I R

I S

AIN

STIT

UT D

E R

EC

HER

CH

E E

N IN

FO

RM

ATIQUE E

T SYSTÈMES ALÉATOIRES

P U B L I C A T I O NI N T E R N ENo

I R I S ACAMPUS UNIVERSITAIRE DE BEAULIEU - 35042 RENNES CEDEX - FRANCEIS

SN

116

6-86

87

884

PRIORITIZED TRANSITIONS FOR UPDATES

MARIE-ODILE CORDIER AND PIERRE SIEGEL

INSTITUT DE RECHERCHE EN INFORMATIQUE ET SYSTEMES ALEATOIRES

Campus de Beaulieu – 35042 Rennes Cedex – France

Tel. : (33) 99 84 71 00 – Fax : (33) 99 84 71 71

Prioritized Transitions for UpdatesMarie-Odile Cordier � and Pierre Siegel ��Programme 3 | Intelligence arti�cielle, syst�emes cognitifs et interaction homme-machineProjet RepcoPublication interne n�884 | Novembre94 | 13 pagesAbstract: An update operation presupposes that one can predict how the world changesalong time. In the absence of a predictive model of evolution, the common sense law of inertiais usually used and justi�es the minimal change approach to the frame problem. Instead ofrelying on an implicit modeling of persistence, we propose to use an explicit modeling of theexpected evolution. We �rst explain why our previous proposal was not quite satisfactory.We then propose a model-driven semantics of the update operation which can take intoaccount an explicit transition model. The transition model provides a more powerful and exible way to represent the persistence of information. It can moreover be stressed thatnon only persistence information but also default and transition rules can be expressed inthis transition model. It can then be used to represent evolutive systems as required forexample in a monitoring or diagnosis context. (R�esum�e : tsvp)�cordier@irisa.fr��Laboratoire d'Informatique de Marseille, siegel@gyptis.univ-mrs.frCentre National de la Recherche Scientifique Institut National de Recherche en Informatique

(URA 227) Universite de Rennes 1 – Insa de Rennes et en Automatique – unite de recherche de Rennes

Transitions avec priorit�es pour la Mise �a JourR�esum�e : La mise �a jour d'une base de connaissances n�ecessite de prendre en compte l'�evolution pr�evisible du syst�eme ou du monde repr�esent�e. Les approches s'appuyant sur leprincipe de changement minimal font l'hypoth�ese que le monde ob�eit �a la loi de l'inertie :si un changement n'est pas explicitement sp�eci��e, on suppose que ce changement n'a paslieu. Dans ce papier, nous montrons les limites d' un tel mod�ele implicite de la persistence etnous proposons d'utiliser un mod�ele explicite de l'�evolution normalement pr�evue, que nousappellons \mod�ele de transition". Nous d�e�nissons alors la s�emantique de l'op�eration de mise�a jour utilisant un tel mod�ele de transition.Ce mod�ele permet de sp�eci�er la persistance des informations de mani�ere nettement plussouple et puissante que ne peut le faire un principe d'inertie maximale. Il permet de plusd'exprimer des r�egles de transition ainsi que des r�egles par d�efaut, et de leur a�ecter despriorit�es. Il peut en particulier etre utilis�e pour mod�eliser des syst�emes �evolutifs dans uncadre de diagnostic ou de supervision.

