Natural Language Pro cessing Using a Prop ositional Semantic Network with Structured Variables Syed S Ali and Stuart C Shapiro Department of Computer Science State University of New York at Bualo Bell Hall Bualo NY fsyali shapirogcsbualoedu Abstract We describ e a knowledge representation and inference formalism based on an intensional prop ositional semantic network in which variables are structured terms consisting of quanti er type and other information This has three imp ortant consequences for natural language pro cessing First this leads to an extended more natural formalism whose use and rep resentations are consistent with the use of variables in natural language in two ways the structure of representations mirrors the structure of the language and allows reuse phenom ena such as pronouns and ellipsis Second the formalism allows the sp ecication of description subsumption as a partial ordering on related concepts variable no des in a semantic network that relates more general concepts to more sp ecic instances of that concept as is done in language Finally this structured variable representation simplies the resolution of some rep resentational diculties with certain classes of natural language sentences namely donkey sentences and sentences involving branching quantiers The implementation of this formal ism is called ANALOG A NAtural Logic and its utility for natural language pro cessing tasks is illustrated Introduction This work is based on the assumption that the kind of knowledge to b e represented and its asso ciated goals have a profound eect on the design of a knowledge representation and reasoning KRR system In particular we present a KRR system for the representation of knowledge asso ciated with natural language dialog We will argue that this may b e done with minimal loss of inferential p ower and will result in an enriched representation language capable of supp orting complex natural language descriptions some discourse phenomena standard rstorder inference This pap er will app ear in the journal Minds and Machines in a sp ecial issue on Knowledge Representation for Natural Language Pro cessing It is also available as technical rep ort from the Department of Computer Science SUNY at Bualo A p ostscript version is available for anonymous ftp from ftpcsbuffaloedu in the le pubtechreportsps inheritance and terminological subsumption We characterize our goals for a more natural logic and its computational implementation in a knowledge representation and reasoning system b elow The mapping from natural language sentences into the representation language should b e as direct as p ossible The representation should reect the structure of the natural language NL sentence it purp orts to represent This is particularly evident in rule sentences such as small dogs bite harder than big dogs where the representation takes the form of an implication x y smallx dogx largey dogy bitesharder x y This is in contrast with the predicateargument structure of the original sentence By comparison the representation of Fido bites harder than Rover is more consistent with the structure of the original sentence bitesharderFido Rover This is so despite the intuitive observation that the two sentences have nearly identical syntactic structure and similar meaning The subunits of the representation should b e what we term conceptually complete By this we mean that any comp onent of the representation of a sentence should have a meaningful interpre tation indep endent of the entire sentence For example for the representation of the sentence as in ab ove we might ask what the meaning of x or y is Presumably some thing in the world Note that the original sentence mentions only dogs We suggest that a b etter translation might b e bitesharder all x such that smalldogx all y such that largedogy where the variables x and y would have their own internal structure that reects their conceptual ization Note that we are suggesting something stronger than just restricted quantication simple type constraints can certainly b e felicitously represented using restricted quantiers Complex internalized constraints that is other than simple type and internalized quantier structures characterize this approach to the representation of variables Thus representation of the sentence Every smal l dog that is owned by a badtempered person bites harder than a large dog should reect the structure of the representation of A high degree of structure sharing should b e p ossible In language multisentence connected discourse often uses reduced forms of previously used terms in subsequent reference to those terms This can b e reected in the representation language by structure sharing and corresp onds to the use of pronouns and some forms of ellipsis in discourse An example of this phenomenon is the representation of intersentential pronominal reference to scop ed terms e g Every apartment had a dishwasher In some of them it had just b een installed Every chess set comes with a spare pawn It is tap ed to the top of the b ox examples from The structures that are b eing shared in these sentences are the variables corresp onding to the italicized noun phrases Logical representations can only mo del this sharing by combining multiple sentences of natural language into one sentence of logic This metho d is unnatural for at least two reasons First when several sentences must b e combined into one sentence the resulting logical sentence as a conjunction of several p otentially disparate sentences is overly complex Second this approach is counter intuitive in that a language user can re articulate the original sentences that heshe represents This argues for some form of separate representations of the original sentences The problem with logic in this task is that logic requires the complete sp ecication of a variable corresp onding to a noun phrase and its constraints in the scop e of some quantier This diculty is not restricted to noun phrases indeed it is frequently the case that entire sub clauses of sentences are referred to using reduced forms such as to o e g John went to the party Mary did too A languagemotivated knowledge representation formalism should mo del this sort of reference minimally by structure sharing Finally collections of logical formulas do not seem to capture the intuitive use of concepts by p eople This representation for knowledge is unstructured and disorganized What is missing is that rstorder predicate logic do es not provide any sp ecial assistance in the problem of what Brachman called knowledge structuring that is the sp ecication of the internal structure of concepts in terms of roles and interrelations b etween them and the inheritance relationships b e tween concepts Any computational theory must incorp orate knowledgestructuring mechanisms such as subsumption and inheritance of the sort supp orted in framebased and semanticnetwork based systems For example a taxonomy provides links that relate more general concepts to more sp ecic concepts This allows information ab out more sp ecic concepts to b e asso ciated with their most general concept so information can lter down to more sp ecic concepts in the taxon omy via inheritance More general concepts in such a taxonomy subsume more sp ecic concepts with the subsumee inheriting information from its subsumers For atomic concepts subsumption relations b etween concepts are sp ecied by the links of the taxonomy A clear example of sub sumption in natural language is the use of descriptions such as person that has children subsuming person that has a son If one were told People that have children are happy then it follows that People that have a son are happy The intuitive idea is that more general descriptions should subsume more sp ecic descriptions of the same sort which in turn inherit attributes from their more general subsumers We have presented some general arguments for considering the use of a more natural with resp ect to language logic for the representation of natural language sentences We have also presented some characteristics of natural language that a knowledge representation and reasoning system should supp ort In the remainder of this exp osition we will clarify the motivations for this work with sp ecic examples present an alternative representation for simple unstructured variables and reify some asp ects of the logic of these variables Structured Variables We are attempting to represent variables as a bundle of constraints and a binding structure quantier We term these bundles structured variables b ecause variables in this scheme are nonatomic terms The implemented language of representation is a semantic network rep resentation system called ANALOG A NAtural LOGic which is a descendant of SNePS Figure gives a case frame prop osed for the representation of variables in ANALOG The shaded no de lab elled V is the structured variable The restrictions on the variable are expressed by no des R R Scoping of existential structured variables with resp ect to universal structured 1 k SYNTAX If V V V n are distinct variable no des and if R R k are prop o 1 n 1 k a sition no des and all the R dominate V then i Vn Depends Quantifier V R 1 Depends V 1 Quantifier Rk is a network actually a class of networks and V is a structured variable no de SEMANTICS b V is an arbitrary quantierconstrained or constrained individual dep endent V V such that all the restriction prop ositions R R hold for on 1 n 1 k that arbitrary