analyses will help us to establish whether associative and

structured knowledge predict reasoning. Third, by incorporating a response time

manipulation, we will be able to examine the degree to which each type of knowledge affects

reasoning under different processing conditions. Finally, by controlling for degree of

association across arguments, and including association as a predictor in our regression

analyses, we will be able to examine whether Shafto et al’s (2007) finding that taxonomic

knowledge is more available to reasoning processes than causal knowledge holds up when

associative strength is controlled for.

Method

Design

The experiment had a 2 (relation: causal or taxonomic) by 2 (property: cells or

diseases) by 2 (timing: fast or slow) by 4 (list) mixed design, with list and timing as between-

subjects variables.

Participants

The 40 participants were from Durham University, and received course credit for their

participation. The mean age was 24.2 years (SD = 5.8 years).

Materials and Procedure

There were 20 items in total. Items consisted of a base category, a causally related

target category and a taxonomically related target category. Causally related targets were

always from different superordinate categories, for example, plants and animals, or mammals

and reptiles. In contrast, taxonomically related pairs were always from the same

superordinate taxonomic category. For example, the causal target for the base category fly

would be frog and the taxonomic target would be ant. We ensured that the degree of

association between the base and the taxonomic (M = 4.86, SD = 1.13) and causal targets (M

= 4.73, SD = 1.01) was approximately equal; t(19) = .81, p = .43 (for association ratings for

both of the arguments in each item, see Appendix 1). We also confirmed that people did

perceive a causal link between the casually related category pairs. In a pre-test, 10 Durham

University students had previously rated the strength of the possible causal link between two

categories on a scale from 1 (unrelated) to 9 (very strong causal relation). Causal strength

ratings for the selected pairs ranged from 3.4 to 6.9 with a median of 4.5 (SD = 1).

For each of the 20 items, we created a taxonomic and a causal induction problem,

resulting in a total of 40 inductive arguments. Participants were told that the base category

had either a blank disease, such as disease 3dfT, or blank cells, such as cells T78. The

participants reasoned about different items for cells and diseases, so each person received 40

problems. Content was counterbalanced across participants in an incomplete Latin-square

design resulting in four different lists.

Participants’ task was to evaluate the likelihood that the cells/disease would be

present in the conclusion category on a scale from 1 (very unlikely) to 9 (very likely).

The premise and conclusions were presented simultaneously and appeared in a red

font. Participants could only enter their response once the font changed from red to green. In

the fast condition, the font changed from red to green after one second. Participants were

instructed to try and respond as quickly as possible. In the slow condition, the font only

changed color after 10 seconds and people could not enter their response before this time had

elapsed. In this condition, participants were instructed to take their time and think carefully

about each item before typing a response.

Post-test. The post-test assessed people’s beliefs about taxonomic and causal

relatedness. For each of the 40 category pairs (20 causal, 20 taxonomic) about which people

had made inferences in the main task, they were asked two questions, resulting in a total of

80 questions. One question asked them whether they believed that the two categories were

from the same biological class. The second question was whether the two categories were

part of the same food chain. Order of presentation was completely randomized. Participants

could respond with YES, NO or DON’T KNOW, but were instructed to use the third option

sparingly, as the emphasis was on their intuitions and beliefs rather than on factual

correctness.

Results

Pre- and Post-Testing

Our post-test confirmed that participants were largely aware of the purported relations

between the category pairs. For the causally related items, the causal endorsement proportion

was .71 (SD = .24), whereas the taxonomic endorsement proportion was .23 (SD = .11). For

the taxonomically related items, the taxonomic endorsement proportion was .75 (SD = .19),

whereas the causal endorsement proportion was .21 (SD = .25). To ensure that our pre-test

measure of associative strength and our post-test measures of structured knowledge taken at

the end of this experiment are dissociated, we calculated the magnitude of the correlation

between the pre-test and post-test measures across all 40 unique category pairs. As may be

seen in Table 1, the correlations between taxonomic and associative knowledge and between

causal and associative knowledge were small and non-significant. To obtain further evidence

for a dissociation we also calculated the correlation between our pre- and post-test measures

of knowledge and the objective measure of conditional co-occurrence. Once again, the

correlation was large and statistically significant in the case of the associative measure and

small and non-significant for the structured measures. The measure of associative knowledge

dissociates from the measures of taxonomic and causal knowledge obtained from the

participants in this experiment.

Analysing Inductive Strength Ratings

Mean inductive strength scores were calculated for the 10 problems representing the

unique property by relation combination, resulting in 4 means for each participant. These

were subjected to a 2 (relation: causal or taxonomic) by 2 (property: disease or cell) by 2

(timing: fast or slow) by 4 (list) mixed-design ANOVA, with list and timing as between-

subject variables. For the analysis by items, inductive strength ratings were averaged across

subjects rather than items and were analysed with a 2 (property) by 2 (timing) by 2 (relation)

mixed-design ANOVA, with relation as between-items variable. In what follows we will

report only effects that were significant in the items and subjects analyses. Cell means can be

found in Table 2. There were no main or interaction effects involving list (all p’s >. 07), so

this counterbalancing variable will not be mentioned any further.

The only significant effect was a two-way interaction between property and relation,

FS (1, 32) = 23.17, p < .0005, η2

p = 0.42, FI (1, 38) = 36.17, p < .0005, η2

p =0.49, suggesting

that people showed some context-sensitive reasoning. Bonferroni post hoc tests showed that

when reasoning about cells, people rated taxonomic inferences (M = 5.01, SE =.2)

significantly stronger than causal inferences (M = 3.79, SE = .22, p < .0005, effect size d =

.9). When reasoning about diseases, people rated causal inferences slightly higher (M = 4.32,

SE = .26) than taxonomic inferences (M = 3.89, SE = .17) although this difference was not

significant (p = .16, effect size d = .3). None of the other higher-order interactions were

significant (all p’s > .08). This result replicates selectivity effects that have been reported in

the literature (see Heit & Rubenstein, 1994).

Finally, the effect of timing was significant by items FI (1, 38) = 18.24, p < .0005, η2

p

= 0.32, and was approaching significance for subjects, FS (1, 32) = 2.82, p = .1, η2

p= .08.

Thus, people gave higher inductive strength ratings when they responded slowly (M = 4.48,

SE = 0.18) than when they responded quickly (M = 4.03, SE = 0.18). Crucially however,

timing did not interact with any of the other variables. This is in sharp contrast to Shafto et

al’s (2007) finding that people who were asked to respond quickly gave lower inductive

strength ratings when evaluating ecological/causal arguments, whereas there was no effect of

timing on taxonomic arguments. Thus, once strength of association had been equated

between knowledge domains, there was no evidence from this paradigm to support Shafto et

al.’s (2007) contention that taxonomic knowledge is more available to reasoning processes

than causal knowledge.

Using Associative and Structured Knowledge to Predict Reasoning

We ran hierarchical regression analyses to see how associative knowledge, as well as

how relevant domains of structured knowledge (causal and taxonomic beliefs) influence

category-based inferences under different timing conditions. For this purpose, mean inductive

strength ratings and taxonomic and causal endorsement proportions were averaged across

participants to predict inductive strength ratings for each item when people responded quickly

or slowly and for the two different properties. Strength of association derived from the pre-

test was entered in the first block of the regression analysis, followed by taxonomic and

causal endorsement proportions in the second block.

Inferences about cells. Shown in Table 3, inferences about cells in the fast condition

(R = .64) were predicted by strength of association (beta = .51, t = 3.76, p = .001) and were

negatively predicted by causal knowledge (beta = -.34, t = -2.5, p = .048). Taxonomic

knowledge was not a significant predictor of inductive strength in the fast condition (beta =

.11, t = .65, p = .52). However, adding the structured knowledge coefficients did explain

some additional variance above strength of association on its own (R2

Change: 16.7%, F (2,

36) = 5.09, p = .011).