Prioritized Transitions for Updates 31 IntroductionUpdate is an operation which turns a knowledge base KBt , describing the state of the worldat time t, into a knowledge base KBt 0 describing the state of the world at time t0. This changeis generally triggered by an event, supposed in the following to be the arrival of some newpiece of information A known to be true at time t0. A then has to belong to KBt 0. An updateoperation presupposes that one can predict how the world changes along time. It requiresthat the tendency for propositions describing the world to persist along time be known. Inabsence of a predictive modeling of evolution, the common sense law of inertia is usuallyused and justi�es the minimal change approach to the frame problem [6]: a proposition trueat time t remains true at time t0 unless it can be proved to be false in t0. KBt 0 describesthe \closest" world to KBt accounting for the new piece of information A. This minimalchange principle is the basis of the syntax-oriented approach (PWA) proposed by [4] as wellas the model-driven approach (PMA) proposed by [9] . In the �rst case, the set of formulasdescribing KBt is changed as little as possible to account for the new piece of information.In the second case, each model of KBt is changed as little as possible to account for the newpiece of information.Instead of relying on an implicit notion of persistence as Winslett does, we propose touse an explicit and symbolic transition model 1; a similar proposal has been done by [3] whoproposed to use an explicit probabilistic model of persistence and causation. This explicitmodeling encodes the expected evolution and provides a more powerful and exible way torepresent how information tends to change along time.A proposal in that direction was made in [2]). Its major aw is its inability to respect themodel-driven principle which was shown to be crucial in an update context [5]. Accordingto this principle, each model of the theory has to be considered independently for update.It is not the case in this �rst proposal and its default-based semantics appears to be notadequate for update. Applying for example [2] to the turkey scenario leads to non-intuitiveresults, as we show in section 2.In this paper, we propose a model-driven semantics for an update operation capable of takinginto account an explicit transition model. It extends the model-driven semantics de�ned in[10] for the Possible Model Approach by allowing an explicit expression of persistence. Thetransition model provides a more powerful and exible way to represent how the world tendsto change along time. It can moreover be stressed that non only persistence informationbut also default and transition rules can be expressed in this transition model. It can thenbe used to represent evolutive systems as required for example in a monitoring or diagnosiscontext.1The word \model" in transition model (as well as in model of persistence or model of transition) has nological connotation. Transition model means here a formal representation of the evolution of a system.PI n�884

4 M.-O. Cordier and P. SiegelThe paper is structured as follows : we begin by showing on a motivating example themain issues of the update operation and we point out the aws of our [2] proposal. Thetransition model is presented in section 3. The semantics of the update operation is de-�ned in section 4 and illustrated by examples in section 5. The relation between PMA andpreferential models (and circumscription) has been highlighted by [10]'s and [8]'s. We showin section 6 that it can be extended to take into account an explicit transition model andhow preferential models can then capture the semantics we de�ned. In the last section, weconclude by comparing our approach to the related ones more precisely.2 A Motivating ExampleThe following example 2 illustrates �rst that updating a knowledge base requires a model-driven approach, as demonstrated by [9] and [5]. In scenario 1, not considering independentlyeach model leads clearly to non intuitive results. Scenario 2 illustrates that common-sensereasoning about change makes use of an a priori ordering on the expected transitions. Thiswas �rst shown by [9] who proposed to extend PMA with priorities.At the end of this section, we rely on this example to point out the major aws of [2]and to justify this new proposal.Scenario 1. Let us suppose that we know that a turkey is sleeping at time t. We know asa constraint that \as soon as the alarm rings, the turkey is awake or it is deaf" 3.KBt = Th(Asleep;Alarm) (Deaf _ :Asleep)).At time t0, we learn that the alarm rings. This corresponds to the arrival of a new piece ofinformation A with A = Alarm. We would like to know what happens to the turkey at timet0, i.e. what is the next state KBt 0 where KBt 0 = Update(KBt ;A). Remember that A hasto belong to KBt 0.Let us see how we would reason (using commonsense) on this scenario. We do not knowif the turkey is deaf or not at time t. Two cases have then to be considered. In the �rstcase, the turkey is deaf at time t; we can consider that it is an immutable information andthat it will still be deaf at time t0; it will then remain asleep. In the second case, the turkeyis not deaf at time t. What happens next depends on the relative persistence of :Deaf andAsleep. Supposing :Deaf to be more persistent than Asleep, (i.e. the change from beingasleep to not being asleep is more expected than the change from being not-deaf to beingdeaf), the turkey remains not-deaf and not to be asleep at time t0. Considering these twocases, we get that the turkey is either deaf and asleep or not-deaf and not-asleep.This �rst scenario demonstrates clearly that the possible worlds in t (or the models ofKBt) and their expected changes have to be considered independently. Not doing so, wewould obtain as KBt 0 ffAsleep;Deaf;Alarmgg which is clearly not the expected result (analarm does not make someone deaf!).2This example is inspired by the hiding turkey scenario from [7].3We do not take into account the short delay between the alarm and its e�ects. Irisa

