Methodology for the Design of Digital Brain Atlases

Artificial Intelligence in Medicine 14 (1998) 53–81

Metareasoning and meta-level learning in a hybridknowledge-based architecture

E. Christodoulou *, E.T. Keravnou

Department of Computer Science, Uni6ersity of Cyprus, PO Box 537, CY-1678 Nicosia, Cyprus

Abstract

Ahybrid knowledge-based architecture integrates different problem solvers for the same(sub)task through a control unit operating at a meta-level, the metareasoner, which coordi-nates the use of, and the communication between, the different problem solvers. A problemsolver is defined to be an association between a knowledge intensive (sub)task, an inferencemechanism and a knowledge domain view operated by the inference mechanism in order toperform the (sub)task. Important issues in a hybrid system are the metareasoning andlearning aspects. Metareasoning encompasses the functions performed by the metareasoner,while learning reflects the ability of the system to evolve on the basis of its experiences inproblem solving. Learning occurs at different levels, learning at the meta-level and learningat the level of the specific problem solvers. Meta-level learning reflects the ability of themetareasoner to improve the overall performance of the hybrid system by improving theefficiency of meta-level tasks. Meta-level tasks include the initial planning of problem solvingstrategies and the dynamic adaptation of chosen strategies depending on new eventsoccurring dynamically during problem solving. In this paper we concentrate on metareason-ing and meta-level learning in the context of a hybrid architecture. The theoretical argumentspresented in the paper are demonstrated in practice through a hybrid knowledge-basedprototype system for the domain of breast cancer histopathology. © 1998 Elsevier ScienceB.V. All rights reserved.

* Corresponding author. {cseleni,elpida}@ucy.ac.cy

0933-3657/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved.

PII S0933-3657(98)00016-5

E. Christodoulou, E.T. Kera6nou / Artificial Intelligence in Medicine 14 (1998) 53–8154

Keywords: Hybrid knowledge-based architecture; Problem solver; Metareasoner; Problemsolving strategy; Meta-level learning

1. Introduction

Knowledge-based architectures for complex, real, domains, need to employmultiple problem solvers in order to perform their task efficiently and effectively.A particular problem solver is associated with a knowledge intensive (sub)taskand comprises an inference mechanism which operates on a specific view of thegiven knowledge domain; it can therefore be abstracted in terms of a (sub)task,an inference mechanism and a knowledge level view of the domain. A hybridknowledge-based architecture integrates multiple problem solvers through ametareasoner for controlling the use of and the communication between thedifferent problem solvers. Each problem solver can either run on a stand alonebasis, or in collaboration with other solvers associated with the same (sub)task,for achieving the required results. Hence the different solvers, for the same task,exhibit a ‘competitive-collaborative’ behaviour. The decision as to which of thecompetitor solvers to deploy for a particular problem case is taken dynamicallydepending on specific meta-level requirements. Such requirements represent taskspecific properties and assumptions over domain knowledge. If during problemsolving the selected solver is shown to be unable to deliver the required interme-diate or final results, other solvers can be used, to support or replace the failingsolver. This means that decisions should be taken dynamically at different pointsduring the problem solving activity, on the basis of which, implicated solvers areeither used competitively or collaboratively. Such dynamic decisions can be quitecomplex and are taken by the metareasoner. The metareasoner operates at ameta-level, the level above the specific problem solvers and is responsible forcarrying out essential and critical (meta-level) tasks of the hybrid system. Suchtasks include the planning of the most appropriate problem solving strategy fora specific case to start with and the reactive adaptation of chosen strategies inorder to take into consideration new events occurring dynamically during prob-lem solving. A problem solving strategy specifies the different problem solvers tobe used and their relative activation patterns. The reactive adaptation of chosenstrategies reflects the reactive behaviour of the metareasoner.

Learning constitutes a critical aspect of a hybrid knowledge-based architecture.Learning should occur at different levels, at the meta-level and at the level of thespecific problem solvers. The latter refers to the ability of the (object-level)solvers to improve their reasoning mechanisms and to enhance their knowledgein order to increase their time efficiency and the correctness of their solutions.Different solvers may use different learning mechanisms depending on theknowledge domain views and the inference mechanisms that they implement.Each solver can evolve on the basis of its accumulated experience independentlyof the other solvers. Learning at the meta-level reflects the ability of the meta-

E. Christodoulou, E.T. Kera6nou / Artificial Intelligence in Medicine 14 (1998) 53–81 55

reasoner to improve the overall problem solving performance of the hybridsystem and hence the overall effectiveness of its meta-level tasks, on the basis ofstrategic experience. Even though learning at the level of the problem solvers isan important aspect of a hybrid architecture, learning at the meta-level is ofgreater importance, because of the critical role assigned to the metareasoner.Meta-level learning aims to improve the initial planning of problem solvingstrategies and the subsequent reactive adaptation of such strategies. Additionally,the metareasoner is responsible for supporting the different problem solvers inimproving their problem solving performance, i.e. it should also support theobject-level learning. For this purpose the metareasoner should transmit new,learned, information between the different problem solvers, in order to enablethem to enhance their knowledge and improve their reasoning mechanisms.

In this paper we concentrate on the definition of the metareasoner and meta-level learning. In Section 2 the metareasoner and its associated tasks areoverviewed. Learning with respect to each of the identified meta-level tasks isdiscussed in Section 3. The examples used for illustration purposes are takenfrom a prototype, hybrid, knowledge-based system, for the domain of breastcancer histopathology, developed by the first author. A short description of thesystem is also given in Section 2. Related research work is discussed in Section 4and finally Section 5 concludes the discussion.

2. The metareasoner

A critical component of a hybrid knowledge-based architecture is a meta-con-trol unit, the metareasoner. The metareasoner has a global view of the behaviourof the system and performs important (meta-)tasks dealing with the appropriateintegration of the multiple problem solvers. The metareasoner is itself a problemsolver consisting of a domain and a control module. The domain module is thestatic part of the metareasoner; it contains different types of knowledge ofrelevance to the meta-tasks. The control module is the dynamic part of themetareasoner; it realizes the meta-level tasks.

2.1. The metareasoner’s domain module

The metareasoner’s domain module consists of three different types of knowl-edge, descripti6e, strategic and general knowledge.

2.1.1. Descripti6e knowledgeDescriptive knowledge consists of knowledge describing the different object-

level problem solvers, the dependencies between them and constraints underlyingsuch dependencies. The metareasoner maintains a list of the problem solvers,given as:

L=PS1, …, PSn


PSi denotes a problem solver. The descriptive knowledge of a problem solver caninclude static and dynamic information. Static information refers to a description ofthe functionality of a problem solver and to properties describing the domain andthe control module of a problem solver which do not change during problemsolving. Dynamic information is concerned with characteristics of a problem solverarising during problem solving. Thus, each problem solver is described by itscharacteristics:

PSi= ({STj}j=1n {DYj}j=1

m )

STj denote the static and DYj the dynamic characteristics of a problem solver. Ata high level of abstraction, the functionality of a problem solver is defined throughthe goal that the solver aims to achieve. It is assumed that the different problemsolvers provide different ways for achieving the same goal.