In the slow condition (R = .72), strength of association was not a significant predictor

of inductive strength (beta = .19, t = 1.52, p = .14). Inductive inferences were however

predicted by taxonomic knowledge (beta = .48, t = 3.48, p = .001), and were negatively

predicted by causal knowledge (beta = -.31, t = -2.29, p = .028). Given that we had selected

causal targets that were always from different superordinate categories (i.e. taxonomically

unrelated) it is not surprising that believing in the existence of a causal link was a negative

predictor of inferences about cells. Adding the structured knowledge predictors in a second

block of the regression analysis accounted for significantly more variance in inductive

strength ratings than strength of association on its own when people responded slowly ( R2

Change: 44.2%, F(2, 36) = 16.33, p < .0005).

Comparing the regression weights (Cohen, 1983) across the two timing conditions

showed that the beta weight for associative strength was significantly larger in the in the fast

than in the slow condition (Z = -2.48, p =.007, one-tailed), whereas the beta weight for

taxonomic knowledge was larger in the slow condition, as predicted (Z = 2.56, p =.005, one-

tailed). For causal knowledge there was no significant difference between the beta weights

across the two timings conditions (Z = 0.17, p =.43, one-tailed).

Inferences about diseases. As may be seen in Table 3, reasoning about diseases in

the fast condition (R= .59) was significantly predicted by strength of association (beta = .45, t

= 3.13, p = .003). When entered in the second block, causal knowledge was also a significant

predictor (beta = .35, t = 2.04, p = .049), whereas taxonomic knowledge was not a significant

predictor (beta = .08, t = .44, p = .67). Together, adding these two structured knowledge

variables accounted for a non-significant amount of additional variance (R2

Change: 9.6%, F

(2, 36) = 2.64, p = .085).

In contrast, reasoning about diseases in the slow condition (R= .68) was no longer as

strongly predicted by strength of association (beta = .24, t = 1.8, p = .08). However, inductive

strength was strongly predicted by causal knowledge (beta = .61, t = 4.34, p < .0005), and

also by taxonomic knowledge (beta = .34, t = 2.33, p = .026). Adding the structured

knowledge predictors in a second block accounted for significantly more variance in

inductive strength ratings than strength of association on its own (R2 Change: 28.1%, F(2, 36)

= 9.64, p < .0005).

A comparison of regression weights across fast and slow conditions showed that the

associative strength beta weight was slightly but not significantly larger in the fast than in the

slow condition (Z = 1.25, p =.1, one-tailed). As predicted though, the beta weight for causal

knowledge (Z = 2.1, p =.018, one-tailed) was significantly larger in the slow condition.

Furthermore, the beta weight for taxonomic knowledge was also significantly larger in the

slow condition (Z = 1.9, p =.029, one-tailed). This might be explained in terms of people’s

belief that taxonomic relations also offer a good explanation for shared diseases (e.g. due to

genetic susceptibility), an effect we have observed previously in adults but not in younger

children (Bright & Feeney, 2014).

Timing Manipulation Check

To ensure that our timing manipulation had been effective, we compared mean

reaction times across the two timing conditions from stimulus onset. As we did not provide

an actual response deadline, one risk is that people might not have responded as soon as

possible, but continued to think about the problem, making their response reaction times

indistinguishable from the slow group. However, our analysis showed that people in the fast

condition responded after an average of 4.4 seconds (SD = 1.26), which was significantly

faster than response time in the slow condition (M = 12.0 seconds, SD = 1.89, t (38) = 14.97,

p < .0005). Thus, our timing manipulation was effective in eliciting diverging response times.

Discussion

We had four aims in running Experiment 1. First, we wished to show that measures of

associative and structured knowledge dissociate. The results clearly show that the experiment

has achieved that aim. Measures of associative and structured knowledge were not

significantly correlated. In addition, the subjective measure of association was strongly

correlated with an objective measure of category co-occurrence whereas the correlations

between measures of structured knowledge and the objective measure of co-occurrence were

much smaller and non-significant. All of these findings suggest that our measures are tapping

into different types of knowledge.

The second aim of the experiment was to show that both associative and structured

knowledge act as input to inductive reasoning. It is clear from our results that associative

knowledge and knowledge about structured relations are both related to judgements of

inductive strength.

With regards to our third aim, of delineating the conditions under which each type of

knowledge exerts its biggest influence, the results of this experiment offer evidence that

associative and structured knowledge have different effects dependent on the processing

conditions. Thus, associative knowledge predicted inference strength when people were

encouraged to respond quickly but not when they responded slowly. On the other hand, the

strongest effects of our measures of structured knowledge were observed when people

responded slowly.

Our fourth aim was to examine whether Shafto et al’s (2007) finding that taxonomic

knowledge is more available to reasoning processes than causal knowledge could be

replicated once strength of association had been controlled for. In fact, the results of this

suggest that the reverse can sometimes be the case. When people reasoned about diseases in

the fast timing condition in this experiment, causal knowledge was a significant predictor of

inferential strength. On the other hand, taxonomic knowledge was not a significant predictor

in any analysis of strength ratings provided by participants when they responded quickly.

Although our results suggest that once associative strength is controlled for,

taxonomic knowledge is no more available to reasoning processes than causal knowledge, we

did use different causal relations than did Shafto et al. and it is possible that this difference

may be important in explaining the differences between our results. The causal relations in

our experiment were based on predation whereas Shafto et al used shared habitat relations

and it is possible that the former are more available to reasoning processes than the latter.

Experiment 2

Experiment 2 was designed to experimentally test the claim that structured knowledge

has a greater effect on reasoning processes under favourable processing conditions. We

presented participants with inductive arguments containing one of three different types of

structured relation. One was taxonomic, a second was causal predictive, both as before. The

third was a causal diagnostic relation. For example, participants might learn that eagles have

a disease and be asked to consider how likely it is that mice also have the disease. We

predicted a causal asymmetry effect, that is, causal inferences should be stronger for

categories with a predictive causal link than for those with a diagnostic causal link (Medin et

al., 2003). Previous work (e.g. Shafto et al., 2008) shows that asymmetry effects are most

likely when the property in the argument may be transmitted from members of one category

in the argument to members of the other, so we expected to observe asymmetry effects with

disease properties rather than with cell properties.

To manipulate processing conditions, we used a secondary task paradigm in which

people had to remember simple or complex dot patterns (De Neys, 2006) whilst making their

inductive strength evaluations. Remembering the simple patterns should only minimally

affect working memory resources, whereas remembering the complex patterns places a much

heavier burden on people’s mental resources. If the retrieval of a causal knowledge structure

and assignment of causal roles is indeed mediated by an effortful process, one might expect

this causal asymmetry effect to be weakened when people are under heavy cognitive load.

Method

Design

The experiment had a 3 (relation: causal predictive, causal diagnostic, taxonomic) by

2 (load: heavy or light) by 2 (property: cells or infection) by 4 (list) mixed design, with list

and load as between-subjects manipulations.

Participants

There were 40 participants who were volunteers from Queen’s University Belfast and

Durham University. Participants received either course credit or were paid £5 for their time.

The mean age was 23.3 years (SD = 6.2 years).

Materials and Procedure

In total there were 16 items. For each item, we created four induction problems: A

causal predictive argument and its taxonomic counterpart, as well as a causal diagnostic

argument and its taxonomic counterpart.

In predictive causal induction problems people were told that the base category

(prey/plant) had either novel cells or a novel infection. The taxonomic counterpart was

created by keeping the same prey/plant base category but replacing the conclusion category

with a taxonomically related category of equivalent associative strength. In contrast to

Experiment 1, we changed the property from diseases to infections in an attempt to

discourage participants from using of taxonomic knowledge when reasoning about properties

that could be causally transmitted and thus demonstrate clearer selectivity effects.

