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.
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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Bealer G., Quality and Concept, London:Oxford University press, 1982.
Belnap N., “Gupta's Rule of Revision Theory of Truth,” Journal of Philosophical Logic 11 (1982), pp. 103–116.
Castañeda H.-N., “Thinking and The Structure of the World”, Philosophia 4 (1974), pp. 3–40.
Cocchiarella N., “Frege, Russell, and Logicism: a Logical Reconstruction,” in Haaparanta L. and Hintikka J. (eds.), Frege Synthesized, Dordrecht, The Netherlands: Reidel, 1986.
Fagin R. and Halpern J. Y., “Belief, Awareness, and Limited Reasoning,” Artificial Intelligence 34 (1988), pp. 39–76.
Geach P. T., “Intentional Identity,” The Journal of Philosophy 20 (1967), pp. 627–632.
Gupta A., “Truth and Paradox,” Journal of Philosophical Logic 11 (1982), pp. 1–60.
Gupta A. and Belnap N., The Revision Theory of Truth, Cambridge, Mass.: The MIT Press, 1993.
Haas A. R., “Sentential Semantics for Propositional Attitudes,” Computational Linguistics 16 (1990), pp. 213–233.
Hadley R. F., “A Sense-Based, Process Model of Belief,” Minds and Machines 1 (1991), pp. 279–320.
Herzberger H. G., “Notes on Naive Semantics,” Journal of Philosophical Logic 11 (1982), pp. 61–102.
Konolige K., A Deduction Model of Belief, London: Pitman, 1986.
Montague R., Formal Philosophy (Thomason R., ed.), New Haven, CN: Yale University Press, 1974.
Orilia F., “Belief representation in a Type-free Doxastic Logic,” Minds and Machines 4 (1994), pp. 163–203.
Orilia F., “Guise Theory, Property Theory, and Castañeda's philosophical Methodology,” forthcoming.
Rapaport W., “Logical Foundations for Belief representation,” Cognitive Science 10 (1986), pp. 371–422.
Russell B., “On Denoting,” Mind 59 (1905), pp. 479–493.
Shapiro S. and Rapaport W., “SNePS considered as a Fully Intensional Prepositional Semantic Network,” in Cereone N.and McCall G. (eds.), The Knowledge Frontier, Berlin: Springer Verlag, 1987, pp. 262–315.
Smullyan R., First-Order Logic, Berlin: Springer-Verlag, 1968.
Turner R., “A Theory of Properties,” Journal of Symbolic Logic 52 (1987), pp. 455–472.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-60437-5_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60437-2
Online ISBN: 978-3-540-47468-5
eBook Packages: Springer Book Archive