In current knowledge engineering research, much work has been carried out oncharacterising the properties of problem solving methods. These properties arerequired for configuring [26], selecting from a library [9], 6erifying and 6alidating[12–15,27,28], such problem solving methods. For the purposes of the metareasonerthe properties of a problem solver present the appropriate abstraction of its domainand control modules for problem sol6ing. The domain module is described by itscomplexity, preciseness, le6el of abstraction and co6erage. The control module isdescribed by its cost and memory-used. The complexity, preciseness, level ofabstraction, cost and memory-used can take one of the values high, middle and low.Coverage takes values like causal-model, deep-model, case-based-model, etc., givingassumptions over the adopted knowledge domain view. In general, the metareasonerdoes not deal with the assignment of values to these properties for the differentproblem solvers. Such assignments are performed a priori during the developmentof the system.

Knowledge describing dependencies between solvers refers to information aboutwhich solvers support others, or are competitors, etc. The dependencies between theproblem solvers can be derived from the domain views used by them. Domain viewscan be complementary or orthogonal. Complementary domain views deal essentiallywith different concepts but they also need to share some concepts which provide thelink between the domain views. Orthogonal domain views deal essentially with thesame concepts but the ways they model these concepts are different. Problem solversdealing with different aspects of a specific (sub)task and based on complementarydomain views are essentially collaborators. This means that they work together ina collaborative fashion in order to achieve the associated (sub)task. Problem solversoperating on the same domain view (this means, that they use the same domain viewbut in different ways) or on orthogonal domain views for achieving a specific(sub)task can be competitors or collaborators or they can be both. For example thetask of medical diagnosis could be achieved by two different problem solvers PS1

and PS2 operating on two orthogonal domain views. PS1 uses heuristic classificationon an etiological taxonomy and PS2 uses abductive assembly on a causal network.PS1 and PS2 can behave both competitively and collaboratively. A relation DTbetween domain views DVi and DVj is defined as a triple:


BDT, DVi, DVj \

e.g.Borthogonal, etiological-taxonomy, causal-network\ . A relation between do-main views can imply a dependency relation between the problem solvers with therespective domain views:

BDT, DVi, DVj\[BST, PSi, PSj\

where ST is the implied dependency between problem solvers PSi and PSj operatingon domain views DVi and DVj respectively. For exampleBorthogonal, etiological-taxonomy, causal-network\[Bcollaborators/competitors, PS1, PS2\ . ST can bethe three relations, collaborators, competitors or collaborators/competitors. Prob-lem solver dependencies are evaluated during problem solving and less effectivedependencies are either adapted or eliminated.

2.1.2. Strategic knowledgeStrategic knowledge defines strategies for problem solving. A problem solving

strategy PSS is a plan of problem solver activations. It is defined as follows:

PSS= (PSi, pri){OPj(PSj, prj)}j=1, j" in

for example

PSS= (PS1, 1)collaborator(PS2, 2)

The operator OPj takes the values collaborator, competitor or competitor/collabo-rator. The problem solving strategy is interpreted as follows: problem solver PSi

with priority pri is the main problem solver. If during its execution the mainproblem solver is faced with difficulties, various fallback procedures are defined.These are specified in terms of other problem solvers, their respective priorities andtheir roles (collaborator, competitor, collaborator/competitor). If a subsequentproblem solver runs into trouble the same reasoning is repeated. This is denoted bythe {OPj(PSj, prj)} part of the PSS. The { } brackets denote that this part isoptional.

2.1.3. General knowledgeIn addition to the descriptive and strategic knowledge the metareasoner has

general knowledge of global problem case parameters (meta-parameters). Theseparameters describe solution types that could potentially be achieved for a specificgoal and also assumptions over domain knowledge. The properties of the solutiontype give the urgency, preciseness, efficiency and degree-of-detail of a solution andthe assumptions over domain knowledge give the type of knowledge to be used. Thetype of knowledge takes the values causal, experienced-based, functional, etc.denoting assumptions over domain knowledge. General knowledge specifies com-patible and incompatible combinations of meta-parameter values, e.g.

C1= ((metaparami, 6aluei)contradicts-with(metaparamj, 6aluej))

C2= ((metaparami, 6aluei)combines-with(metaparamj, 6aluej))


For example C1 could be ((preciseness, high)contradicts-with(urgency, high)).Meta-parameters are used for planning appropriate solving strategies for a specific problemcase by matching meta-parameters against problem solver characteristics.

2.2. The metareasoner’s control module

The metareasoner’s control module is responsible for the planning of problemsol6ing strategies and the reacti6e adaptation of such strategies on the basis of eventsoccurring dynamically during the execution of the strategies. Such events are eitherexternal to the system or materialize in the context of the operation of the activatedproblem solvers. Another significant task of the metareasoner is to improve the overallperformance of a hybrid system through meta-level learning. Meta-level learning isdiscussed in the next section.

The proposed meta-level tasks have been demonstrated in practice through aprototype hybrid knowledge-based system for the domain of breast cancer histo-pathology [10]. The examples used are taken from this system. The particular hybridsystem has been developed to assist histopathologists in the histological classificationof a new breast cancer case. The overall task of the system is the classification ofa breast cancer case as an instance of Mucinous Carcinoma, Tubular Carcinoma,Lobular Carcinoma, Medullary Carcinoma, etc. Such a classification is based on anumber of diagnostic factors extracted from a manual microscopic analysis of breastbiopsies. The prototype system incorporates three different problem solvers, eachpotentially capable of solving a given problem on its own and a metareasoner. Thethree problem solvers are a rule-based solver, a case-based solver and a deep-modelsolver.

The deep-model solver views the domain in terms of classes for the differentcarcinoma types. A class is a cluster of descriptive parameters including nuclear andcytoplasmic features. Each feature is associated with a factor of importance withrespect to the given class. Every histological breast cancer type is described throughits own class. In addition the deep-model solver has knowledge of constraints onpossible combinations of features relating different classes as well as constraints onthe values of the features. Constraints on possible combinations of features are usedfor the identification of possible coexistences of histological classes. The TubularCarcinoma class is illustrated below.

=present (E)tubule-formation=present (E)single-layers-oI-cells

tubular-structures =dispersed (E)myoepithelia-cells =absent (E)

=mild (M)nuclear-atypiadiameter-oI-tumor =1-2 cm (M)

=absent (M)necrosis=absent (M)mitoses=mild (L)pleomorphism=present (H)invasion-oI-fat=absent (E)basement-membrane


The factors (E, H, M, L) are interpreted as:E= the feature is essential to the classH= the feature is of high importance to the classM= the feature is of middle importance to the classL= the feature is of low importance to the classThe rule-based solver uses a set of rules associating the most important nuclear

and cytoplasmic features with relevant conclusions. Each carcinoma type has itsseparate set of rules. The rule set for Tubular Carcinoma is given below:

TUBULAR-RULE0 in classRulesif:

tubule-formation == present;single-layers == present;

then:tubular-class=present;}

TUBULAR-RULE1 in classRules{if:

tubular-class == present;tubular-structures == yes;myopethelia-cells == absent;basement-membrane == absent;

then:class= tubular;}

The case-based solver uses a network of diagnosed cases. The format used forrepresenting a case is similar to the one used for the classes of the deep-modelsolver. In fact the diagnosed cases are entered as instances of these classes.