Prioritized Transitions for Updates 5Scenario 2. In this second scenario, the only thing we know at time t is that the turkey isnot deaf. KBt = Th(:Deaf;Alarm) Deaf _ :Asleep). We learn that the alarm rings attime t0. In this case, supposing as before that :Deaf is more persistent than Asleep, we donot need to wonder whether or not the turkey was sleeping at time t. The turkey remainsnot-deaf and will be awaken : KBt 0 ff:Asleep;:Deaf;AlarmggThis second scenario demonstrates that common-sense reasoning about change makesuse of an a priori ordering on the expected transitions. Not doing so would result in theturkey being still not-deaf and awake or being asleep as long as it is now deaf! This lattercase clearly disagrees with our common-sense expectations.Using this example, we can now point out the major aws of the [2]'s approach whichcannot correctly dealt with these two scenarios.Applied to scenario 1, it leads to the non intuitive result explained before : not knowingwhether the turkey is Deaf or not, persistent formulas concerning Deaf cannot be applied;on the contrary, persistent formulas concerning Asleep can be applied and the turkey isconsidered as deaf. Let us recall brie y that, in [2], persistence is expressed by elementarytransitions which can be seen as temporal defaults. An axiomatisation was proposed tocombine the elementary transitions by three operators : �(substitution), ^(and) and _(or).The _ operator was quite important in that it allowed to get the persistence of a disjunctiveformula. It was quite adequate to solve the well-known examples of the update literature,as the door-and-window example. Knowing that a door or a window is open at time t, youdo not want that the closure of the door at time t0 makes you infer that the window is now(magically) closed. But it was not su�cient to provide a model-driven approach, assuringthat each model is updated independently. The key point in this scenario is not the questionof the persistence for a disjunctive formula, but that of considering for updates the twocases, deaf and not-deaf, separately. The default-based semantics we used proved to be notadequate for that.Concerning the scenario 2, only three classes of formulas can be expressed in our [2]transition model, constraints, immutable and persistant formulas 5 , which appears not tobe su�cient. :Deaf and Asleep are both persistant formulas; no preference can be given toone on the other. As we see in section 3, we propose now a transition model where formulascan be ordered in a more powerful way by giving them priorities.These scenarios have motivated the main points of this new proposal : to de�ne a model-driven semantics for an update operation while taking into account an explicit model oftransition where formulas can be ordered by priorities.3 The Transition ModelLet us �rst de�ne the transition model which allows us to explicitly express the way infor-mation tends to persist along time.A state of the world is represented by a deductively closed set KB of �rst-order formulas.A formula belonging to KBt is a formula true at time t. 44We suppose a discrete representation of time.PI n�884

6 M.-O. Cordier and P. SiegelThe transition model TM is composed of a set of elementary transitions. An elementarytransition is described as a pair hX;Y i where X and Y are formulas. There exist two kindsof elementary transitions : sure transitions ST and (more or less) expected transitions ET .� A sure transition ST : hX;Y i expresses that : if X is true in a state KBt , then Y mustbe true in the successing state KBt 0.� An expected transition ET : hX;Y i expresses that : if X is true in a state KBt , then Yis expected to be true in the successing state KBt 0. Expected transitions are partiallyordered : ETi > ETj means that ETi is more expected than ETj.This model allows us to express constraints, time-dependent formulas such as immutableand persistent formulas, 5 and other typical kinds of change.A constraint (or protected formula) K is a formula which is always true. It is expressedby a sure transition ST : hTrue;Ki. For example, ST : hTrue;Male_ Femalei means thatMale _ Female has to be true in the world at any time.An immutable formula F is a formula which as soon as it has become true remains truealong time. It is expressed by a sure transition ST : hF;F i. For example ST : hDead;Deadior ST : hDeaf;Deafi means that if we know at time t that someone is dead (or deaf), weconsider it to be true in all the subsequent states.A persistent formula is a formula which, if true at time t, remains true as long aspossible; it is then expected to be true at time t0 unless it leads to a inconsistency. Apersistent formula F is expressed by an expected transition ET : hF;F i. For example,ET : hMarried;Marriedi means that if we know that someone is married, we expect it tobe true as long as there is no evidence to the contrary.Other typical kinds of change can also be expressed in this formalism by ST : hF;Gi orET : hF;Gi : they correspond to sure or expected change from F to G. As for example :ST : hclock(i); clock(i+1)i states that the clock is increased of one unit at each transition.ET : hTrue; F i expresses default formulas as ET : hTrue;On(Switch)i which expressesthe default value of a switch.ET : hlighton; deadbatteryi expresses that if the lights have been on, we expect that thebattery will be dead in the next state 6.In the following we consider that the partial ordering between the expected transitionsallows us to partition the set of expected transitions into strata, numbered from S1 to Sn.For i > j, the transitions of the ith stratum are more expected than the transitions of thejth stratum. We have Sn > Sn � 1 > ::: > S1. Each element of Si � 1 are those directlyless than the elements of Si.It must be noticed that an expected transition belonging to the maximal stratum (thenth stratum) does not have the same semantics as a sure transition. A sure transition5Notice that we changed our vocabulary to conform to common use : what we named persistent formulasin [2] are now named immutable formulas and remanent formulas are named persistent formulas.6The model of transition depends on an implicit period of time between two updates : after one day,when the lights of a car have been on, the battery is expected to be dead; after one second, it will not be thecase. After one second, when the key has been turned, the car is expected to start; after on day, it makesno sense. Irisa