As a variation of causal structure, for each of these items we then reversed the order

of the categories for the predictive causal problems (base category: predator/consumer →

conclusion category: prey/plant), resulting in a diagnostic causal induction problem. This was

matched again with a taxonomic induction problem by keeping the predator/consumer base

category but substituting the conclusion category for a taxonomically related alternative.

Thus, there were a total of 64 problems. For example, participants might be presented with

one of the following induction problems:

Mice have infection 9TT7. (causal predictive/ infection)

How likely is it that Eagles have infection 9TT7?

Mice have infection 7rR4. (taxonomic / infection)

How likely is it that Squirrels have infection 7rR4?

Eagles have 45T-cells. (causal diagnostic/ cells)

How likely is it that Mice have 45T-cells?

Eagles have e2T-cells. (taxonomic / cells)

How likely is it that Parrots have e2T-cells?

Based on the pre-test ratings of strength of association between category pairs, we

ensured that the strength of association was identical for the causal category pairs (M = 4.98,

SD = 1.21) and their taxonomic counterparts (M = 4.94, SD = 1.14; t (31) = .25, p =.81).

Association ratings for each item are presented in Appendix 2.

For each problem, participants reasoned either about a predictive or diagnostic causal

category pair and its taxonomic match. This meant that each participant rated 32 inductive

arguments. The items for which participants reasoned about cells or infections in a predictive

or diagnostic direction was counterbalanced in an incomplete Latin square design, resulting

in four lists. We ensured that there were an equal number of strongly and weakly associated

items in both the cell and infection condition.

Before rating each inductive argument, participants were shown a 4 by 4 grid with 4

dots for 2 seconds. In the heavy load condition, the dots were displayed in a random order

with the constraint that they could never form a straight line or diagonal. In contrast, in the

light load condition, the dots always formed a straight line or diagonal, placing minimal

burden on working memory. Once participants had read the induction question, they entered

their response on the keyboard by pressing a number between 1 and 9. They then saw an

empty matrix and had to try and recall the location of the four dots by pressing on an

appropriate box with the mouse cursor. Participants received no feedback on their recall

performance

Post-test. The post-test was identical to the one used in Experiment 1. Participants

answered two questions about the 32 category pairs, assessing their beliefs about biological

group membership, as well as their beliefs about causal relatedness.

Results

Analysis of Inductive Strength Ratings

We calculated 6 mean inductive strength ratings for each participant and analysed

these with a 3 (relation: predictive, diagnostic or taxonomic) by 2 (property: cells or

infection) by 2 (cognitive load: heavy or light) by 4 (list) mixed-design ANOVA, with load

and list as between-subjects variables. For the analysis by items we used a 2 (property) by 2

(load) by 3 (relation) mixed-design ANOVA, with relation as a between-items variable.

There was no significant main effect of list, F (3,32) = 0.92, p = .44, η2

p= 0.08, and

none of its interactions with other variables were significant (all p’s > .33), so no further

reference is made to this counterbalancing variable. There was a significant main effect of

relation, FS (1.66, 53.03)1

= 6.09, p = .007, η2

p= 0.16, FI (2, 61) = 7.22, p = .002, η2

p= 0.19.

Post-hoc comparisons showed that there was a difference in inductive strength ratings for

causal predictive (M = 3.90, SE = .24) and causal diagnostic inferences (M = 3.33, SE = .23, p

= .038, effect size d = .42), but no significant difference between causal predictive and

taxonomic inductive strength ratings (M = 4.3, SE = .25, p = .42, effect size d = .19). The

difference between diagnostic and taxonomic inferences was significant (p = .005, effect size

d = .54).

There was a significant interaction between property and relation, FS1 (1.97, 62.87) =

5.48, p = .007, η2

p= 0.15, FI (2, 61) = 11.08, p < .0005, η2

p= 0.27. When people made

inferences about cells, taxonomic inferences (M = 4.50, SE = .27) were significantly stronger

than both causal predictive inferences (M = 3.50, SE = .24, p =.017, effect size d = .47) and

causal diagnostic inferences (M= 3.26, SE = .27, p = .001, effect size d = .60), whereas there

was no difference between the latter two types of relation (p = .94, effect size d = .16).When

reasoning about infections, people rated causal predictive inferences (M= 4.30, SE = .33)

significantly higher than causal diagnostic inferences (M= 3.39, SE = .30, p = .025, effect size

d = .45). However, there was no difference between causal predictive and taxonomic

inductive strength ratings (M= 4.11, SE = .25, p = .99, effect size d = .07), or between

taxonomic inferences and causal diagnostic inferences (p = .5, effect size d = .32).

There was a significant three-way interaction between property, load and relation, FS

(1.97, 62.87) 1 = 3.22, p = .047, η

2p= 0.09; FI (2, 61) = 3.95, p = .024, η

2p= 0.12. The cell

means across all conditions are shown in Table 4. To further examine this interaction and to

explore our a-priori prediction that the causal asymmetry effect would be less evident under

cognitive load, we carried out two separate 2 (causal relation: predictive versus diagnostic)

by 2 (load: heavy versus light) mixed-model ANOVAs, one for cells and the other for

infections.

Inductive strength ratings when reasoning about infections. For infections, there

was a significant main effect of causal relation, FS (1, 38) = 8.99, p = .005, η2

p= 0.19, FI (1,

30) = 7.59, p = .01, η2

p = 0.2. However, the main effect of causal relation was modulated by

the significant interaction between load and causal relation, FS (1, 38) = 4.04, p = .051, η2

p=

0.1, FI (1, 30) = 7.77, p = .009, η2

p = 0.21, presented in Figure 1. Bonferroni post-hoc tests

showed that people who were not burdened by a heavy secondary memory load were able to

take causal structure into account. Indicative of a significant causal asymmetry effect,

inferences with a causal predictive relation (M = 5.01, SE = .44) were rated much stronger

than inferences with a diagnostic causal link (M = 3.49, SE = .41, p = .001, effect size d =

.73). In contrast, the causal asymmetry effect was absent when people had to contend with a

heavy secondary memory load. Thus, inductive strength ratings were almost identical for

causal diagnostic inferences (M = 3.29, SE = .41) and causal predictive inferences (M = 3.49,

SE = .41, p = .49, effect size d = .17).

This finding suggests that the causal asymmetry effect arises because people consider

how the underlying causal structure might influence the distribution of properties such as

infections or diseases. When people are cognitively burdened, they may not be able to take

the underlying causal structure into account, instead forcing them to rely on the existence of

an association between the categories.

Inductive strength ratings when reasoning about cells. As expected, for inferences

about cells, there was no effect of causal relation, FS (1, 38) = 1.05, p = .31, η2

p= 0.03, FI (1,

30) = 0.97, p = .33, η2

p= 0.03. People rated inferences about category pairs with a predictive

causal relation (M = 3.50, SE = .24) the same as when the relation between the two categories

was diagnostic (M = 3.26, SE = .27).

The main effect of load was non-significant, FS (1, 38) = .007, p = .93, η2

p< .001, FI

(1, 30) = 0.2, p = .88, η2

p= 0.001, as was the interaction between load and causal relation, FS

(1, 38) = 1.29, p = .26, η2

p = 0.03, FI (1, 30) = 0.99, p = .33, η2

p = .180.03.

Pre-and Post-Testing

Across items, causally related categories attracted a causal endorsement proportion of

.74 (SD = .21) and a taxonomic endorsement proportion of .11 (SD = .18). In contrast,

taxonomically related categories received a taxonomic endorsement proportion of .73 (SD =

.18) and a causal endorsement proportion of .23 (SD = .10).

