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Sasa Buvac

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AAAI Conference 1996 Conference Paper

Quantificational Logic of Context

Sasa Buvac

In this paper we extend the Propositional Logic of Context, (Buvac & Mason 1993; BuvaE, BuvaE, & Mason 1995), to the quantificational (predicate calculus) case. This extension is important in the declarative representation of knowledge for two reasons. Firstly, since contexts are objects in the semantics which can be denoted by terms in the language and which can be quantified over, the extension enables us to express arbitrary first-order properties of contexts. Secondly, since the extended language is no longer only propositional, we can express that an arbitrary predicate calculus formula is true in a context. The paper describes the syntax and the semantics of a quantificational language of context, gives a Hilbert style formal system, and outlines a proof of the system’ s completeness.

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AAAI Conference 1993 Conference Paper

Propositional Logic of Context

Sasa Buvac

In this paper we investigate the simple logical properties of contexts. We describe both the syntax and semantics of a general propositional language of context, and give a Hilbert style proof system for this language. A propositional logic of context extends classical propositional logic in two ways. Firstly, a new modality, ist(K, 4), is introduced. It is used to express that the sentence, 4, holds in the context 6. Secondly, each context has its own vocabulary, i. e. a set of propositional atoms which are defined or meaningful in that context. The main results of this paper are the soundness and completeness of this Hilbert style proof system. We also provide soundness and completeness results (i. e. correspondence theory) for various extensions of the general system.

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