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Abstract : |
Contexts were first suggested in McCarthy's Turing Award Paper, (McCarthy 1987), as a possible solution to the problem of generality in AI. McCarthy's concern with the existing AI systems has been that they can reason only about some particular, predetermined task. When faced with slightly different circumstances they need to be completely rewritten. In other words, AI systems lack generality. Cyc (Guha & Lenat 1990), a large common-sense knowledge-base currently being developed at MCC, is one example of where contexts have already been put to use in attempt to solve the problem of generality. Because of the complexity of the problem of generality, it has been speculated that any reasoning system which would be able to solve this problem would itself be computationally unacceptable. The purpose of this paper is to show that propositional contextual reasoning is decidable. Propositional logic of context extends classical propositional logic with a new modality, ist(c; OE), used to express that the sentence, OE, is true in the context c. We first give a short sketch the syntax and the semantics of the language of context, as proposed in (McCarthy 1993) and formalized in (Buvac & Mason 1993). To define the syntax, we begin with two distinct countable sets: K the set of all contexts, and P the set of propositional atoms. The set, W, of well-formed formulas is built up from the propositional atoms, P, using the usual propositional connectives (negation and implication) together with the ist modality: W = P [ (:W) [ (W!W) [ ist(K; W): To define the semantics we first need to introduce some mathematical notation. If X is a set then P(X) is the set of subsets of X. X, |