To ensure that our pretest measure of associative strength and our post-test measures

of taxonomic and causal knowledge taken at the end of this experiment are dissociated, we

calculated the magnitude of the correlation across all 64 unique category pairs between the

pre-test and post-test measures. As may be seen in Table 1, the correlations between

structured knowledge and associative knowledge were small and non-significant. The

correlations between subjective and objective measures of associative knowledge were large

and significant whereas the correlations between structured knowledge and the objective

measure of associative knowledge were small and non-significant. As before, our pre- and

post-test measures of different types of knowledge were dissociated.

Secondary Task Analysis

In a dual task paradigm, dissociable effects of the secondary task can reflect strategic

trade-offs between primary and secondary tasks (Hegarty, Shah, & Miyake, 2000). To guard

against the possibility that the effect of memory load on causal inferences reflected such a

strategic trade-off, we calculated the number of correctly recalled dots separately for the trials

preceding each of the unique property by load by relation conditions. A 2 (relation: causal

predictive, causal diagnostic or taxonomic) by 2 (property: cell of infection) by 2 (load:

heavy versus light) by 4 (list) mixed-design ANOVA, with list and load as between-subjects

variables showed that the only significant difference in the number of dots recalled was

between the two load conditions, F (1, 31) = 17.71, p < .0005, η2

p = 0.36. In the heavy load

condition, participants recalled a mean of 3.2 dots (SE = .1), whereas they recalled on average

3.8 dots (SE = .1) when they were only under a light memory burden. This suggests that

people were consistent in how they allocated their mental resources to the primary and

secondary tasks across all problems and verified that the more complex patterns were harder

to remember than the simple dot patterns.

Discussion

The results from Experiment 2 strongly suggest that the influence on inductive

reasoning of different types of knowledge is dependent upon processing conditions. Thus, the

causal asymmetry effect was not observed when participants were under heavy cognitive

load. This finding supports our contention that drawing on structured knowledge is mediated

by an effortful, time-consuming process, unlike the use of associative knowledge, which

influences the reasoning process relatively automatically.

As might be expected given other findings in the literature, the results of Experiment

2 also contain evidence of inductive selectivity (see Heit & Rubenstein, 1994). Thus, people

were sensitive to causal direction only when reasoning about infections, and found arguments

containing taxonomically related categories more convincing only when reasoning about

cells.

Experiment 3

Thus far we have shown that both associative and structured knowledge drive

reasoning processes but to different extents under different processing conditions. The

experimental task used in both of the experiments described so far required people to evaluate

inductive arguments. One disadvantage of this method is that people may lack the relevant

structured knowledge (see Coley, Shafto, Stepanova, & Barraff, 2005), forcing them to rely

on associative strategies that they wouldn’t normally use. In addition, such a task may not be

very similar to how we make everyday inductive inferences. In real life we are likely to learn

new facts about categories and then generate other categories to which those new facts may

generalise. In the final experiment to be described here we asked our participants to carry out

an inductive generation task of this sort. One disadvantage of such a task is that it gives us

less control over our materials than we have exerted in Experiments 1 and 2. Thus, because

we cannot control the categories which people generate, it may not be possible to carry out all

of the analyses we performed on the results of the earlier experiments. Nonetheless, to make

the strongest argument possible about the involvement of associative and structured

knowledge in inductive reasoning, it is important to generalise our findings to a range of

different paradigms.

In Experiment 3, people were told that a base category had a novel infection or cells

and were asked to infer which other category was most likely to also have the infection or

cells. Based on the previous two experiments, we predicted that when people were under

heavy cognitive load, they would generate conclusion categories which were more strongly

associated with the base category. In contrast, we expected more complex structured

knowledge to guide inferences when people were under light load. Because separate groups

of participants rated the degree of association and the existence of structured relations

between the categories in the arguments generated by a first group of reasoners, the

experiment had three phases, induction generation, associative rating, and structured relation

rating.

Method - Induction Generation Phase

Design

In this experiment, we manipulated whether people generated an open-ended

inference under heavy or light load..

Participants

Twenty-three students (M age = 24.2 years) from Durham University received course

credit for their participation. 11 were randomly assigned to the heavy load condition, whereas

12 completed the inductive task under minimal cognitive load.

Materials and Procedure

Participants (the reasoners) were presented with 20 base categories and told that each

category had a novel property, either an infection (e.g. has infection 5y5u) or cells (e.g. has 3-

yu-cells). We did not expect the two properties to differ in how structured versus associative

knowledge might affect the inference drawn. However, we included this variation to try and

encourage people to think about why a conclusion category might share the property with the

base rather than simply recalling a strong association. Participants were then asked to

generate ONE other category that they believed was most likely to also have the property. For

example, people would read the following generative induction problem:

Weasels have 4Ou-cells / infection 4Ou.

Which other category is most likely to also have 4Ou-cells/ infection 4OU?

People wrote down their response and also gave a rating of inductive strength on a scale from

1 (very unlikely to share the property) to 9 (highly likely to share the property).

Akin to Experiment 2, participants completed a secondary task (4 by 4 dot matrix),

either under heavy (complex 4-dot configuration) or light cognitive load (simple 4-dot

configuration) conditions. Participants had to memorize the location of the dots, then

complete the inference task before attempting to recall the location of the dots in an empty 4

by 4 matrix.

Method - Association Rating Phase

Participants

Participants consisted of a group of 92 students (the raters) from Durham University

(M age = 22.4 years) who had not taken part in the first phase. They completed the task at the

beginning of a lecture.

Materials and Procedure

Each individual participant’s 20 category pairs from phase 1 were transcribed onto an

association rating sheet and interspersed with 15 weakly associated distracter items.

Participants in phase 2 received one of 23 different sheets (approximately 4 participants per

sheet) and were asked to rate the strength of association on a scale from 1 (unrelated) to 9

(very highly associated) between the 35 category pairs. They were instructed to respond as

fast as possible, based on the first intuitive answer that came to mind.

Method - Structured Relation Ratings Phase

To identify different types of structured relations, the experimenter and a second blind

coder rated whether there was a taxonomic and/or causal or interaction-based relationship

between the 20 category pairs participants had generated in phase 1. Table 5 below shows an

example of the different types of relation.

Category pairs were assigned 0 if there was no apparent link between the base and the

generated category (e.g. alligator → soil), 1 if they were taxonomically related (e.g. zebra →

horse), 1 if they were related through a causal link or ecological interaction (e.g. hawk →

mouse) and 2 if there was both a taxonomic and interaction-based relation between the

categories (e.g. cod → shark). Concordance rate across the two primary coders was 67%.

Disagreements were resolved through discussion with two further colleagues.

Results

Relations between Association Ratings, Index of Structured Relations and Co-

occurrence

To create an associative strength measure we averaged the mean strength of

association scores attached to each reasoner’s 20 category pairs across the four raters from

phase 2. For each participant’s 20 category pairs, we also calculated the web-based

conditional co-occurrence using the formula described in Experiment 1. To measure the

degree to which each the categories in each argument were structurally related, we used the

structured relation measure described above.

For each of the 23 participants we calculated the correlation between the associative

strength and structured knowledge measures across their 20 category pairs, the correlation

between the measure of structured knowledge and the measure of co-occurrence, and the

correlation between the measure of associative knowledge and the measure of co-occurrence.

