Epistemic Logic for AI and Computer Science
Epistemic Logic for AI and Computer Science
Reasoning About Knowledge
Dealing with logical omniscience
TARK '07 Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge
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We present a new logic-based approach to the reasoning about knowledge which is independent of possible worlds semantics. $${\in_K}$$ (Epsilon-K) is a non-Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom K i 驴 驴 驴 and some minimal conditions concerning common knowledge in a group. Knowledge is explicit and all forms of the logical omniscience problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc. can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between $${\in_K}$$ and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self-referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic "paradoxes" can be solved in $${\in_K}$$ . Every specific $${\in_K}$$ -logic is defined as a certain extension of some underlying classical abstract logic.