Abstract
We examine a new logical system, capturing the intuition of ‘most’ by means of generalised quantifiers over ultrafilters, with the aim of providing a basis for generic reasoning. This monotonic ultrafilter logic is a conservative extension of classical first-order logic, with which it shares several properties, including a simple sound and complete deductive system. For reasoning about generic objects, we introduce ‘generic’ individuals as those possessing the properties that most individuals have. We examine some properties of these ‘generic’ individuals and internalise them as generic constants, which produces conservative extensions where one can correctly reason about generic objects as intended. A many-sorted version of our ultrafilter logic is also introduced and employed to handle correctly distinct notions of ‘large’ subsets. Examples similar to ones in the literature illustrate the presentation. We also comment on some perspectives for further work: interesting connections with fuzzy logic, inductive reasoning and empirical reasoning suggest the possibility of other applications for our logic.
Work supported by FAPESP and CNPq research grants.
(on leave from Dept. of Informatics, PUC- Rio de Janeiro)
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© 1997 Springer-Verlag Berlin Heidelberg
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Carnielli, W.A., Veloso, P.A.S. (1997). Ultrafilter logic and generic reasoning. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1997. Lecture Notes in Computer Science, vol 1289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63385-5_31
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DOI: https://doi.org/10.1007/3-540-63385-5_31
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