We then compared these three correlation coefficients across the 23 reasoners using a

repeated-measures one-way ANOVA, which was significant, F (2, 44) = 20.81, p < .0001, η2

p

= 0.49. As expected, Bonferroni post-hoc tests showed that the mean correlation coefficient

between association ratings and co-occurrence (M Kendall’s τ =.41, SD = .12) was

significantly larger than the mean correlation coefficient between association ratings and the

index of structured knowledge (M Kendall’s τ = .14, SD = .20; p = .045, effect size d = 1.25)

and the mean correlation coefficient between web-based co-occurrence and structured

knowledge (M Kendall’s τ = .23, SD = .18; p = .048, effect size d = 0.77). These results

suggest, as did the results of Experiments 1 and 2, that our measures of structured and

associative knowledge are dissociated.

Comparing Strength of Association and Structured Knowledge across Processing

Conditions

We predicted that people under heavy load would generate conclusion categories that

were more strongly associated (M = 6.42, SD = 1.09) than those generated under light load

(M = 5.96, SD = 1.08). This prediction was confirmed with a between-subjects t-test across

participants who had assigned a strength of association rating to each category pair, t (89) =

2.01, p = .048, effect size d = 0.42.

In contrast, we expected structured knowledge to be important under favourable

reasoning conditions. For each reasoner, we counted the number of structural relations across

all items. A score of 0 would mean that there were no discernable structural relation between

base and conclusion category and 40 would mean that there were multiple relations between

every generated category pair. A between-subjects t-test on the sum of structured relations

showed that there were more structured relations under light load (M = 24.25, SD = 1.29)

than under heavy load conditions (M = 20.63, SD = 2.5), t (21) = 4.41, p < .0005, effect size d

= 1.8.

Relations between Inductive Strength Ratings, Structured Relations and Associative

Strength

In line with our second and third aims - to show that both structured and associative

knowledge influence inductive reasoning and to delineate the importance of each type of

knowledge under contrasting processing conditions - we used the associative strength

measure and the index of structured relations described above to predict inductive strength

ratings.

For each participant who had taken part in phase 1, we carried out a regression

analysis, using associative strength and structured relation measures to predict his/her

inductive strength ratings. The beta weights were analysed with a 2 (load: heavy or light) by

2 (type of beta weight: associative versus structured relation) mixed-design ANOVA, with

type of beta weight as the repeated-measures variable.

There was no significant main effect of type of beta weight, F(1, 21) = .068, p = .80,

η2

p = 0.003 and no main effect of load, F(1, 21) = 3.22, p = .09, η2

p = 0.13. However, there

was a significant cross-over interaction between beta weight type and load, F(1, 21) = 6.53, p

= .018, η2

p = 0.24. This is illustrated below in Figure 2. Bonferroni posthoc tests showed that

when participants were under heavy memory load, the associative strength beta weight (M

beta= .20, SE = .07) was larger than the structured relation beta weight (M beta = .02, SE =

.02), although this difference was not quite statistically significant due to the small number of

participants in this condition (p = .065, effect size d = 1.2). A one-sample t-test confirmed

that associative strength beta weight was significantly above zero, t(10) = 3.79, p = .004, but

that the structured relation beta weight was not significantly above zero, t(10) = 0.45, p = .66.

The pattern was reversed when participants were not under a heavy cognitive load.

Thus, the structured relation beta weight (M beta = .28, SE = .05) was slightly but not

significantly larger in magnitude than associative strength beta weight (M beta = .11, SE =

.07, p =.11, effect size d = .62). However, the one-sample t-test showed that whereas the

structured relation beta weight was significantly above zero, t(11) = 5.24, p <.0005, the

associative strength beta weight was not statistically different from zero, t(11) = 1.56, p = .15.

Across the two load conditions, the associative strength beta weight was slightly but

not significantly larger for reasoners who generated their inferences under heavy load

compared to those who were only under light load (p = .44, effect size d = .32). In contrast,

the mean structured relation beta weights were significantly larger when participants were

only under minimal cognitive load compared to those who had generated their inferences

under heavy cognitive load (p = .001, effect size d = 1.6).

Discussion

The results of Experiment 3 support and extend the conclusions suggested by our

earlier experiments. Thus, the results suggest that measures of associative and structured

knowledge dissociate, and that both types of knowledge drive reasoning, but to different

extents depending on processing conditions. Because we have used a generation paradigm in

Experiment 3, our conclusions can be generalised beyond situations where participants

simply make a judgement about an argument, to situations where inductive targets are

retrieved from memory prior to the operation of a judgement process. It is unclear exactly

how associative and structured knowledge are used to retrieve targets from memory, and this

would be an interesting topic for further study.

As mentioned at the outset, one of the disadvantages of the generation paradigm is

that we lose control of the arguments that participants evaluate. Accordingly, we have been

unable to present an analysis comparing taxonomic and causal inferences. Although

participants tended to generate more taxonomically related targets under low load,

preliminary analysis revealed that categories which were taxonomically related were rated as

more strongly associated than categories that only shared more causal interaction-based

relations. The nature of the paradigm meant that this confound could not have been avoided,

and as the confound makes it impossible to draw inferences about availability differences

between taxonomic and causal knowledge from the final experiment, we have not presented

the analysis here. However, this should not detract from our central conclusion that structured

knowledge drives open-ended induction under favourable processing conditions, whereas

associative knowledge is more influential under unfavourable conditions. This underscores

our main conclusions from Experiment 1 and 2, but using a completely different paradigm

that makes different demands on the reasoner.

It is also important to compare the results of the regression analyses from this

experiment to the regression results from Experiments 1. Of course, because the analyses of

Experiment 1 were calculated by item whereas those in Experiment 3 were averaged across

participants, and we had no control over the relations between premise and conclusion

category in Experiment 3, a direct comparison is not possible. Nonetheless, there are some

interesting conclusions to be drawn. The effects of associative knowledge are particularly

interesting. One response to our arguments that associative and structured knowledge are

dissociated could be that structured knowledge is simply more complex than associative

knowledge but that these two types of knowledge are not qualitatively different. However, in

this case we would expect associative knowledge to always act as input to inductive

reasoning. Our results suggest otherwise; when cognitive resources are available, associative

knowledge is not a particularly good predictor of inductive reasoning. Associative knowledge

was not a significant predictor of reasoning about cells or diseases in the delayed conditions

of Experiment 1, and the average beta weight for associative reasoning in the light load

condition of Experiment 3 did not differ significantly from zero. This suggests that when

resources are available, participants are selective in the type of knowledge that they draw

upon for reasoning.

General Discussion

The results described in this paper make several important contributions to what we

know about cognition in general, and inductive reasoning in particular. We have devised a

simple method to measure the strength of the association between two categories. By

showing that results using this method are strongly related to an objective measure of

association, we have established its validity, and we have shown that it dissociates from

measures of people’s knowledge of various structured relationships that might hold between a

pair of categories. Using our measures of knowledge, we have shown that in many

circumstances, associative and structured knowledge influence inductive reasoning but that

this depends upon processing environment. It is also clear from our results that structured

knowledge has more influence on inductive inferences when processing conditions are

favourable, whereas associative knowledge has more effect on reasoning under adverse

processing conditions. Of course, these results have implications for theories of inductive

reasoning, but they are also relevant to a range of questions about theories of cognition more

generally.

Implications for Theories of Inductive Reasoning

Different models of induction make different assumptions about whether knowledge

is represented in associative or structured form, and our results show that both associative and

structured knowledge influence reasoning under different processing conditions. We can see

no way for structured (e.g. Osherson et al., 1990; Kemp & Tenenbaum, 2009) or associative

(Rogers & McClelland, 2004) theories of reasoning to account for all of our findings.

Although the structured Bayesian approach copes very impressively with the effects of

different types of structured knowledge which seem to be evoked by manipulations of the

property reasoned about, it assumes that all knowledge is structured. Our results contradict

this assumption. A measure of the extent to which the categories in the argument are

associated, which itself is dissociated from measures of knowledge about more structured

relations between the categories, predicts inductive strength judgements. Contrary to the

predictions of connectionist accounts which hold that all knowledge is associative, those

measures of structured knowledge also predict reasoning performance, particularly under

favourable processing conditions. Our results suggest that to fully capture people’s

judgements of argument strength, hybrid models will be required.

