Choi Key-Sun

Han Sang-Ki

English

Han, Sang-Ki

48901

Choi, Key-Sun

48902

Waseda University Repository

Computational Considerations onInterpreting Even If ConditionalsSang-Ki Han, Key-Sun Choi(Korea Advanced Institute of Scienceand Technology)I. IntroductionSituation logic proposed by Barwise and Perry [BP83; BAR84; BAR85]has been paid much attention in the natural langauge and discourseunderstanding. One of its major contributions is the analysis of the mean-ing of sentences based on the constraints between the situation types. Inparticular, Barwise used the situation semantics in interpreting conditionals[BAR85] . Recently, based on Barwise and Perry's work, Lee and Yoo[LY86] proposed a treatment of even-if statements in English based on thesituation semantics. They classified the even-if statements into two cases(necessary and sufficient conditions) and suggest the constraint updatingstrategy according to the change of background conditions for each cases.In this paper, we propose the computational model of the situationsemantics and show how this model can handle the conditionals and even-if statments. For this, we use the knowledge representation system developedat KAIST called the PROKB (PROlog Knowledge Base) system [1-ILC86].It is basically based on the Prolog, which is one of the Artificial Intelligence(AI) language and can support the semantic networks, frames, and logicalrepresentation as the representational formalism. It also provides severalprogramming paradigms such as the logic programming, object-orientedand access-oriented programming paradigms which are useful for a numberof AI applications.We also present the representational scheme for the situation types andthe involve relations and the mechanism to handle and maintain the involverelations. By combing situation logic with the conventional knowledgerepresentation system in AI, we can get more expressiveness power. Forexample, the domain knowledge represented in the knowledge base can be6768	 Sang-Ki Han, Key-Sun Choihelpful in understanding sentences and answering to questions related tothe semantics or meaning of objects themselves in the discouse.II. PreliminariesOver the past few years, Barwise and Perry [BP83; BAR85] havedeveloped a significant theory of meaning based on their situation seman-tics. The main idea is that a situation s can contain information in virtueof some constraint that holds between type of situation. The situation typemeans the abstraction representing the way things stand in a situation andthe constraint is the relation holding between types of situations. We denotethe situation types as S, and the constraints as S = => S'. We readS = => S' as S involves S'.Unlike other theories of meaning, Barwise and Perry distinguished bet-ween the meaning of a declarative sentence and the interpretation of anutterance of that sentence. They argued that the interpretation of an ut-terance is the fact, situation, or event it describes. In other words, it is atype of situation. On the other hand, the meaning of a sentence is consideredas a constraint. Especially, they analyzed the conditionals based on this ap-proach in [BP85]. For example, let's consider the following sentence.(1) If Claire rubs her eyes, then she is sleepy.When let S be the type of situation where at 1, Claire is rubbing her eyesand S' be the type of situation where at 1, Claire is sleepy, S and 5' arewritten as follows:S = [s in s: at 1: rubbing, Claire's eyes, Claire; 1]= [s I in s: at 1: sleepy, Claire; 1]In this case, the constraint S = => S' means that if at some specific space-time location 1, s is of type S(l) (the where the parameter 1 is anchored to1), then there is a real situation s'...SY1). In other words, at that very loca-tion, Claire is sleepy in s'.In general a constraint C of the form S = => 5' will have manyparameters, and every parameter in S' will also be a parameter of S. Givenany such constraint, and any anchor f for some or all of the parametersin S, that is, any assignment of appropriate values to the parameters, thenthe result of replacing the parameters by the values will give rise to an ac-tual constraint. That is, ifS= => S'is actual, the so isComputational Considerations on Interpreting Even If Conditionals	69S(f) = => S'(f).Most constraints to which we are attuned do not apply to every situa-tion, but only under certain conditions. In situation semantics, these con-ditions are called the background condition. Thus, the involves relation isrepresented as a three-place relation between types of situations:S involvesS' given that B, which is written as:S = => S'I B.Thus, they introduced the parametric constraint so that the interpretationof a general conditional statement is a parametric constraint CAB, whereB is a parameter anchored to the prevailing background, and where