Quantificational Logic of Context

In this paper we extend the Propositional Logic of Context, (Buvac & Mason 1993; Buvac, Buvac, & 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. Introduction Contexts first appeared in declarative AI when they were presented as a possible solution to the problem of generality in McCarthy's Turing Award Paper, (McCarthy 1987). ..