The effects of timing and secondary task manipulations observed in our experiments

have particular implications for structured Bayesian accounts of reasoning. Rational analyses

of cognition (see Anderson, 1990) of the kind exemplified by Causal Bayes nets accounts of

reasoning (e.g. Kemp & Tenenbaum, 2009; Shafto et al., 2008) tend not to consider the

processes underlying participants’ judgements of inferential strength (although see Griffiths,

Vul, & Sanborn, 2012). For example, Shafto et al. (2008) show how a structured Bayesian

account of induction predicts causal asymmetry effects similar to the ones observed here, but

do not speculate on the processes underlying such effects. Our results place processing

constraints on Shafto et al.’s model as we show that one of its key predictions is confirmed

only when people’s processing resources are relatively uncompromised. This finding raises

interesting questions about how reasoning consistent with a Bayesian analysis might be

instantiated in the mind to which we will return below.

Implications for Theories of Cognition

Structured versus associative accounts. As well as carrying implications for

theories of inductive reasoning, our results also bear on recent debates about theories of

cognition more generally. For example, because our experiments were designed to contrast

the effects of structured and associative knowledge on inductive reasoning, their results have

implications for conclusions about the relations between specific structured and connectionist

accounts of thinking (see Griffiths, Chater, Kemp, Perfors, & Tenenbaum, 2010; McClelland

et al., 2010). There has been recent discussion about whether structured Bayesian (see Kemp

& Tenenbaum, 2009) and connectionist (see Rogers & McClelland, 2004) accounts of

semantic cognition are complementary (see Griffiths et al., 2012). One argument is that they

are because they operate at different levels of analysis (see Kemp & Tenenbaum, 2008).

Another view is that these models exemplify different frameworks for explaining complex

cognition (see Rogers & McClelland, 2008). Regardless of the level at which they are cast or

whether they are radically different due to the nature of their ontological commitments, these

theories seem likely to account for different patterns in our data. Thus, a connectionist

account should easily be able to predict effects of the strength of the association between the

categories in the argument on strength judgements whereas it will have more difficulty in

predicting effects of knowledge about shared category or food chain membership. A

structured Bayesian model, on the other hand cannot explain the effects of associative

strength that we have observed. Thus, our results suggest that the accounts are

complementary because neither on its own is likely to be able to account for all of the data.

On the other hand, the argument that the accounts are complementary because each explains

the data, but at different levels (see Kemp & Tenenbaum 2008), is incompatible with our

claim that neither account will be able to explain all of the data.

Dual process theories. Our results also have implications for claims that there are

two processes for thinking (Chaiken & Trope, 1999; Evans, 2008). Such claims have been

widely made in the literatures on social and cognitive psychology (for recent reviews see

Evans & Stanovich, 2013; Evans, 2008), and have also been made about inductive reasoning

specifically (see Feeney, 2007; Feeney & Heit, 2007; Evan Heit & Hayes, 2011; Rotello &

Heit, 2009; Sloman, 1998). Although there is some disagreement about the characteristics

that have been ascribed to these processes, Type 1 processes are generally held to be fast,

automatic and independent of general cognitive resources such as working memory. They are

commonly equated with the operation of associative processes (see Morewedge &

Kahneman, 2010; Sloman, 1996). Type 2 processes are slow and sequential, and they process

structured representations in a rule-based manner (Sloman, 1996). On the face of it, our

results are relatively straightforward to interpret in a dual process framework: Whereas

associative knowledge influences inductive inferences in a fairly automatic and effortless

manner, akin to the operation of Type 1 processes described in dual process theories, for

structured knowledge to influence reasoning often requires the availability of time and mental

resources, both hallmarks of Type 2 processes.

Dual process theories have their critics (see Keren, 2013; Kruglanski, 2013;

Kruglanski & Gigerenzer, 2011; Osman, 2013) and even proponents of the approach

acknowledge that finding effects of a secondary task or response time manipulation can be

inconclusive (see Lieberman, 2008). Our results seem to be particularly powerful evidence

for a dual process approach. In addition to obtaining more standard effects of secondary task

and timing manipulation on reasoning performance, we have shown that the extent to which

two dissociated measures of knowledge predict reasoning performance is dependent on

processing conditions. There are good a priori reasons for expecting that associative or Type

1 processes will take associative knowledge as input and that Type 2 processes will take

structured knowledge as input. We have shown not only that reasoning performance is

influenced by the imposition of a secondary load or time limit, but that the influence of

knowledge which we expect to inform Type 2 processing is decreased under unfavourable

processing conditions. This finding, that the degree to which structured knowledge informs

reasoning is dependent on processing conditions, is highly novel evidence for the dual

process position.

Relations between Bayesian and dual-process accounts. It is interesting in this

context to consider the implications of our data for ideas about the relation between Bayesian

and dual-process accounts of thinking. As we have already pointed out, our data constrain

psychological theorising about structured Bayesian accounts. They turn out to do so in an

unexpected way. Although the primary goal of a rational analysis is not a process-level

specification of performance, there has been some speculation about the relation between

Bayesian inference and dual process theories of thinking. For example, Oaksford and Chater

(2001) speculated that the probabilistic approach offers a computational-level account of

Type 1 processes for thinking, which they claim to be much more widely used than are Type

2 processes. Consistent with this claim is Chater, Tenenbaum and Yuille’s (2006) tentative

suggestion that the cognitive system draws on a set of heuristic strategies to approximate a

Bayesian solution, rather than engaging in explicit probabilistic computations. Certainly, if

one considers the complexity of the solutions that must be approximated, then it seems

unlikely that slow, sequential, working memory intensive processes are responsible.

Recent work on how people make inductive inferences about objects when their

categorisation is uncertain appears to support these views. Chen, Ross and Murphy (2013)

asked participants to make an inductive inference about an object that could belong to one of

two categories. Previous findings show that, contrary to the Bayesian account of this task (see

Anderson, 1990), people consider only the most likely category when making their prediction

(e.g. Murphy & Ross, 1992). In a verbally presented task, participants displayed a tendency

to ignore the alternative category. However, in an isomorphic speeded, action-based task,

consistent with a Bayesian account, people took both possible categorisations into

consideration. To account for their data, Chen et al. appeal to the distinction between implicit

and explicit cognition which is often made when contrasting Type 1 and Type 2 processes

(see Evans, 2007). They argue that participants are precluded from using working memory by

the speeded action-based task, and so must fall back on implicit (or Type 1) processing which

approximates a Bayesian solution.

At first inspection, our findings - that the causal asymmetry effect is not observed

under conditions of load, and that causal knowledge best predicts reasoning under favourable

processing conditions – seem to run counter to the suggestions described above. That is, they

suggest that performance in line with Bayesian accounts is more likely under conditions

favourable to Type 2 processing. However, one way in which the two sets of results may be

reconciled depends on recognising the constraints placed by the reasoning context on

decisions about which knowledge is most relevant for a particular inference. Once sufficient

time is available reasoners may attempt to suppress or delay a response that is driven by

associative knowledge in order for structured knowledge to play a role. Thus, it may not be

the application of structured knowledge that requires Type 2 processing, but the inhibition of

associative knowledge. Such a possibility is consistent with findings suggesting that Type 2

processes are often required to inhibit the output of Type 1 processes (see De Neys & Van

Gelder, 2009; Handley, Capon, Beveridge, Dennis, & Evans, 2004; Lieberman, Hariri,

Jarcho, Eisenberger, & Bookheimer, 2005).

It is possible that inhibitory control may play a role in our experimental results also.

