Relative knowledge and belief: SKL preferred model frames

Abstract

The partial SKL**-logic, defined by P. Doherty in A Three-Valued Approach to Non-Monotonic Reasoning (1990) is based upon the three valued logic of S.C. Kleene. The logic of Doherty provides a flexible framework in defining, we hope in a suitable way, epistemic notions of Knowledge, Belief, Aposteriori Knowledge, and Potential Knowledge, together with some relations between them. The underlying ideas in our definitions of knowledge and belief are the same as those using the semantics of possible worlds proposed by J. Hintikka. Our definitions are constructive and recursive instead. Using the undefined truth value from SKL**, it allows a not known or not believed status for a sentence.