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.
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I wish to thank Anil Gupta, Achille Varzi and an anonymous referee for some useful comments. The first paragraph of this work is drawn from a forthcoming review of [8] by this author and Achille Varzi.
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Orilia, F. (1995). Knowledge representation, exemplification, and the Gupta-Belnap theory of circular definitions. In: Gori, M., Soda, G. (eds) Topics in Artificial Intelligence. AI*IA 1995. Lecture Notes in Computer Science, vol 992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60437-5_18
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DOI: https://doi.org/10.1007/3-540-60437-5_18
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