Technical Report CS0593

TR#:CS0593
Class:CS
Title: All We Believe Fails in Impossible Worlds: A Possible-World Semantics For a "Knowing At Most" Operator
Authors: S. Ben-David and Y. Gafni
PDFCS0593.pdf
Abstract: We extend the familiar possible-world semantics of modal logic by considering the 'impossible' worlds of a Kripke structure. We obtain a simple semantics for Levesque's "All I know" logic. We provide a natural proof theory and prove the expected soundness and completeness theorems. From a mathematical point of view we offer ~ natural generalization of modal logic that significantly strengthens its expressive power. Cpnsidered in the context of Knowledge Representation, such a logic is a standard monotonic logic that allows formal treatment of default reasoning.
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