This suggestion is consistent with classic ideas about the interplay between automatic and

controlled processes in semantic priming (see Neely, 1977) and reading (Gernsbacher &

Faust, 1991). In order for the relevant structured knowledge to dominate responding,

participants may need to inhibit or suppress the effects of quickly processed associative

knowledge. That such control processes are known to take time and effort is consistent with

our secondary task and timing findings. Assuming a role for control processes also allows for

the claim that once the relevant structured knowledge has been selected, the psychological

instantiation of Kemp and Tenenbaum’s structured Bayesian model draws on relatively

effortless processes.

Causal Asymmetry Effects

As we pointed out in the introduction, our experiments also speak more generally to

accounts of asymmetry effects in causal thinking. The original demonstration that people

treated prediction inferences from cause to effect differently to diagnostic inferences from

effect to cause, was provided by Tversky and Kahneman (1980). They showed that people

thought it more likely that a daughter would have blue eyes given that her mother did than

that a mother would have blue eyes given that her daughter did. Tversky and Kahneman

(1980) argued that it is easier or more natural to go from cause to effect than from effect to

cause. Recently however, Fernbach et al. (2011) questioned this account and provided

evidence that Tversky and Kahneman’s example does not produce an asymmetry effect under

certain experimental conditions. They also suggest that, in the majority of cases, a cause

provides more evidence for an effect than an effect does for a cause, and suggest that the

reasoning of participants in earlier experiments (e.g. Medin et al., 2003) may have been

consistent with the predictions of a Bayesian analysis. Our results are relevant to this debate

because we have shown that causal asymmetry effects are not observed when participants are

placed under heavy cognitive load.

In this context, there are two possible interpretations of our results. First, it may be

that, as Tversky and Kahneman argued, it is easier to reason from cause to effect than from

effect to cause. A second interpretation is that people are better Bayesians in less challenging

environments. Under this interpretation, if a Bayesian analysis holds that predictive

arguments are often stronger than diagnostic arguments, then we might expect to observe that

people are better able to distinguish one from the other in favourable processing conditions. .

Our data seems more consistent with this set of predictions, although it is probably too early

to come to a definite conclusion and because there are arguments that people are better

Bayesians in more challenging environments (see Chen, Ross & Murphy, 2013), it is not

clear that this second interpretation coheres with other findings and explanations in the

literature.

Future Research

One important direction for future research will be in determining the importance of

individual differences to inductive reasoning. Dual process accounts equate individual

differences in performance with variability in the operation of Type 2 processes and Feeney

(2007) has already shown associations between cognitive ability and inductive reasoning. The

discussion here suggests that other sources of differences between individuals might predict

inductive reasoning performance. For example, individual differences in inhibitory control

might predict performance on certain inductive reasoning problems. Of course there are

different types of inhibitory control so it will be interesting to see whether inductive

reasoning is best predicted by the ability to inhibit prepotent responses based on associative

knowledge (see Handley et al., 2004) or by individual differences in the ability to inhibit

associative knowledge itself (see Burgess & Shallice, 1996). Should the ability to inhibit

semantic knowledge turn out to predict inductive reasoning performance, then this will have

theoretical consequences for debates about the merits of Bayesian and associative accounts as

well as for assumptions about the type of processes that approximate structured Bayesian

models of reasoning.

We also hope that our method, of using dissociated measures of different types of

knowledge to predict performance, will be taken up by researchers in other areas of

psychology. We can certainly envision possible uses for the method in the study of semantic

priming or recognition memory. Our method is also likely to be useful in the study of how

reasoning develops. For example, an important question for future research concerns the

relative importance of associative and causal knowledge (see Hayes & Thompson, 2007) in

children’s inductive reasoning. It would also be extremely interesting to examine more

generally the extent to which an objective measure of association and children’s own

structured knowledge predicts their pattern of inductive projections. Such a study would be

particularly helpful in resolving recent debates about the role of associative and structured

knowledge in children’s reasoning (Hayes, McKinnon, & Sweller, 2008; Sloutsky & Fisher,

2004; Wilburn & Feeney, 2008).

Conclusions

There is currently much debate over the relative merits of, and relations between,

Bayesian and associative approaches to cognition (see Jones & Love, 2011; McClelland et

al., 2010). The results we have described here suggest that accounts derived from these

approaches will not suffice to explain inductive reasoning. Each approach makes different

assumptions about how knowledge is represented and our experiments show that associative

and structured knowledge differentially affect reasoning depending on processing conditions.

In addition, whether causal asymmetry effects, which can only be explained by accounts that

allow for structured knowledge, are observed is also dependent on processing conditions.

These results suggest that either a hybrid theory or some entirely new account that takes into

account different representational formats in semantic memory will be required in order to

capture the richness of human inductive inference.

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Footnotes

1. Degrees of freedom adjusted for non-sphericity using Greenhouse-Geiser corrections.

Acknowledgements

The research described in this paper was supported by a postgraduate studentship awarded to

the first author by the Economic and Social Research Council and were carried in the

Department of Psychology at Durham University. The details of Experiment 3 were

presented at the 32nd

Annual Conference of the Cognitive Science Society. The authors wish

to acknowledge Dave Knight for his assistance in programming the experiments.

Table 1: Correlations between Mean Association Ratings, Co-Occurrence and Structured

Knowledge Measures in Experiments 1 and 2

Z-score

Exalead Co-

Occurrence

Causal

Beliefs

Taxonomic

Beliefs

Experiment 1

(40 Items)

Mean Association

Rating

Spearman’s rho .63 .14 .16

p <.0005 .41 .31

Z-score Exalead

Co-Occurrence

Spearman’s rho -.15 .06

p .36 .70

Causal Beliefs Spearman’s rho -.54

p <.0005

Experiment 2

(64 Items)

Mean Association

Rating

Spearman’s rho .59 .20 .001

p <.0005 .11 .99

Z-score Exalead

Co-Occurrence

Spearman’s rho .04 ..07

p .75 .56

Causal Beliefs Spearman’s rho -.80

p <.0005

Table 2: Mean Inductive Strength Ratings (and Standard Deviations) across the Two Timing

Conditions in Experiment 1

Cells Infections

Timing Condition Slow Fast Slow Fast

Relation

Causal 3.9 (1.4) 3.6 (1.4) 4.6 (1.6) 4.1 (1.7)

Taxonomic 5.3 (1.3) 4.7 (1.2) 4.1 (1.0) 3.7 (1.2)

Table 3: Summary Regression Results and Beta Weight Differences in Experiment 1

Expt 1 Beta

Weights

Fast

Cell

Slow

Cell

Diff Z-

score

p-

valuea

Fast

Disease

Slow

Disease

Diff Z-

score

p-

valuea

Strength of

Association .51

** .19

ns 2.48 .007 .45

** .24

ns 1.25 .10

Causal

Knowledge -.34

* -.31

* 0.17 .43 .35

** .61

** 2.10 .018

Taxonomic

Knowledge .11

ns .48

** 2.56 .005 .08

ns .34

** 1.90 .029

R2 Change 16.7 %

* 44.2 %

** 9.6 %

ns 28.1 %

**

* p < .05

** p < .01

ns p > .05

a right-tailed p-value

Table 4: Mean Inductive Strength Ratings (and Standard Deviations) for Cells and

Infections across the Load Conditions for the Three Types of Relation in Experiment 2

Property

Cells Infections

Load Light Heavy Light Heavy

Relation

Causal Predictive 3.4 (1.6) 3.6 (1.4) 5.0 (2.2) 3.6 (1.7)

Causal Diagnostic 3.4 (1.9) 3.1 (1.5) 3.5 (1.7) 3.3 (2.0)

