All I Know: An Abridged Report

Hector J. Levesque

Current approaches to formalizing non-monotonic reasoning using logics of belief require new metalogical properties over sets of sentences to be defined. This research attempts to show how some of these patterns of reasoning can be captured using only the classical notions of logic (satisfiability, validity, implication). This is done by extending a logic of belief so that it is possible to say that only a certain proposition (or finite set of them) is believed. This research also extends previous approaches to handle quantifiers and equality, provides a semantic account of certain types of non-monotonicity, and through a simple proof theory, allows formal derivations to be generated.

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