Prioritized Transitions for Updates 7cannot be overruled by any arriving piece of information. It has to be satis�ed. An expectedtransition, even if it belongs to the maximal stratum, can be overruled by an arriving pieceof information; however, it maintains in any case priority over other expected transitionsbelonging to inferior strata.4 Semantics for Updates using a Transition ModelThe update operation of a state KBt by some piece of information A using a transitionmodel TM is denoted UpdateTM(KBt;A) or Update(KBt ;A) for short. This update opera-tion corresponds to considering each possible world at time t (or model of KBt) in turn; foreach of these models, looking for the set of models which account for A and are the \closest"to what is expected to be true in t0 for this model according to TM . As explained in section3, we note TM : f ST , ET g where ST (resp. ET ) represents here the set of sure (resp.expected) transitions, and ET : f S1; S2; : : : ; Sn g where Si represents the ith stratum.We de�ne an update operation on KBt by �rst de�ning update operations on the mod-els M of KBt , noted Update-Model(M;A).We want to evaluate the distance between an interpretationM of KBt and an interpretationM 0 of KBt 0 with respect to the transition model. Let us �rst de�ne Diffi(M;M 0) whichevaluates the distance between two interpretations with respect to the ith stratum Si of ET .This distance is evaluated by looking at the expected transitions belonging to Si and whichare not satis�ed when M is changed to M 0.Diffi(M;M 0) = fhX;Y i 2 Si where X is true in M and Y is false in M 0g.It is then possible to map each interpretation M to a partial order 7 �M by :Let M 0 and M 00 be two interpretations.M 0 <M M 00 i�� 9i such that Diffi(M;M 0) � Diffi(M;M 00)� 8j > i Diffj(M;M 0) = Diffj (M;M 00).M 0 =M M 00 i� 8i Diffi(M;M 0) = Diffi(M;M 00).We de�ne �M as M 0 �M M 00 i� M 0 <M M 00 or M 0 =M M 00.We can then de�ne Update-Model(M;A) as the set of models M 0 such that :1. M and M 0 have the same universe and agree on all functions2. A is true in M 0 (M 0 is a model for A)7Remark that, due to the transition model, this assignment is not a faithful relation as de�ned in [5].We don't have that 8M 0M �M M 0. Let us take TM to be fET1 : hA;:Bi; ET2 : hB;:Aig (describing a ip- op), M be fA;:Bg and M 0 be f:A;Bg. We have M 6�M M 0.PI n�884