The metareasoner of this system knows the characteristics of the three prob-lem solvers and the dependencies between them. For example, the rule-basedsolver is characterized by its time-efficient and approximate problem solving, thecase-based solver by its detailed and more time consuming problem solving andthe deep-model solver is characterized by its detailed and even more time con-suming problem solving. All three problem solvers can work in a competitive/collaborative way.

2.2.1. Planning of problem sol6ing strategiesA problem solving strategy is planned on the basis of meta-parameters and

problem solver characteristics. For a specific problem case, selected meta-parame-ters are assigned values and respective priorities. Unassigned meta-parameterscan attain default values and priorities. Meta-parameters are then partitionedinto groups of compatible values using general knowledge. Each meta-parametergroup represents a different strategy. Groups are individually consistent but dif-ferent groups are mutually inconsistent. The overall problem solving combinationscheme, S, is the set of meta-parameter groups:

S={Gi � i=1, …, n}


The algorithm that constructs S is given below:ALGORITHM create-combination-schemeInput: ps={(metaparami,6aluei, priorityi) for i :=1 to n}Output: S combination scheme of meta-parameters

Let S :={}; ps % :=ps ; i :=1;while ps%"{} do

select (p, 6, pr) � ps % (� selection heuristic based on priority �)Gi :={(p, 6, pr)};

repeat for every (p %, 6%, pr %) � ps %/{(p, 6, pr)}if (p, 6) combines-with (p %, 6%)

thenGi :=Gi {(p %, 6%, pr %)};ps % :=ps %/{(p %, 6%, pr %)};

endendS=S {Gi};i := i+1;

endreturn (S);The meta-parameter groups in S are then matched against problem solver

characteristics in order to obtain appropriate alternative strategies for the partic-ular case. Initially, the group including the meta-parameter with the highestpriority is selected. The problem solving strategy corresponding to this group isthen composed. Strategies for the remaining groups are also composed but theseare of lower priority. The priority of a strategy is given by the priority of themain problem solver included in the strategy. Normally, the main problem solveris the solver matching the meta-parameter with the highest priority in the partic-ular parameter group. The main problem solver in a strategy is assigned thehighest priority among other solvers (competitors or collaborators) comprisingthe strategy.

For example, let (c1, 61),…, (cn, 6n) represent the characteristics of problem sol-ver PS1, (d1, 6i),…, (dn, 6n) represent the characteristics of PS2, (r1, 61), …, (rn, 6n)represent the characteristics of PS3 and S={G1, G2} be the combination schemefor a specific problem case where:

G1={(p1, 61, pr1), (p2, 62, pr2)}

and

G2={(p3, 63, pr3)}

In addition pr1 is higher than pr2, pr2 is higher than pr3 and PS1 can behavecollaboratively with PS2. If (p1, 61) and (p2, 62) match with (c1, 61) and (d2, 62),respectively and (p3, 63) matches with (r3, 63), the two problem solving strategies


PSS1= (PS1, priority1)collaborator(PS2, priority2)

and

PSS2= (PS3, priority3)

can be generated for the specific problem case, where priority1 is higher thanpriority2 and priority3.

The algorithm plan-sol6ing-strategies given below defines the steps for planningproblem solving strategies.

ALGORITHM plan-solving-strategiesInput: S combination scheme of meta-parameters

PSL list of problem solverscharacteristics (ck,1, uk,1)…, (ck,m, uk,m) of each problem solver PSk

Output: PPSi different solving strategies

Let S %:=S ; i:=1;while S %"{} do

select Gi � S %;S %:=S %/{Gi};Li :={}; (� intermediate list of problem solvers �)PSSi :={};

repeat for every (p, 6, pr) � Gi (� for every meta-parameter p �)repeat for every PS � PSL(� for every problem solver PS �)

repeat for every (c, u) of PS(� for every characteristic of PS �)if (p, 6) matches with (c, u)

thenLi := ((PS, pr): Li); (� PS is entered in the list of possible

problem solvers with priority pr �)end

endend

endselect PS � Li with the highest priority, pr ;PSSi :={(PS, pr)}; (� A problem solving strategy with PS as its mainproblem solver �)Li :=Li/{PS};domain-view-check (PSSi, Li); (� find the collaborators/competitors ofPS �)i := i+1;

endThe algorithm for domain-6iew-check uses the relations between domain views in

order to decide whether problem solvers can be used as collaborators, competitorsor collaborators/competitors.


2.2.2. Reacti6e adaptation of chosen strategiesThe reactive behaviour of the metareasoner reflects its ability (a) to react to

unexpected situations arising during the execution of a problem solving strategy,(b) to support activated problem solvers to overcome such situations and (c) toadapt the given strategy in accordance with new events occurring during theresolution of the particular unexpected situations. During its operation, an acti-vated problem solver may be faced with various difficulties, such as missing dataor contradictory data. As a result, it may be unable to continue its operationunless the encountered difficulties are resolved. The problem solver will first tryto resolve the problematic situation by itself, through its own knowledge andreasoning abilities. If the problem solver manages to resolve the given problem-atic situation by itself, it can locally memorize the specific situation together withthe appropriate answer. If the problem solver fails, it will turn to the metarea-soner for support by referring the unresolved problematic situation to the metar-easoner. Hence, during the execution of a problem solving strategy themetareasoner may be dynamically requested by activated problem solvers tosupport their decision making. The metareasoner should be able to react torequests from problem solvers by providing new strategic steps to be undertakenin order to continue problem solving.

Requests coming from the different solvers are regarded as impasses.1 In gen-eral, an impasse occurs when an activated problem solver is unable to continueproblem solving and thus is unable to come up with an appropriate conclusion.Impasses could be described as requests for support to overcome difficulties.Impasses are of different types, since there are different reasons as to why anactivated problem solver cannot continue its problem solving. Every type needsto be interpreted differently (see Table 1). For each type of impasse, a differentreasoning method is activated by the metareasoner.

Table 1Different types of impasses and methods for handling them

Handled by metareasoner’sImpasse type

Violation of data value constraints Check-domain-constraints-methodCheck-hypothesis-methodContradiction (inconsistency) of data with pursued hypothesisCheck-domain-knowledge-methodContradictory data

1 The idea of an impasse in the context of learning is taken from the SOAR system [16–18]. In SOARan impasse occurs when the system is unable to make progress in achieving a specific problem goalbecause the directly available knowledge may be incomplete or inconsistent. In such a case a problemsubgoal to be achieved is defined. If the processing of the subgoal can be captured in an efficient form,so that the results of the subgoal can be produced directly without problem solving, the impasse andassociated problem solving can be avoided in future. The use of impasses in SOAR is simpler than inour system, because only one problem solver is involved and occurred impasses are resolved by splittinga single goal into multiple subgoals.