Taxonomic 4.4 (1.5) 4.6 (1.7) 4.2 (1.5) 4.0 (1.8)

Table 5: Coding Scheme for Structured Relations in Experiment 3

Taxonomic Relationship

Category

Membership

Both categories belong to the same class or category

(e.g. carrot & parsnip)

Physiological

Similarity

Both categories are similar with respect to specific

organs or systems (e.g. bat & bird)

Causal/ Interaction-Based Relationship

Similar Habitat Both categories share similar or the same habitat

(e.g. trout & shrimp)

Behavioural

Interaction

Both categories interact via some aspect of behaviour

(e.g. monkey & tree)

Food Chain

Interaction

Both categories interact with respect to diet or eating,

i.e. one category eats or is eaten by the other (e.g.

heron & fish)

Figures

Figure 1: Causal Asymmetry Effect (Mean Inductive Strength Rating and Standard Error

Bars) across Load Conditions when reasoning about Infections in Experiment 2

Figure 2: Beta Weights (and Standard Error Bars) across the Two Load Conditions in

Experiment 3

1.0

2.0

3.0

4.0

5.0

6.0

Light Load Heavy Load

Predictive

Diagnostic

Appendix 1: Post-Test Endorsement Proportions and Strength of

Association in Experiment 1

Proportion who

believe

Categories are

Causally

Related

Proportion

who believe

Categories

are from same

Taxonomic

Group

Strength of

Association

Z-score

Conditional

Co-

Occurrence

Causal

Acorn & Squirrel 0.95 0.75 6.1 -0.1

Butterfly & Swallow 0.58 0.00 4.7 -0.54

Cabbage & Snail 1.00 0.05 4.1 -0.63

Carrot & Rabbit 0.90 0.05 6.1 0.56

Fly & Frog 0.85 0.25 5.0 -0.32

Grass & Sheep 0.90 0.00 6.9 -0.22

Grasshopper & Toad 0.67 0.45 3.8 -0.59

Krill & Penguin 0.86 0.08 3.6 -0.42

Meerkat & Eagle 0.69 0.11 3.4 -0.59

Mouse & Buzzard 0.84 0.87 3.8 -0.61

Penguin & Orca 0.70 0.08 4.8 -0.42

Rabbit & Fox 0.93 0.03 6.0 -0.12

Salmon & Grizzly 0.93 0.50 5.9 1.33

Scorpion & Eagle 0.35 0.11 4.5 -0.57

Shrimp & Salmon 0.55 0.05 5.3 4.32

Snail & Frog 0.30 0.10 4.5 -0.32

Snail & Hedgehog 0.62 0.43 4.3 -0.56

Squirrel & Cat 0.13 0.11 3.9 2.04

Toad & Snake 0.51 0.05 3.8 -0.28

Wheat & Mouse 0.90 0.25 4.4 -0.64

Mean 0.71 0.21 4.7 0.07

Taxonomic

Acorn & Walnut 0.21 0.98 6.30 -0.14

Butterfly & Ant 0.43 0.83 4.70 -0.5

Cabbage & Rapeseed 0.08 0.77 3.70 -0.54

Carrot & Radish 0.20 0.98 6.40 1.85

Fly & Ant 0.05 0.75 5.20 -0.45

Grass & Bamboo 0.30 0.95 6.70 -0.05

Grasshopper & Lice 0.27 0.63 3.70 -0.64

Krill & Woodlice 0.06 0.27 2.80 -0.35

Meerkat & Badger 0.13 0.87 4.40 -0.55

Mouse & Squirrel 0.19 0.83 4.40 -0.08

Penguin & Duck 0.48 0.80 4.30 -0.46

Rabbit & Squirrel 0.26 0.90 5.70 -0.46

Salmon & Herring 0.34 0.90 6.60 2.03

Scorpion & Spider 0.23 0.60 5.70 0.11

Shrimp & Barnacle 0.33 0.69 4.70 -0.48

Snail & Squid 0.13 0.78 3.20 0.12

Snail & Limpet 0.29 0.35 5.60 -0.5

Squirrel & Prairie Dog 0.28 0.70 4.30 -0.21

Toad & Salamander 0.20 0.64 5.00 0.46

Wheat & Bamboo 0.16 0.93 3.80 -0.48

Mean 0.23 0.75 4.9 -0.07

Appendix 2: Post-Test Endorsement Proportions and Strength of Association in

Experiment 2

Proportion who

believe

Categories are

Causally

Related

Proportion

who believe

Categories

are from same

Taxonomic

Group

Strength of

Association

Z-score

Conditional

Co-

Occurrence

Causal

Acorn & Squirrel 0.98 0.00 6.1 -.25

Butterfly & Swallow 0.57 0.08 4.7 -.55

Cabbage & Snail 0.92 0.00 4.1 -.60

Carrot & Rabbit 0.95 0.05 6.1 .19

Flower & Butterfly 0.71 0.00 6.4 1.30

Fly & Frog 0.92 0.05 5.0 -.40

Frog & Heron 0.72 0.03 4.3 -.53

Grass & Sheep 0.98 0.00 6.9 -.33

Grasshopper & Toad 0.72 0.16 3.8 -.58

Krill & Penguin 0.68 0.11 3.6 -.46

Meerkat & Eagle 0.64 0.06 3.4 -.57

Shrimp & Salmon 0.44 0.57 5.3 2.70

Snail & Hedgehog 0.67 0.03 4.3 -.56

Squirrel & Cat 0.21 0.54 3.9 1.18

Tree & Bark Beetle 0.90 0.03 7.3 3.32

Wheat & Mouse 0.85 0.05 4.4 -.61

Mean 0.74 0.11 5.0 0.20

Taxonomic

Acorn & Pecan 0.27 0.50 5.8 -.50

Bark Beetle & Praying

Mantis

0.32 0.66 6.0 -.59

Butterfly & Ant 0.16 0.75 4.7 -.52

Butterfly & Bee 0.22 0.95 6.2 .17

Cabbage & Horseradish 0.22 0.79 4.7 -.10

Carrot & Radish 0.40 1.00 6.4 1.05

Cat & Badger 0.11 0.89 3.5 -.49

Eagle & Penguin 0.15 0.85 3.7 -.56

Flower & Grass 0.20 0.90 6.2 -.01

Fly & Ant 0.25 0.65 5.2 -.48

Frog & Newt 0.32 0.85 6.6 .11

Frog & Salamander 0.42 0.74 5.8 .48

Grass & Dandelion 0.28 1.0 6.2 -.22

Grasshopper & Lice 0.32 0.75 3.7 -.61

Hedgehog & Shrew 0.37 0.79 4.3 -.45

Heron & Penguin 0.30 0.85 4.0 -.59

Krill & Woodlice 0.26 0.43 2.8 -.42

Meerkat & Skunk 0.06 0.85 4.6 -.59

Mouse & Squirrel 0.27 0.84 4.4 -.24

Penguin & Chicken 0.00 0.52 3.1 -.56

Rabbit & Beaver 0.06 0.57 5.1 -.49

Salmon & Goldfish 0.15 0.95 5.0 -.55

Sheep & Goat 0.15 1.0 6.4 2.73

Shrimp & Barnacle 0.38 0.95 4.7 -.50

Snail & Limpet 0.25 0.79 5.6 -.10

Snail & Squid 0.20 0.55 3.2 -.52

Squirrel & Prairie Dog 0.25 0.65 4.3 -.32

Squirrel & Prairie Dog 0.30 0.65 4.3 -.32

Swallow & Parrot 0.10 0.75 5.6 -.60

Toad & Salamander 0.25 0.75 5.0 .12

Tree & Bush 0.15 0.95 7.1 -.34

Wheat & Bamboo 0.15 0.85 3.8 -.51

Mean 0.23 0.78 4.9 -.20