C isS = => S' , these types being the interpretations of the antecedent and .consequent, respectively.III. Overview of The PROKB SystemThe basic conceptual element of PROKB is the Concept. It is therepresentation of the entity or relationship of the world being modelled.It consists of several conceptual elements such as the Role, Domain, andLinks. The Role represents the attribute of the entity or the relationshipbetween other Concepts and the Domain is a value set of the Role values.The Link represents the conceptual subsumption relation between Concepts.It is also used to represent the inheritance hierarchy in the knowledge base.Since the inheritance hierarchy in the PROKB system is a kind of lattice,we can provide the multiple inheritance.A Concept can be considered as an aggregation of properties and rela-tions of the entity. With this feature, it can support the frame as in otherknowledge representation systems [RG77; BW76]. However, the basicrepresentational formalism provided in the PROKB system is rather thestructured semantic networks [BS85; SFS80]. This means that the Conceptcan be considered as a node in the semantic networks and it consists ofa number of other nodes which denote their conceptual subcomponents.There are two types of Concepts, one of which is the Generic Concept andthe other is the Individual Concept. The Generic Concept is the classifica-tion of the Individual Concept, which is the abstract representation of thereal entity in the world. Figure 2.1 shows an example of the Concept defini-tion and its diagram is illustrated in Figure 2.2.All conceptual elements in PROKB are represented internally as a setof Horn clause since the PROKB system is based on the logic program.Thus, it has very clear semantics and its internal representation has boththe declarative semantics and procedural semantics as the logic programlabstudentmax-enrollment	ISApersoninegerid_norequiredcreditsdept departementnadvisorprofessors_no70	 Sang-Ki Han, Key-Sun Choidoes. In other words, the internal representation can be regarded as thedeclaration of semantics of each components and, simultaneously, it canbe used as a procedure to check the semantic constraints or to obtain thenecessary knowledge.defConcept student isa [person]with[s_no : id_no,advisor : professor,dept : department,lab (default) : laboratory,required_credits : integer,max_enrollment : integer]actions[assign_advisor : assign_advisor,assign lab : lab_assign].Figure 2.1 The Definition of 'student' ConceptBasically, the PROKB system can be divided into two major componentsone of which is the terminological definition component and the other isthe assertional component as other hybrid systems [BFL83; RIC85; VIL85}.The terminological component is for the definition of the conceptualelements and the assertional component is to assert a fact and query forthe knowledge base constructed by the terminological component.We can classify knowledge represented in PROKB into two categories.One is the definitional knowledge and the other is the incidental knowledge.As our system is based on the logic clauses. For the incidental knowledge,we use the default logic developed by R. Reiter [REI80]. Therefore, we canlaboratory	 integerFigure 2.2 The Diagram for A Concept in PROKBComputational Considerations on Interpreting Even If Conditionals	 71represent and process both kinds of knowledge based on the logic program.By combining the incidental or default knowledge with the definitionalknowledge, we can support the prototype of Rosch's prototy theory [CM84].The PROKB system is a component of the knowledge programmingsystem called Sphinx [HLC86]. For a number of AI applications, it alsoprovide several programming paradigms such as the logic programming,object-oriented, and access-oriented programming. The logic programm-ing is used in the knowledge query for the knowledge base and in theknowledge definition mode. The object-oriented programming paradigmis used to represent the behavioral knowledge and transaction, and to carryout the actions by sending messages. Access-oriented programming is similarto the demon processing and triggered procedure in other knowledge,representation systems. The procedures represented by the access-orientedparadigm are invoked when a certain situation happens or a certain condi-tion is satisfied.V. The Representation of SituationsTo represent the situation based on the situation logic, we can use ourrepresentational scheme without much difficulties. The situation type cor-responds to the Generic Concept in PROKB. For example, the followingsituation type can be represented as in Fig. 3.1S = [s I in s: at 1: rubbing, Claire's eyes, Claire;1]defConcept eye_rubbingwith[sit : situation,loc : location,exp : [rubbing (claire's eyes, claire)],polarity : 1].Figure 3.1 The Representation of