8 M.-O. Cordier and P. Siegel3. 8hX;Y i 2 ST , if X is true in M , then Y is true in M 04. There is no other model M 00 such that� M 00 satis�es 1-3� M 00 <M M 0Update(M;A) are the models of A satisfying the sure transitions with M and being the\closest" to M by �M .We can then de�ne Update(KBt ;A) byKBt 0 = Update(KBt ;A) = SM2Models(KBt)Update-Model(M;A).We have Update(KBt ;A) j= F i� F is true in all the models preferred by the Update-Model operation.It can be noticed that this de�nition extends the de�nition given in [10] by taking intoaccount the transition model (see section 7 for a more detailed comparison).5 Illustrative examples.Let us see now how the scenarios presented in 2 are solved by using the transition model asde�ned in section 3 and the semantics proposed for update in section 4.The transition model allows us to express the constraint as well as the persistence of theformulas by :ST1 : hTrue;Alarm) (Deaf _ :Asleep)iST2 : hDeaf;Deafi \Deaf is an immutable fact"ET1 : h:Deaf;:Deafi \:Deaf is a persistent fact"ET2 : hAsleep;Asleepi \Asleep is a persistent fact"with ET1 > ET2. \:Deaf is more persistent than Asleep"Scenario 1 continued. We haveKBt = Th(Asleep;Alarm) (Deaf _ :Asleep)) and A = Alarm.KBt has three models :M1 : fAsleep;Deaf;Alarmg,M2 : fAsleep;Deaf;:Alarmg,M3 : fAsleep;:Deaf;:Alarmg.By looking to the models of KBt and applying the de�nitions given in section 4, we get :Update-Model(M1; A) = ffAsleep;Deaf;AlarmggUpdate-Model(M2; A) = ffAsleep;Deaf;AlarmggUpdate-Model(M3; A) = ff:Asleep;:Deaf;Alarmgg.KBt 0 = Update(KBt ;A) = SM2Models(KBt)Update-Model(M;A)We get thenKBt 0 = Th(Alarm;Deaf , Asleep), which is the expected result. Irisa

Prioritized Transitions for Updates 9Scenario 2 continued. We haveKBt = Th(:Deaf;Alarm) (Deaf _ :Asleep)).In the same way as before, by looking to the models of KBt and applying the de�nitions,it can be checked that we obtainKBt 0 = Update(KBt ;A) = Th(Alarm;:Deaf;:Asleep), which is what is expected.6 Preferential Models for Updates.In section 4, we de�ned the semantics of update by de�ning a distance between interpre-tations and looking to the \closest" models (with respect to the transition model) to eachmodel of KBt . The relation between PMA and preferential models and circumscription hasbeen highlighted by [10]'s and [8]'s. We show in the following that it can be extended totake into account an explicit transition model. With an adequate change of representation,the semantics of the update operation can be expressed as the preferred models of a theoryT , according to a preference relation which is given below. The updated theory can then beobtained by using the corresponding circumscriptive schema. Preferred models and priori-tized circumscription can then give a formal account to the semantics described in section4. The �rst thing to do is to change the language L used to describe a state KB into a newlanguage L:� Each predicate P of L correspond to two new predicates in L denoted Pt and Pt0 withthe same arity as P . Pt is used to describe facts true at time t and Pt0 to describe factstrue at time t0 8. In the following, Ft denotes the formula of L obtained by replacingall the predicates P of the formula F of L by the corresponding predicates Pt of L. Inthe same way, Ft0 denotes the formula obtained by replacing all predicates P of F bythe corresponding predicates Pt0. We note P the set of predicates of L and Pt the setof predicates indexed by t.� New predicates denoted Abk are needed to rewrite the transition model.KBt is then rewritten as a set of formulas KB of L by replacing the predicates P by Ptin all the formulas representing KBt .The information A, true at time t0, is rewritten as A = At0.The transition modelTM is rewritten as TM by applying to each n-uple of TM the followingrules :STk : hX;Y i is replaced by the formula of L : Xt) Y t0ETk : hX;Y i is replaced by the formula of L : Xt ^ :Abk ) Y t0 where Abk is a new0-ary predicate. We assign to these Ab-predicates priorities and we consider that they canbe partitioned into n strata Sn > Sn � 1 > ::: > S1 with Abk 2 Si i� ETk 2 Si.Example : scenario 1.8The propositional constant True (resp. False) correspond to two new propositional constants: Truet andTruet' (resp. Falset and Falset'). These new propositional constants are assigned the truth values t (resp f).PI n�884