In general, Ii represents an impasse of type Ti coming from problem solverPSi while attempting to justify hypothesis Hi. Ti gives, in addition to the impassetype, the data d1, …, dn that further describe the cause of the impasse. Themetareasoner should be able to activate an appropriate method M to suggeststeps for resolving the impasse. A successfully resolved impasse is associated witha triple (PSj, Ti, Ai) giving an answer Ai to the impasse Ii which was generatedby problem solver PSj. For example, Ai could give a different hypothesis. Thus:

Ii= ((PSi, Ti, Hi)[ (PSj, Ti, Ai))

The metareasoner’s impasse handling methods (Table 1) take as input theimpasse, they perform the relevant steps for resolving the given impasse andreturn an answer. The answer depends on the method activated and it can be analternative solution hypothesis to the one currently pursued, or it can give ad-justments to data values, or constraints to be satisfied by the current hypothesis.The check-hypothesis-method is activated when there is an inconsistency of datawith the pursued hypothesis. This means that some data exists that is not ‘nor-mal’ for the current hypothesis. For example, the datum (tubules-formation,present) is not normal for the hypothesis of ‘Mucinous Carcinoma’. If such dataexists the hypothesis of ‘Mucinous Carcinoma’ should be replaced with a newone, for example the coexistence of ‘Mucinous and Tubular Carcinoma’.

The domain-constraints-method is activated when there is a violation of datavalue constraints. Such a violation implies that some data values are out of theexpected value ranges for the specific hypothesis. This violation is only subtlydifferent from the inconsistency handled by the previous method. The formermethod deals with clear violations while this method deals with apparent viola-tions that may actually turn out not to be violations. For example, the datum(cells-size, 12 mm) appears to violate the constraint that the size of the cellsshould be between 8 and 10 mm for the hypothesis of ‘Lobular Carcinoma’. Thedomain-constraints-method tries to justify the detected constraint violation as apotential exception.

The domain-knowledge-method is activated when there is contradictory data.Contradictory data means that different data values contradict with each other,but each one individually does not contradict with the current hypothesis. Forexample, the datum (basement-membrane, present) is compatible with the hypoth-esis of ‘Tubular Carcinoma’ and so is the datum (in6asion-of-fat, present). How-ever, the simultaneous existence of these data causes a contradiction. If thebasement-membrane is present, there can be no invasion-of-fat. The domain-knowledge-method aims to eliminate the detected contradiction between the databy value adjustment and in so doing the hypothesis may be changed.

The three methods share many steps and thus for illustration purposes weonly discuss the check-hypothesis-method, the algorithm of which is given below.First, the problem solver that generated the impasse is put on halt, anotherproblem solver potentially able to resolve the impasse is selected and an appro-priate message is sent to the selected problem solver. The three methods differon the message sent to the selected solver. The selected problem solver returns


an answer (resolution of the impasse) to the metareasoner, on the basis of which themetareasoner evaluates the performance of the impasse problem solver and decideswhether to reinstate it for continuing the problem solving or to replace it with a(competitor) problem solver as dictated by the strategy under execution.

ALGORITHM check-hypothesis-methodInput: PSi impasse problem solver

Ti impasse type together with its dataHi currently pursued solution hypothesisPSSi problem solving strategyPSL list of problem solvers

Output: Ai answer to given impasse

PSi.status := ‘stopped’; (� The impasse problem solver is put on halt �)(� select-problem-solver(…) returns a problem solver, PSj, potentially able toresolve the impasse �)

PSj :=select-problem-solver (PSSi, PSi, PSL);(� SEND-MESSAGE is the primitive for exchanging messages betweenproblem-solvers. In this context it is used for sending a message by themetareasoner to the selected problem solver, PSj, instructing it to carry outits verify-hypothesis method. The result of this method is a new hypothesis,the one that has the highest score among a group of selected hypotheses.The hypothesis selection and scoring mechanisms are specific to PSj. Thenew hypothesis is communicated back to the metareasoner through the ‘re-sult’ argument of the SEND-MESSAGE. This constitutes the answer Ai, tothe impasse. �)

SEND-MESSAGE (PSj, verify-hypothesis (Ti, Hi), result, metareasoner);

(� problem-solver-evaluation(PSi) carries out an evaluation of the impasseproblem solver PSi, using the answer of PSj on the basis of which themetareasoner decides whether PSi should be reactivated for continuing theproblem solving �)

problem-solver-evaluation (PSi);

if PSi.evaluation \min-acceptable-performancethen

PSi .status:= ‘activated’;elseBactivate competitor on the basis of the strategy in operation\

endThe result of select-problem-solver is a new problem solver PSj, potentially able

to continue problem solving. PSj is selected from among collaborators, if any, ofPSi as given in the problem solving strategy. If no collaborators are specified, PSj

is selected from among the overall set of problem solvers as given in the global listof problem solvers. In the latter case, a collaborator of PSi is dynamically decidedusing the relations between the domain views of problem solvers.

The selected problem solver, PSj, then executes its verify-hypothesis method inorder to determine alternative solution hypotheses. Each hypothesis is assigned a


score. The hypothesis with the highest score is communicated back to the metar-easoner. The hypothesis selection and scoring mechanisms are specific to PSj.

The evaluation of the performance of the impasse problem solver takes intoconsideration information such as how much time the specific problem solverhas already spent and the number of impasses produced so far by it. If theperformance of the problem solver is weighted to be below a minimum level ofacceptable performance the solver is permanently excluded from the particularproblem solving activity.

3. Meta-level learning

Meta-level learning reflects the ability of the metareasoner to improve theoverall performance of the hybrid system by improving the effectiveness of thecritical meta-level tasks. More specifically meta-level learning addresses the fol-lowing:� How to improve the planning of the initial problem solving strategy for a

particular problem case, so that the most appropriate strategy is initiallyactivated.

� How to improve the reactive adaptation of activated strategies, i.e. how toimprove the reactive behaviour of the metareasoner.

� How to best support the different problem solvers in improving their problemsolving performance, i.e. how to improve support for object-level learning.

In the following subsections each of the above meta-level learning tasks is dis-cussed in turn.

3.1. Impro6ing the planning of problem sol6ing strategies

The performance of a hybrid system is certainly improved, if for every prob-lem case the most appropriate problem solving strategy is initially selected. Asmentioned in the previous section, the planning of a solving strategy is based onmeta-parameters describing the problem case and on problem solver characteris-tics. For example, if a fast solution is requested for some problem case, asuitable strategy should aim to utilize those problem solvers that can come upwith a solution faster than the others. Normally, a combination of solvers wouldbe used for achieving the desired results. During problem solving a sol6ing path,tracing the whole activity in a detailed way, is kept by the metareasoner, forcontrolling the overall process. The results achieved through the execution of thestrategy are recorded on the solving path. In order for the metareasoner toimprove the planning of strategies, i.e. to improve its ability to select for aspecific problem case the best strategy to be used, past, successful, solving pathsare stored as successful strategic cases for future use. Thus, past successes inproblem solving can be regarded as situations giving opportunities for learning.A paradigm, appropriate for the learning of successful strategic cases, is thecase-based one [1–3]. New problems can be effectively solved by retrieving and


adapting existing strategic cases. This way the metareasoner learns from its accumu-lated experience, so that successful solving paths are repeated, rather than continuouslydevising new strategies.