A Situation TypeIn Fig. 3.1, 'eye_rubbing' denotes the identifier of the situation type andthere is no situation type which has the same identifier. When it is an un-bound variable, the system provides the generated identifier. As shownabove, the 'sit' Role must be a situation and the 'loc' Role must be a loca-tion in PROKB. When one of these parameters is anchored, it is representedas the partially instantiated Generic Concept. For example, S11 situation72	 Sang-Ki Han, Key-Sun Choitype can be defined as a specialized Concept as follows:define_concept (eye_rubbingl, eye_rubbing, loc,ll)., which means that the 'eye_rubbing 1 ' Concept is a subConcept of the'eye rubbing' Concept whose 'loc' Role is 11. The subConcept inherits anyother properties, which is not declared specifically, from its superConcepts.One of the must distinguished features of the situation logic is the con-sideration of the meaning by the constraint. The constraint is a three placerelation as we explained before. It is represented in our system as follows:involve(S,S',B)., where S and S' are types of situations and B is the prevailing backgroundcondition. We can interpret conditionals by using this involve relation. Ifthe conditional of the form [if (1), then tin and S is the interpretation of(1) and S' is the interpretation of IP, then the interpretation is a parametricproposition, a proposition relative to the background conditions B. If theconstraint is represented as above, we can deduce the actual situation s':S'if S is realized and B holds. For example, let's consider (1) in Section II.In this case, S and S' are the same as shown in Section II, and assume thatB is as follows:B = [s I in s: at 1: pollen X;0].The procedure used in our system to handle conditionals is: if a situa-tion type represented as a Concept is instantiated (realized), the situationtype appeared in the involve relation is also instantiated (realized) if theprevailing background conditions are hold. If one of the parameters of thesituation type is anchored, it is represented as a partially instantiated Con-cept and the same procedure is applied. Thus, if 1 in S is anchored to aspecific space-time location 1, then SW) is also defined if B(1) holds. Figure3.2 shows the procedure written in Prolog.define_situation (X, SitType, RoleRestriction):-define_concept (X, SitType, RoleRestriction),existed (prokb, involve(SitType, Sitype2 BackCond),hold (BackCond),define _ concept (Y, SitType2, RoleRestriction).Figure 3.2 Situation Specialization ProcedureTherefore, we can determine and answer if Claire is sleepy or not, afterComputational Considerations on Interpreting Even If Conditionals	 73we know she is rubbing her eyes by the above procedure. That is, if theprevailing background conditions for that senetence hold, the consequent,Claire is sleepy, become exist in PROKB for the current situation. Therefore,we can obtain information contained in conditionals from the representa-tion of the constraints.IV. Understanding of Even If StatementIn the case of even if statements, Lee and Yoo [LY86] suggest a treatmentbased on the situation semantics. They viewed that an even-if statementdenies either a sufficient or a necessary condition which is presumed to bepart of some conditional knowledge. This can be summarized as the follow-ing rules:[1] In case a conditional of the form [if A, then C] is interpreted as statingthat A = => C Bl, that is, on the ground that Bl, A is a sufficientcondition for C, its denial is coherently expressed by an even-if state-ment (e.g. even if Al, not C) describing the constraint Al =\=> CB, where Al c A.[2] In case a conditional of the form [if A, then C] is interpreted as statingthat C = = >A I B2, that is, on the ground that B2, A is a necessarycondition for C, its denial is choerently expressed by an even-if state-ment (e.g. even if not A, C) describing the constraint C = \ = > f‘, AIB,where Agry A.In order to represent and handle with these problems in PROKB, wemust develop the representational scheme for = \ = > relation and the nega-tion of the situation type. To represent the not-involve relation, it is onlyrequired to assert the following fact in PROKB:"'involve (S,S',B).The relation c between types of situations can be also easily representedas 'isa' Links. For example, in the case of [1], the constraint given by theeven-if statement can be represented as follows:"involve (Al, C, B,).This will not conflict with involve (A, C, Bl) because A is one of the super-Concept of Al and the background condition B is different from Bl.Therefore, if the current situation is compatible with B and Al is realized,then we can not deduce the actual situation of C. To do this, we must up-74	 Sang-Ki Han, Key-Sun Choidate the 'define situation' procedure by adding the followings:define_situation(X, SitType, RoleRestriction) :-define