Technical Report CS0593

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
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.
CopyrightThe above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information

Remark: Any link to this technical report should be to this page (, rather than to the URL of the PDF files directly. The latter URLs may change without notice.

To the list of the CS technical reports of 1989
To the main CS technical reports page

Computer science department, Technion