3.1.1. Component parts of a strategic caseA strategic case has two major components: the problem description and the solution.

The main difference between an object case and a strategic case is that an object casesimply states the solution, while the essence of a strategic case is the representationof how the solution was derived. Also an object case gives the problem descriptionin relatively great detail while a strategic case only points out the aspects of the problemdescription that directly impinge on choices comprising the solution derivation. Thecomponents of a strategic case represent the derivation of a solution to a problemat the appropriate level of abstraction. This is because a strategic case should provideappropriate guidance regarding the solution of specific (types) of problems. Morespecifically, the two components of a strategic case are defined as follows:� Problem description : gives a high level description of the problem in hand.� Solution : gives, at a high level, the steps used in reasoning a solution to the

problem.The accumulation and efficient indexing of past, effective, strategic cases is

important for enhancing the overall performance of a hybrid system. The num-ber of strategic cases is anticipated to be relatively small at any time (in com-parison to the number of object cases). A strategic case encompasses a numberof object cases. It is an abstraction of these object cases from a strategic pointof view and therefore brings out the similarities between these object cases thathave resulted in the same (or almost the same) strategy for deriving their solu-tions. It is quite possible though, that at the problem description level, therelevant object cases exhibit significant differences. A strategic case is a declara-tion of the significant steps that were undertaken in solving actual problems. Itdoes not give how exactly these problems were solved since the actual problemsolving is performed by the implicated object level solvers. A new problem issolved by retrieving a past relevant strategy on the basis of the description ofthe problem and meta requirements and if necessary adapting the proposedstrategy to the new situation.

The problem description in a strategic case gives the following:� Goal achieved in solving the problem(s)� Constraints on the specific goal� Characteristics of the problem situation

The goal describes the main aim to be achieved. Constraints give conditions on thegoal. Conditions are expressed through the meta-parameters, by assigning values andrelative priorities to selected meta-parameters. Characteristics of the problem situationis the catchall that holds any other information of relevance to the specified goal.Such information includes the main- and other-characteristics of a problem situationnecessary for inferring a first solution approximation (hypothesis) to the problem.This is the minimum information needed for reaching a decision about a first solutionhypothesis.


The solution part of a strategic case gives the first solution approximation, theproblem solving strategy per se, whether the current case is based on a previouscase, adaptations on the retrieved case and also the achieved result. The overallschematic for a strategic case is given below:

Problem Description:Goal: e.g. diagnoseConstraints: meta-parameter expressionSituation Description:

main characteristics (main piece of information)other characteristics

Solution:problem solving strategyfirst solution approximation (hypothesis)resultpast strategic case based onrepair strategies on the past strategic case

3.1.2. Organizational structure of a strategic case baseIn general, a strategic case contains only information relating to the strategy

used in solving specific problems. It does not contain information regarding theactual execution of the strategy. All the components of a strategic case areshown below.

strategic-casecproblem-case-parameters: BA group of required meta-parameters\

BAn appropriate problem solving strategy\problem-solving-strategy:BMain characteristics of the problem case\main-characteristics:BA first solution approximation\hypothesis:B0ther characteristics of the problem case\other-characteristics:

result: BA result\retrieved-case: BThe best matched strategic case\

BAdaptations on the retrieved strategic case\repair-strategy:references: BNumber of references\

BNumber of successful references\successful-references:BNumber of failed references\failed-references:

date-of-reference: BDate of last reference\

References information gives the number of times the specific strategic case hasbeen retrieved for solving new problem cases. Successful-references and failed-references respectively, give the number of successful and failed uses of thestrategic case. Such information is used in order to keep the number of thememorized strategic cases and thus the size of the strategic case base, to aneffective minimum. Only frequently used successful srategies are kept in thestrategic memory. Retrie6ed-case gives an existing strategic case that the current


case is based on. Repair-strategy gives adaptations carried out on the retrievedstrategic case. The date-of-reference gives the date that the specific strategic casewas last used. Strategies not retrieved for a long period of time are deleted fromthe memory.

The organizational structure of the strategic case-base is a flat memory wherecases are stored sequentially one after the other. Flat memories are mainly usedwhen the case library is relatively small. The main advantage of such a memorystructure is that adding new cases to the case library is cheap. Below we explainwhy a flat memory structure is believed to be appropriate for storing the strate-gic cases of a hybrid knowledge-based system.

(1) Even though the most important feature of a hybrid knowledge-basedsystem is the multiplicity of problem solvers, there must be a limit on thenumber of problem solvers which in reality are involved in any problem solvingactivity, if we are to have the required efficiency. As each strategic case repre-sents a viable combination of problem solvers, the number of strategic cases isexpected to be relatively small. Not every combination of solvers is viable.

(2) A strategic case is underlined by value assignments to certain meta-parameters. In general, the number of meta-parameters and their associatedvalue sets will be small. This also restricts the domain of viable strategies.

3.1.3. Indexing and retrie6al of strategic casesIn a flat memory, cases are normally retrieved by applying a matching func-

tion sequentially to each case, keeping track of the degree of match of each caseand returning those cases that match best. Although the retrieval algorithm isvery simple, there are major disadvantages. The biggest disadvantage is the highcomputational cost. As the case library gets larger, so does the time needed forretrieval. In order to avoid this, direct addressing is provided through multipleindexes. The indexing scheme used is similar to the multiple indexing mechanismused in database systems. Three different descriptors of a problem case are usedas indexes, the main-characteristics, the meta-parameters and the other-character-istics. Indexing and retrieval is carried out in two steps (see Fig. 1). In the firststep, the strategic case base is searched for those cases that match the requiredcombination of meta-parameters. Additionally, the strategic case base is searchedfor those cases that match the main-characteristics of the new problem. Theoverall result is the union of cases found using the indexes of the main-charac-teristics and the meta-parameters. In the second step, the other-characteristics ofa problem case are used to find the best strategic case out of the matched ones.The matching on the basis of both the main-characteristics and the meta-parameters can be partial.

There are a number of advantages in using multiple indexes. First, there are twoindependent paths that can be followed for finding relevant cases. Second, theproblem of missing information is alleviated. If no meta-parameter assignments arerequired for a specific problem case, the strategic case-base is searched on the basisof the main-characteristics alone. If on the other hand the main characteristics are


Fig. 1. Multiple indexing in a strategic case base.

incomplete, the meta-parameter assignments are used. The fact that partialmatches are allowed also helps alleviating the problem of missing information.

If the strategic base is empty or no appropriate strategy can be found, theplan-solving-strategies algorithm is used for planning a strategy from scratch.The use of two alternative ways provides flexibility in deciding appropriate prob-lem solving strategies.