10 M.-O. Cordier and P. SiegelTM = f Alarmt0 ) Deaft0 _ :Asleept0, Asleept ^ :Ab1 ) Asleept0, :Deaft ^ :Ab2) :Deaft0, Deaft ) Deaft0 g with Ab2 > Ab1.KB = fAsleept, Alarmt ) Deaft _ :Asleept g.A = fAlarmt0g.T = Th(TM[ KB [A).Consider T as the deductive closure of TM [ KB [A. We can now de�ne the prefer-ence relation between the models of the theory T . Let [P ]M1 and [P ]M2 be the extension ofthe predicate P in M1 and M2. We de�ne a partial order � between two models M1 andM2 of T by :M1 < M2 i� :1. 8Pt 2 Pt [Pt]M1 = [Pt]M22. 9i such that� fAbk 2 Si s.t. Abk is true in M1g � fAbk 2 Si s.t. Abk is true in M2g,� 8j > i fAbk 2 Sj s.t. Abk is true in M1g = fAbk 2 Sj s.t. Abk is true in M2g.M1 =M2 i� :1. 8Pt 2 Pt [Pt]M1 = [Pt]M22. 8i fAbk 2 Si s.t. Abk is true in M1g = fAbk 2 Si s.t. Abk is true in M2g.M1 �M2 i� M1 < M2 or M1 = M2.The minimalmodels for this order are the preferred models of T and is denoted as Min(Mod(T )).It can be noticed that the preferred models of the theory are exactly those correspondingto minimal \abnormal" changes (taking into account priorities between changes) under thehypothesis that the predicates concerning t are not allowed to vary : it re ects the fact thatwe want to minimize changes but without making any further hypotheses on how thingswere at time t.Theorem Let T ' = [ Min(Mod(T )). We have :KBt 0 =Update(KBt ;A) = fF / Ft0 belongs to all the models of T ' g with Update(KBt ;A)as de�ned in section 4.The proof is not given here.Directly related to this preference relation, we can de�ne the corresponding circumscrip-tive schema. Let T is the theory to be circumscribed. T ' is obtained by using a prioritizedcircumscription of all Ab-predicates with all predicates indexed by t being not allowed tovary. As remarked before, we want to minimize the abnormal transitions by giving adequatevalues to the predicates at time t0, but without making any hypothesis on the state at timet . KBt 0 can then be obtained from T ' by keeping the only formulas indexed by (and onlyby) t0. We omit to give here the circumscriptive schema. Irisa

Prioritized Transitions for Updates 11Example : scenario 1 continued. Let us circumscribe T . By minimizing Ab1 and Ab2 withAb2 > Ab1 and with Asleept and Deaft not allowed to vary, we get among other formulas:Asleept0 , :Deaft0.Example : scenario 2.With the scenario 2, we would have :KB = f:Deaft; Alarmt ) Deaft _ :Asleept g,T = Th(TM[ KB [A).By minimizing Ab1 and Ab2 with Ab2 > Ab1 and with Asleept and Deaft not allowed tovary, we get among other formulas::Deaft0 and :Asleept0.7 Related WorksAs remarked before, this work extends the Possible Model Approach with priorities proposedby [10]. Instead of relying on an implicit notion of persistence as she does, we propose touse an explicit model of transition and we give a model-based semantics for update takinginto account this model. [10] relies on an implicit transition model where protected formu-las correspond to the constraints and all the predicates are considered as persistent (withpriorities).We propose to use an explicit transition model; we can then express constraints andpersistent information; but also immutable information, certain and expected transitions,and all what is known about the way the world is going to change. If, for example, anupdate contradicts a fact known to be immutable (once it is known, it cannot change), it isrejected. It is possible to describe instantaneous (or contingent) pieces of information: i.einformation which can be true in KBt , but will be true in KBt 0 only if it can be deducedfrom other facts known to be true in t0. For example, a noise can happen in KBt but we haveno reason to think that it will be true in KBt 0. These formulas have no proper persistence,and consequently, nothing has to be said about them in the transition model. Transitionconstraints, as used in databases, can be expressed by sure transitions, as for example thatthe age of a person (or the salary?) cannot decrease from one time to the successing one.Default rules and expected transitions can be quite useful to describe the behaviour of evo-lutive systems. All this cannot be taken into account by an implicit model as the one by [10].[1] propose to use some kind of strati�ed priorities in order to choose the minimal mod-els of the new theory T'. Their approach is not far away from [10]'s approach with priorities.These priorities are not given a priori but result from causal relations existing between for-mulas. This is an interesting point as it is clear that there exists a link between persistenceand causal relations.If A causes B, then the persistence of :B depends on A: If A is true at time t0, even if:B was true at time t, it cannot persist at time t0. Before deciding of the persistence of :Bwe have to look if A will be true or not at time t0. The degree of persistence of :B shouldthen be less than the degree of persistence of A.PI n�884