concept(X, SitType, RoleRestriction),existed(prokb, ,N,involve (SitType, SitType2, BackCond),hold(BackCond).The situation type described by the negation of statement, say not A, meansthat the polarity of the expression stated by A is reversed. Let's considerthe following dialogue:Sue: If Paul wears a coat, he won't be cold.Lee: No, even if he wears a coat, he will be cold.In this dialogue, Lee simply states that wearing a coat is not sufficient forhis getting warm. Let S donote the situation type is which Paul wears acoat and S' denote the type of situation in which he will be cold. Then,Sue's statement means:S = = > S' I B1where r‘,S' means the situation type of [s I in s: at 1: be_cold, pau1;0]. Lee'sstatement means that the constraint does not hold in the current situationsince the the background condition B1 on which Sue's statement has beenbased differs from the present background condition B which Lee assumes.This is represented as follows:S =\= >Then, after Lees saying, we will be able to say that Paul will be cold evenif we know that he wears a coat in the current situation. This can be il-lustrated by the following session in our system using the formal language.?- define_concept(X,wearing_coat, Lloc:today, exp: [wear(paul,coat)],polarity: 1]).?- define_concept(X,weather,[loc:today,exp:[so_cold(weather)],polarity: 1]).?- find_situation(X, [loc:today, exp: [be_cold(paul)J, polarity:1]).When the final query is satisfied and the variable X is unified to a certainsituation type, we can say that Paul is cold today.Computational Considerations on Interpreting Even If Conditionals	 75The case of [2] can be dealt with by the similar method. That is, if thecurrent conditional means the necessary condition, the constraint will berepresented as explained in [2]. If the even-if statement is stated, the not-involve relation shown in [2] is asserted in PROKB.VI. ConclusionsUntil now, we consider the representational scheme for situations basedon the situation semantics. We also examined how this representation canhandle with the conditionals and even-if statements. The knowledgerepresentation system developed for AI systems - the PROKB system - isproved to be useful for representing the situations and constraints. In ad-dition, since the PROKB system can contain the domain related knowledge,our system is very expressive in understanding the natural languagesentences.To be a complete natural language understanding system, we mustdevelop a parser which can parse the natural language sentences into theforms used in situation semantics. Furthermore, a maintenance module forthe 'involve' relations must be developed to handle with the world chang-ing dynamically. Finally, an appropriate logic language to define and querythe situations should be also developed as a further research.References[BAR84] Barwise, J., "The Situation in Logic--I," CSLI-84-2, CSLI, Stan-ford University, March 1984.[BAR85] Barwise, J., "The Situation in Logic-II: Conditionals and Con-ditional Information," CSLI-85-21, CSLI, Stanford University,January 1985.[BFL83] Brachman, R., J., Fikes, R. E., and Levesque, H.J., "Krypton:A Functional Approach to Knowledge Representation," IEEEComputer, Vol. 16, No. 10, pp. 67-73, 1983.[BP83] Barwise, J., and Perry, J., Situations and Attitudes, Cambridge:The MIT Press, 1983.[BS85] Brachman, R. J., and Schmolze, J. G., "An Overview of the KL-ONE Knowledge Representation System," Cognitive Science 9,pp. 171-216, 1985.[BW76] Bobrow, D.G., and Winograd, T., "An Overview of KRL: AKnowledge Representation Language," AIM-293, Stanford76	 Sang-Ki Han, Key-Sun ChoiAILab., November 1976.[CM84] Cohen, B., and Murphy, G. L., "Models of Concepts," CognitiveScience 8, pp. 27-58, 1984.[HLC86] Han, S., Lee, Y. J., and Cho, J. W., "A MultiparadigmKnowledge Representation System," CS-TR-86-16, Dept. of CS,KAIST, 1986.[LY86] Lee, K., and Yoo, S., "On 'Even If'-Statements," SICOL '86,Seoul, 1986.[REI80] Reiter, R., "A Logic for Default Reasoning," Artificial Intelligence13, pp. 81-132, April 1980.[RG77] Roberts, B., and Goldstein, I. P., "The FRL Manual," AI Memo409, MIT AILAB, September 1977.[RIC85] Rich, C., "The Layered Architecture of a System for Reasoningabout Programs," in the Proc. of IJCAI-85, Los Angeles, Calif.,August 1985.[SFS80] Smith, R. G., Friedland, P., and Stefik, M., "Unit Package User'sGuide," HPP-80-28, HPP, Stanford University, December 1980.[VIL85] Vilian, M., "The Restricted Language Architecture of a HybridRepresentation System," in the Proc. of IJCAI-85, Los Angeles,Calif., August 1985.

Computational Considerations on Interpreting Even If Conditionals

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Computational Considerations on Interpreting Even If Conditionals

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