3.1.4. Matching and ranking of strategic casesMatching is the process of comparing two cases against each other and deter-

mining their degree of match (similarity). Ranking is the process of ordering(partially-)matching cases according to goodness of match or usefulness. Whenwe match cases, we can either produce a score that signifies a degree of match,or we can simply determine whether: yes, a case matches sufficiently, or no, itdoes not. When we rank cases, we determine which of several cases—all ofwhich match at least partially—is better than the others.

Through indexing a number of partially-matching strategic cases are selected.For each retrieved case its matching degree with the current situation is computedby means of a similarity measure. The case with the maximum matching degree isselected. The similarity measure is calculated using the priorities of the differentmeta-parameters and the number of matched main- and other-characteristics. More


specifically three matching functions, mpf, mcf and mof are used. These respec-tively compute the similarity between the problem case Ca and a selected strate-gic case Sa on the basis of meta-parameters, main-characteristics andother-characteristics respectively. Function mpf is calculated as follows, where pi

and ps denote a meta-parameter of Ca and Sa, respectively.

mp(pi, ps)=!1 if(pi=ps)�pi · value=ps · value)� (pi ·pr=ps ·pr)

0 otherwise

Then, mpg(pi Sa)=�ps�Samp(pi,ps) gives the evaluation of pi with respect to all

the meta-parameters of the selected case Sa. Finally, mpf(Ca, Sa)=�pi�Ca

mpg(pi, Sa) gives the evaluation of all the meta-parameters of the currentcase Ca with respect to all the meta-parameters of the selected case Sa.

Functions mcf and mof are similarly calculated. The overall similarity measure,SM, of a problem case with respect to a strategic case is given as the sum of thethree matching functions:

SM(Ca, Sa)=mpf(Ca, Sa)+mcf(Ca, Sa)+mof(Ca, Sa)

The strategic case with the highest similarity measure is given top ranking.

3.1.5. Adapting and learning of strategic casesThe strategic case base is part of the knowledge of the metareasoner. Strategic

cases are learned incrementally; initially the strategic case base is empty andcases are incorporated one by one during problem solving. The solution of anew problem case based on a retrieved strategic case is added to the strategiccase base if it has a different outcome or the outcome is the same but arepair-strategy had been carried out on the retrieved strategy. Such a repairstrategy may prove to be necessary because of the existence of additional charac-teristics not included in the retrieved case.

The following example taken from the breast cancer system illustrates how aproblem solving path is saved as a successful strategic case for future use.Suppose that the requirements for a new problem case are for an approximateand a time efficient solution. The metareasoner plans (or retrieves) an appropri-ate problem solving strategy as explained above. Let us assume that it decidesthat the utilization of the rule-based solver with the case-based solver as acompetitor and the deep-model solver as a collaborator (either to the rule-basedor the case-based solver) is the most appropriate strategy. The rule-based solverhas a priority of one and both the case-based and the deep-model solver have apriority of two. A priority of one represents the highest priority. A solver withthe highest priority will normally be used first. In order for the system to exhibitfocused behaviour, after initially planning/selecting some strategy, a first approxi-mation to the solution, based on the main piece of information (main-character-istics) describing the problem in hand, is formulated by a special problem solverwhich is automatically invoked by the metareasoner. For example, if the maincharacteristic of the problem case is the existence of the substance MUCIN, thehypothesis of the existence of a ‘Mucinous Carcinoma’ is made. If the rule-based


solver comes up with a classification of ‘Mucinous Carcinoma’, the hypothesis isaccepted and the resulting solving path for the specific problem case is saved asthe following successful strategic case in a strategic case base.

strategic-case 1problem-case-parameters: approximate, time-efficient solution

(rule-based-solver, 1)problem-solving-strategy:competitor (case-based-solver, 2)collaborator (deep-model-solver, 2)

(MUCIN, present)main-characteristics:Mucinous Carcinomahypothesis:

other-characteristics: noneresult: Mucinous Carcinoma

noneretrieved-case:repair-strategy: none

nonereferences:onesuccessful-references:nonefailed-references:Bactual-date\date-of-reference:

The next time a new problem case has similar meta-requirements (time-effi-cient, no-detailed diagnosis) as the already learned strategic case, the existingstrategic case will be retrieved and the same strategy, i.e. the deployment of therule-based solver, will be followed. If the main and the other characteristics ofthe new problem case are the same with those of the past case, the same firstsolution approximation (hypothesis) will be made. If during problem solving theselected strategy proves to be inappropriate for the new problem case, the metar-easoner would need to decide whether to continue or halt the specific problemsolving. A halt is chosen if all the suggested activation patterns of the problemsolvers involved in the selected strategy, thus the use of the case-based and thedeep-model, do not result in a conclusion. In the event of a continuation of thespecific problem solving, the metareasoner analyses the reasons of failure anddecides about new strategic steps to be followed. The way the different reasonsof failure are analysed and new strategic steps are suggested reflects the reactivebehaviour of the metareasoner. It is important that new strategic steps aresuggested and undertaken for continuing the problem solving. In the aboveexample it is possible that the activated rule-based solver failed to come to aconclusion because a satisfied rule antecedent (MUCIN-POOLS, absent), is in-consistent with the pursued hypothesis. A new strategic step could be that thecase-based solver should take over the problem solving (the case-based solverbehaves as a competitor to the rule-based solver). The retrie6ed-case componentof the strategic case is adapted to include the new information. The repair-strat-egy component gives pointers to the occurred impasses during the execution ofthe strategy. The way such impasses are represented is discussed in the nextsection. A repair strategy refers to impasses that have resulted in adaptations of


the original strategy. If the adapted strategic case leads to a successful conclu-sion, it will be saved as a new strategic case as shown below.

strategic-case 2time-efficient, no-detailed diagnosisproblem-case-parameters:

problem-solving-strategy: (case-based-solver, 1)collaborator (deep-model-solver, 2)(MUCIN, present)main-characteristics:

hypothesis: Mucinous CarcinomaMUCIN-POOLS absentother-characteristics:

result: Mucinous Carcinomaretrieved-case: strategic-case 1repair-strategy: Bassociated impasses\

nonereferences:successful-references: onefailed-references: nonedate-of-reference: Bactual-date\

If the case-based problem solver can not provide an appropriate solution, themetareasoner is again responsible for suggesting new strategic steps after takinginto consideration the dependencies between the different solvers. A new strate-gic step could be to activate the deep-model as a collaborator to the failedcase-based solver in order to check whether the absence of MUCIN-POOLSimplies the existence of a different hypothesis. If this is established the hypothe-sis could be replaced by a new hypothesis (for example the co-existence ofMucinous Carcinoma with another type of carcinoma) and the case-based solvercould then continue in order to justify the new hypothesis. In the event ofsuccess the following adapted strategic case would be learned:

strategic-case 2problem-case-parameters: time-efficient, no-detailed diagnosis

(case-based-solver, 1)problem-solving-strategy:collaborator (deep-model-solver, 2)

main-characteristics: (MUCIN, present)hypothesis: co-existence of MUCINOUS with

LOBULAR carcinomaMUCIN-POOLS absentother-characteristics:

result: co-existence of MUCINOUS withLOBULAR carcinomastrategic-case 1retrieved-case:Bassociated impasses\repair-strategy:nonereferences:onesuccessful-references:nonefailed-references:

date-of-reference: Bactual-date\


For reasons of efficiency, the activation of the deep-model solver (in a collaborativefashion) is kept as information in an impasse given in the repair-strategy.