12 M.-O. Cordier and P. SiegelThis is exactly the case in the above example. There is a causal link between :Deaf and:Asleep (i.e. awaken); in the case of an alarm, :Deaf causes :Asleep. This is why beforedeciding if Asleep true at time t remains true at time t0, we have �rst to look at :Deaf.But it seems also clear that causal relations are not the only source of the ordering con-cerning the persistence of information. Let us discuss the following example : we know asa constraint that \in the case of an alarm, if the turkey is not deaf and if it is not tired,then it will get up from bed". Suppose we know that, at time t, it is in its bed, it is nottired and that it is not deaf. We learn at time t0 that the alarm rings and that the turkeydoes not get up. We are probably be more willing to suppose that it changes from not-tiredto tired than from not-deaf to deaf. The persistence of not-deaf is greater than the persis-tence of not-tired. And there is clearly no causal link between these two pieces of information.Finally, we can compare this work with [3] who propose to use a probabilistic model ofpersistence. The truth value of a fact at time t depends on whether or not it was true at thepreceding time t. This dependency is represented by conditional probabilities. They encodethe change expectation of facts. It can then be seen as the probabilistic equivalent of ourtransition model. In such approaches, the persistence degree of a fact varies according totime. The time between two updates can be taken into account, which is not the case inour approach. The main problem is that you need to be aware of each possible cause-e�ectrelation in order to get valid probabilistic information. In our approach, we only require apartial ordering between elementary transitions.8 ConclusionIn this paper, we argue that updating a knowledge base requires to have information on howthe world change along time. We propose to use an explicit transition model and to orderthe transitions by priorities. We de�ne a model-driven semantics of the update operationwhich extends [10] by taking into account the transition model. The main approaches inupdate do not use an explicit model of evolution and rely on the simple but limited minimalchange principle. Our formalism provides a more powerful and exible way to represent thepersistence. We focussed on persistence in this paper; however it can be stressed that nononly persistence but also default and transition rules can be expressed as well. This pointis quite interesting to represent evolutive systems, as required for example in a monitoringor diagnosis context. We are currently investigating the updating problem when multiple,successive or even concurrent, transitions have to be considered.References[1] Gerhard Brewka and Joachim Hertzberg. How to do things with worlds: on formalizingactions and plans. Journal of Logic and Computation, 1994.[2] Marie Odile Cordier and Pierre Siegel. A temporal revision model for reasoning aboutworld change. In Bernhard Nebel, Charles Rich, and William Swartout, editors, Prin-Irisa

Prioritized Transitions for Updates 13ciples of Knowledge Representation and Reasoning (KR'92), pages 732{739, MorganKaufmamm, 1992.[3] Thomas Dean and Keiji Kanazawa. A model for reasoning about persistence and cau-sation. Computational Intelligence, 5:142{150, 1989.[4] Matthew L. Ginsberg and D. E. Smith. Readings in Non Monotonic Reasoning. MorganKaufmann, 1988.[5] Hirofumi Katsuno and Alberto O. Mendelzon. On the di�erence between updating aknowledge base and revising it. In Principles of Knowledge Representation and Reason-ing (KR'91), pages 387{394, 1991.[6] John C. McCarthy and Patrick H. Hayes. Some philosophical problems from the stand-point of arti�cial intelligence, pages 463{502. Volume 4, American Elsevier, New-York,1969.[7] Erik Sandewall. Features and Fluents. to appear, 1994.[8] Ken Satoh. Nonmonotonic reasoning by minimal belief revision. In Proceedings of theInternational Conference on Fifth Generation Computer Systems, ICOT, 1988.[9] Marianne Winslett. Reasoning about actions using a possible model approach. InProceedings of the Seventh National AAAI Conference, pages 89{93, 1988.[10] Marianne Winslett. Sometimes updates are circumscription. In Proceedings of the IJCAIConference, pages 859{863, Detroit, 1989.

PI n�884