From: AAAI Technical Report FS-95-02. Compilation copyright © 1995, AAAI (www.aaai.org). All rights reserved. Syntax, Semantics, and Pragmatics of Contexts John F. Sowa philosophy andComputers and Cognitive Science State University of NewYork at Binghamton Abstract. The notion of context is indispensable in discussions of meaning, but the word context has often been used in conflicting senses. In logic, the first representation of context as a formal object was by the philosopher C. S. Peirce; but for nearly eighty years, his treatment was unknownoutside a small group of Peirce aficionados. In the early 1980s, three newtheories included related notions of context: Kamp’sdiscourse representation theory; Barwiseand Perry’s situation semantics; and Sowa’sconceptual graphs, which explicitly introduced Peirce’s approach to the AI community. More recently, John McCarthyand his students have begunto use a closely related notion of context as a basis for organizing and partitioning knowledgebases. Each of the theories has distinctive, but complementaryideas that can enrich the others, but the relationships betweenthem are far from clear. This paper analyzes the semantic foundations of these theories and showshow McCarthy’s ist(c,p) predicate can be interpreted in terms of the semantic notions underlying the others. 1. Theoriesof Contexts In the AI literature, the term context has been Someof the confusionabout contexts results applied to a profusion of ideas that have not been from an ambiguity in the English word. Die- clearly distingafished. Someof them concern the tionaries list two major senses of the word syntactic representation of contexts; others refer context:. to the semanticrelationship of a linguistic context ¯ The basic meaningis a section of the linguis- to a physical situation; and still others introduce tic text or discourse that surrounds some pragmatic notions concerning the purpose or use wordor phrase of interest. of a context in various applications. Each of these major areas can be subdivided further. ¯ The derived meaz~gis a nonlingnistic situ- Syntactically, there are three distinct aspects of ation, environment, domain, setting, back- context: ground, or milieu that includes someentity, subject, or topic of interest. 1. A mechanismfor grouping, associating, or packaging information that can be named Thesetwo informal senses suggest intuitive crite- and referencedas a single unit. ria for distinguishing the various functions of contexts: 2. The contents of that package, which have ¯ Syntax. The syntacticfunction of context is been called anything from quoted formula to to group, delimit, or package "a section of microtheory. linguistic text." Formally, a context behaves 3. The permissible operations on the informa- like the QUOTEoperator in Lisp together tion in the package and the constraints on with the parentheses that delimit the portion importing and exporting information into of text that is quoted. and out of a package. ¯ Semantics. The quoted text of a context re- All three of these notions represent syntactic fers to something, which may be a physical mechani.mls for representing and manipulating entity or situation, a mathematical con- logical formulas without any consideration of struction, or someother expression in a na- their relationship to the real world, a possible tural or artificial language. world, or somemodel of the world. Muchof the ¯ Pragmatics. The word interest, which occurs controversy about contexts results from the lack in both senses of the English definition, sug- of a formalsemantics that relates these operations gests somereason or purpose for distinguish- to a Tarski-style model. Even an informal se- ing "a section of linguistic text" or "a mantics that displays the intuitive meaning of nonlinguistie situation." That purpose con- contexts in terms of real-world objects and situ- stitutes the pragmatiesor the reason whythe ations would be helpful as a guide to further text is being quoted. In Lisp, the QUOTE analysis and formaliTation. operator blocks the execution of the standard Lisp interpreter to allow nonstandard oper- 85 ations to be performed for someother pur- ated with c. The predicate ~s-in represents the pose. In logic, a quote blocks the standard syntactic relationship of c to p; and the predicates rules of inference and allows the definition of refers-to and describes represent the semanticre- newrules for somespecial purpose. lationships of c and p to the external entity x. As this analysis indicates, the notion of context McCarthy, Guha, and Buva~ have primarily is intimately connectedwith a complexof related considered the syntactic operations associated ideas. Muchof the confusion results from which with the ~s-in componentof the ist predicate. To