3.1.6. Controlling the size of a strategic case baseThe main disadvantage of a flat organizational structure of a case base is that the

size of such memories can quickly increase influencing negatively the performanceof the algorithms used for retrieving strategic cases. A way of controlling the sizeof such a memory is to ensure that only frequently and successfully used strategiccases are kept in the memory. A strategic case whose lifetime is above a certainminimum age and its frequency of successful usage is below a certain minimum ofsuccess is pruned. Another control mechanism uses the date of last reference so thatstrategies that have not been used recently are pruned. In addition to the above controlmechanisms a generalization mechanism is used, so that cases that share theirmeta-parameters and have resulted in the same conclusions are replaced with a singlemore general case.

3.2. Impro6ing the reacti6e beha6iour of the metareasoner

Improving the reactive behaviour of the metareasoner means improving theperformance of the metareasoner with respect to the handling of requests, impasses,for support from the problem solvers and the relevant adaptation of the pursuedstrategies. In general, an impasse occurs when an activated problem solver is unableto continue problem solving and thus is unable to arrive at an appropriate conclusion.The reactive behaviour of the metareasoner can be improved by memorizingsuccessfully resolved impasses for future use. This information gives the specificstrategic steps that had to be undertaken in order to resolve the given problematicsituation and the results achieved.

In a hybrid system every successfully resolved impasse can be saved as a case inan impasse case base that also constitutes part of the knowledge of the metareasoner.The main components of an impasse case are similar to those defined for a strategiccase. They are divided into those describing the problem and those describing thesolution. The problem description includes the goal to be achieved, that is the resolvingof an impasse and the features relevant to the resolution of the specific impasse. Theimpasse solution gives the answer and the impasse resolver, i.e. the problem solverthat generated the answer.

3.2.1. Organization, indexing and generalization of an impasse case baseAn impasse case is represented as follows:

impasse-casecBThe problem solver sending the impasse\impasse-

originator:BThe type of the impasse\type:

hypothesis: BThe hypothesis that the impasse-originator was trying tojustify\


impasse- BThe problem solver that was used for resolving the specificresolver: impasse\

BThe answer achieved by the impasse-resolver\answer:

The type of an impasse encompasses the class of the impasse as well as thedata describing the cause of the given impasse. The structure of the impasse casebase is a flat memory with multiple indexes. The indexes are the impasse-genera-tor, the type of the impasse and the hypothesis that the impasse-generator wasattempting to justify. For a new impasse, the impasse case base is searched forthose cases that match the impasse-generator and the hypothesis and also forthose cases that match the type of impasse and the hypothesis. The union ofcases found under each index is used. The features of each case are then (par-tially) matched against those of the new impasse and the case that gives the bestmatch is returned.

As for strategic cases, impasse cases are learned incrementally one by one,starting with an empty impasse case base. In order to keep the size of the basemanageable a generalization algorithm is carried out, so that impasse cases dif-fering only on their data features are grouped together and a new generalizedimpasse case is created. The strategic and impasse case bases are closely related.The repair-strategy component of a strategic case has pointers to impasses mem-orized in the impasse case base and their resolutions. This means that the resultsof impasses are used to repair (adapt) the problem solving strategy of a specificstrategic case and such adaptations are memorized for future use.

3.2.2. Examples of impasses impro6ing the reacti6e beha6iour of the metareasonerThe following example, also taken from the breast cancer system, illustrates

the use of impasses as opportunities to improve the reactive behaviour of themetareasoner (see Fig. 2; for the sake of a clearer illustration only some of theslots of a strategic case are included in the figure). For a specific problem case aproblem solving strategy, using the rule-based solver as the main problem solverand the deep model solver as its potential collaborator is composed. The rule-based solver is activated for justifying the hypothesis of ‘Mucinous Carcinoma’.The activated solver is unable to justify the hypothesis because of one satisfiedrule antecedent, Fi=LOBULES, having a value Vi=present that is not consis-tent with the hypothesis of ‘Mucinous Carcinoma’. An impasse then occursIi= (PSi, Ti, Hi), where: PSi=rule-based-sol6er, Ti= ((Fi, Vi), inconsistency-with-hypothesis-Mucinous-Carcinoma), Hi=Mucinous-Carcinoma. The meteareasonerresponds to this impasse by activating the check-hypothesis method which in turnselects the deep-model solver as an appropriate solver for checking whether(Fi, Vi) implies a different hypothesis. The deep-model solver concludes that thevalue of Fi implies the coexistence of Mucinous with Lobular Carcinoma. Thegiven impasse is therefore successfully resolved through the answer (PSj, Ti, Ai),where: PSj=deep-model-sol6er, Ti= ((Fi, Vi), inconsistency-with-hypothesis-Mu-cinous-Carcinoma), Ai=coexistence-Mucinous-with-Lobular-Carcinoma. The im-passe together with its answer is saved for future use. Thus the following


impasse case is created in the impasse case base:

impasse-case 1impasse- Brule-based solver\

originator:Binconsistency with Mucinous Carcinoma, (LOBULES,type:present)\

hypothesis: BMucinous Carcinoma\impasse- Bdeep-model solver\

resolver:answer: Bcoexistence Mucinous and Lobular Carcinoma\

Consequently, the solving path of the specific problem case is adapted toinclude the use of the deep-model solver, the additional characteristic (LOB-ULES, present) and the new hypothesis of the coexistence of Mucinous withLobular Carcinoma (see Fig. 2). Finally, the adapted problem solving path issaved as a new successful strategic case as follows:

Fig. 2. Illustrating the resolution of an impasse.


strategic-case 3time-efficient, no-detailed diagnosisproblem-case-parameters:(rule-based-solver, 1)problem-solving-strategy:collaborator (deep-model-solver, 2)(MUCIN, present)main-characteristics:co-existence of MUCINOUS with LOBULARhypothesis:carcinoma(LOBULES, present)other-characteristics:

result: co-existence of MUCINOUS with LOBULARcarcinomastrategic-case1retrieved-case:Bimpasse-case1\repair-strategy:

references: noneonesuccessful-references:

failed-references: noneBactual-date\date-of-reference:

The repair-strategy gives the relation of the strategic case base to the impasse casebase, through pointers to associated impasses.

For a new impasse, an answer is found either by retrieving a similar impasse fromthe impasse case base or by invoking the relevant method (Section 2). If the answersuggested in response to a specific impasse does not result in a successful continua-tion of the problem solving, the metareasoner can either try to obtain anotheranswer or it can declare the specific impasse unresolvable. An unresolved impasseresults in the termination of the problem solver by which it was generated.

