Knowledge representation, exemplification, and the Gupta-Belnap theory of circular definitions

Abstract

Gupta's and Belnap's revision theory of circular definitions (RTD) provides a general technique for specifying circular definitions in a way that at worst gives rise to some “vacuous” uses of definienda, but never to contradiction. This is a first step in applying RTD to the problem of constructing a type-free theory of properties, relations and propositions (in short, PRP's). To this end, exemplification is viewed as a circular concept analyzed in terms of RTD. This yields a formal semantics system, P*, wherein the generality of lambda-conversion is circumscribed so as to avoid, e.g., Russell's paradox. The construction of P* is motivated by showing how it can provide a foundation for a knowledge representation system capable of dealing with belief (or more generally intensional) contexts and with inferences involving PRP's in subject position.