Syntax, Semantics, and Pragmatics of Contexts

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 unknown outside a small group of Peirce aficionados. In the early 1980s, three new theories included related notions of context: Kamp’s discourse representation theory; Barwise and Perry’s situation semantics; and Sowa’s conceptual graphs, which explicitly introduced Peirce’s approach to the AI community. More recently, John McCarthy and his students have begun to use a closely related notion of context as a basis for organizing and partitioning knowledge bases. Each of the theories has distinctive, but complementary ideas that can enrich the others, but the relationships between them are far from clear. This paper analyzes the semantic foundations of these theories and shows how McCarthy’s ist(c,p) predicate can be interpreted in terms of the semantic notions underlying the others. 1. Theories of Contexts In the AI literature, the term context has been applied to a profusion of ideas that have not been clearly distingafished. Some of them concern the syntactic representation of contexts; others refer to the semantic relationship of a linguistic context to a physical situation; and still others introduce pragmatic notions concerning the purpose or use of a context in various applications. Each of these major areas can be subdivided further. Syntactically, there are three distinct aspects of context: 1. A mechanism for grouping, associating, or packaging information that can be named and referenced as a single unit. 2. The contents of that package, which have been called anything from quoted formula to microtheory. 3. The permissible operations on the information in the package and the constraints on importing and exporting information into and out of a package. All three of these notions represent syntactic mechani.mls for representing and manipulating logical formulas without any consideration of their relationship to the real world, a possible world, or some model of the world. Much of the controversy about contexts results from the lack of a formal semantics that relates these operations to a Tarski-style model. Even an informal semantics that displays the intuitive meaning of contexts in terms of real-world objects and situations would be helpful as a guide to further analysis and formaliTation. Some of the confusion about contexts results from an ambiguity in the English word. Dietionaries list two major senses of the word