In general, the reactive behaviour of the metareasoner is improved by memoriz-ing successful answers to dynamic demands from the different problem solvers.During the execution of some strategy, different failure situations can arise resultingin different impasses. The metareasoner is responsible for analysing the impasses inorder to obtain answers for overcoming the encountered difficulties. If the sug-gested answers result in a successful continuation of the problem solving, they arelearned together with their corresponding answers for future use.

3.3. Impro6ing the performance of the different problem sol6ers

A problem solver should be able to improve its reasoning mechanisms and toenhance its knowledge in order to increase its time efficiency and the correctness ofits conclusions. For example a case-based solver enhances its knowledge byincluding new successfully solved problem cases in its case base. The metareasoneris responsible for supporting the different problem solvers in their learning efforts.This can be achieved by communicating back to the solvers new informationlearned dynamically during problem solving. Such information can arise, forexample, through the successful resolution of impasses. A problem solver isresponsible for deciding how to utilize the communicated information, i.e. whetherto use it for enhancing its factual knowledge or improving its reasoning mechanism.


Fig. 3. An example of the metareasoner supporting problem solvers to learn new information.

This is illustrated in the following example (see Fig. 3). Let us suppose that for agiven problem case the rule-based solver is activated for justifying the hypothesis of‘Mucinous Carcinoma’. The rule-based solver is unable to justify the hypothesisbecause the value for feature CUT-SURFACE-COLOUR does not belong to theexpected set of values for that feature. Consequently an impasse occurs. Themetareasoner tries to resolve the impasse by activating the deep-model solver. Theanswer of the deep-model solver is that the value brown assigned to the featureCUT-SURFACE-COLOUR does not violate the hypothesis of ‘Mucinous Car-cinoma’. This information is communicated by the metareasoner to the case-based


solver. As a result the case-based solver creates a new case for ‘Mucinous Car-cinoma’ in its case base with the relevant information. Additionally, the sameinformation is transmitted to the rule-based solver. The rule-based solver adaptsits rule sets to include the possibility that the feature CUT-SURFACE-COLOUR can obtain the value brown in the context of ‘Mucinous Carcinoma’.Thus, the given information is used by both the rule-based and the case-basedsolvers for improving their knowledge.

4. Related work

Even though different research groups are presently working towards the de-velopment of knowledge-based architectures exploiting multiple problem solvers,only some of these efforts address metareasoning and strategic learning [11].Hybrid architectures addressing learning make only a weak reference to meta-level learning. For example within the ANALOG project [4–6,22,23] a knowl-edge modelling framework has been developed integrating different inference andlearning methods. The philosophy of the framework is that different methodscan be used for achieving solutions to a specific task and methods can bedecomposed into elementary subtasks that use a set of elementary methods. Forexample a case-based reasoning method can be decomposed into the elementarysubtasks of retrieve, select and reflect and a number of methods can be providedfor achieving these subtasks. Once a chosen method cannot provide appropriatesolutions, an impasse occurs to a meta-level reasoner deciding which of theprovided methods should be used next. Learning is a kind of meta-level inferenc-ing where successful and failed methods and impasses arising during problemsolving are remembered for future use, but there is no planning of problemsolving strategies.

BOLERO [19–21] is a hybrid system exhibiting reactive behaviour and meta-level planning. In BOLERO the problem solving strategy to be followed isplanned by a meta-level case-based solver and is consequently executed by arule-based solver. Important events occurring during the solving process aretaken into consideration and new plans are constructed, thus reflecting the dy-namic nature of the requirements imposed on the problem solving process.Meta-level learning concerns the memorization of successful problem solvingplans by the meta-level case-based solver. A limitation of BOLERO is that theplanning of solving strategies is based on case factual knowledge and not onglobal problem solving meta-parameters. CHROMA [7,8] is a hybrid systemintegrating induction and case-based reasoning for problem solving. Meta-knowl-edge is used to select the most adequate reasoner for every case to be solved.This meta-knowledge depends only on some factual knowledge and not on meta-parameters of the current problem. This means that no problem solving strate-gies are planned or learned. A simple form of meta-level learning is exhibited bythis hybrid system, where impasses arising during problem solving are stored forsolving future cases. In the proposal of Voß et al [29], a knowledge-based


architecture is enhanced by a suitable configuration of competence problemsolvers (specialists). The problem solvers can run on a stand alone basis and areinvoked according to specific requirements like time to be spent and number ofsolutions. One of the problem solvers (the case-based reasoner) uses a library ofsuccessful combinations of problem solvers to shortcut the entire problem solvingprocess and modifies the case library by adding new successful solving cases.Thus the meta-learning aspect in this architecture refers to the saving of success-ful combinations of problem solvers by the case-based reasoner. The idea ofidentifying different failure types occurring during problem solving and choosingappropriate strategies in order to avoid similar mistakes in the future shows alsosome similarities to the work done by [24,25]. In this work a meta-model is usedto represent the system’s reasoning, the decisions it took while performing thereasoning and the results of the reasoning. If a difficulty or failure is encoun-tered, the system introspectively examines its own reasoning processes to deter-mine where the problem lies and uses this introspective understanding toimprove itself using the appropriate strategies. Thus the above system consists ofonly one problem solver which controls its reasoning through the existence of ameta-model.

5. Conclusions and further research

Hybrid knowledge-based systems provide the appropriate technology for thecomputer-based solution of complex, real-life problems, like those encountered inmedical domains. Metareasoning and meta-level learning constitute importantaspects of a hybrid knowledge-based architecture. Metareasoning refers to theexistence of a meta-control unit responsible for controlling the behaviour of thesystem and in general the integration of the different problem solvers. Learningcan occur at the level of the different problem solvers or at the level of themetareasoner. The latter is referred to as meta-level learning. It reflects theability of a hybrid system to improve its overall performance by improving theeffectiveness of the tasks associated with the metareasoner. Such tasks are theplanning of problem solving strategies, the reactive adaptation of chosen strate-gies and the support of object-level learning, i.e. learning at the level of thedifferent problem solvers. In this paper we concentrate on metareasoning andmeta-level learning because of their significance in a hybrid architecture.Through meta-level learning the knowledge of the metareasoner is continuouslyenhanced and furthermore the knowledge and reasoning mechanisms of the dif-ferent problem solvers can be enhanced. Successfully applied strategies and alsosuccessfully resolved impasses are stored in different case bases for future use.The planning of problem solving strategies is improved by making use of paststrategic choices and the reactive behaviour of the metareasoner is improved byusing the impasse case base. Further research on metareasoning will address themore exact identification and description of meta-parameters and characteristicsof problem solvers. Categories of meta-parameters and problem solver character-


istics could be defined. Depending on the identified categories various matchingalgorithms could be investigated providing more effective combinations of prob-lem solvers. Future research on meta-level learning for a hybrid system willaddress the issue of using not only successful but also unsuccessful problemsolving strategies and impasses for improving the performance of the hybridsystem.

Acknowledgements

The research reported here has been partly conducted in the context of theproject ‘Quantitative Immunohistochemical Assessment of Prognostic Factors InCarcinoma of the Breast’ which was supported by the University of Cyprus.

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Methodology for the Design of Digital Brain Atlases

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