of them happens to be called a context:, some justify those operations, the semantics of the people apply the word to the package; and others refers-to and describes componentsmust also be to the information contained in the package, to addressed. the thing that the information is about, or to the Muchof the controversy about contexts re- possible uses of either the information or the suits from the abundanceof notation and termi- thing. The ideas themselves may be compatible, nologyin different theories, their application to but they must be carefully distinguished and diverse phenomena, and the lack of commlmi- sorted out. cation betweenthe different schools of thought. These intuitive criteria provide a basis for The purpose of this paper is to emphasize the analyzing John McCarthy’s (1993) "Notes underlying similarities and to promote cross- Formalizing Context" and relating the ideas to fertilization of ideas. Thefollowing five theories the other theories. McCarthy’sbasic notation is will be considered: the predicate ist(c,p), which may be read "the 1. Charles Sanders Peirce (1885) invented the propositionp is true in context c." In his disser- modernalgebraic notation for predicate cal- tation written under McCarthy’sdirection, R. V. culus; but a dozen years later, he developed Guha (1991) applied McCarthy’sapproach to the an alternate notation, which he called problem of partitioning a large, monolithic existential graphs (Roberts 1973). Although knowledgebase into a collection of smaller, more Peirce’s algebra and graphs had equivalent modular microtheories. Guha implemented the expressive power,the graphic structure served microtheories in the Cyc system (I.gnat & Guha as a heuristic aid that led himto explore op- 1990), in which they have becomea fundamental erations and applications that were over- mechanism for organizing and stnmturing a looked by logicians who used only the knowledge base. McCarthy and Buva~ (1994) algebraic notation. In particular, Peirce’s have also applied contexts and the /st predicate graphic notation for contexts was isomorphic to the analysis and representation of natural lan- to the discourse representation structures guagediscourse. (DRSs) invented by Hans Kampeighty years Although McCarthy, Guha, and Buva~ have later. His rules of inference were based on shownthat the /st predicate can be a powerful operations of iterating and deiterating infor- tool for building knowledgebases and analyzing mation to and from contexts in a way that discourse, they have not clearly distinguished the resembles John McCarthy’slifting rules. syntax of contexts and propositions from their 2. Hans Kamp(1981) developed discourse rep- semantic relationship to some domain of dis- resentation theory (DRT)to express the log- course. In fact, the ist predicate itself mixesthe ical constraints on anaphofic references in syntactic notion of containment(~s-in) with the natural language. Because of the difficulty semanticnotion of truth (/s-true-of). To clarify of expressing those constraints in the alge- these relationships, it maybe helpful to analyze braic notation for logic, Kampintroduced the the ist predicate as a conjunction of three more graphic DRSnotation, which allowed a tim- primitive predicates, ~s-in, refers-to, and pler formulation of his rules. Si~iBcantly, describes: the nested contexts in Kamp’s DRSs are ist(c,p)-- (~3x:Entity)(is-in(c,p) isomorphicto the nestof contexts in Peirce’s refers-to(c,x)^ describes(x,p)). EGs, even though Kamp had no previous knowledgeof them. Kampdeserves credit for Accordingto this analysis, the proposition p is discovering the constraints on anaphora in true in context e ff and only if there exists some DRT, but DRSsand EGs are equally suit- entity x such that p is in c, c refers to x, and p able for expressingthose constraints. describes x. The formula distinguishes the ab- stract context c from somenonlingulstic entity x, 3. Jon Barwise and John Perry (1983) devel- which represents the "situation, environment, oped situation semantics as a theory of domain, setting, background, or milieu" assoei- meaning in natural langq_~age. Unlike 86 Montague’s approach (1975), which related 5. John McCarthyis one of the founding fathers the semanticsof languageto potentially infi- of AI, whose collected work (McCarthy nite models of the real world or possible 1990) has frequently inspired and sometimes worlds, Barwiseand Perry adopted finite sit- revolutionized the application of logic to uations as their basis. Each situation is a knowledge representation. His work on bounded region of space-time containing context, although published later than the physical objects and processes, as well as previous four approaches, has grownout of other situations. A great deal