Minimal knowledge problem: A new approach

In this paper we propose a new logic of minimal knowledge. Our approach falls into the general scheme of Shoham's preference semantics. It stems from an earlier work on logics of minimal knowledge by Halpern and Moses, Lin and Shoham, and Lifschitz. The novelty of our work is in a procedure for minimizing knowledge which we propose in this paper, and which is different from earlier proposals. We show that our logic preserves most desirable properties of earlier formalisms and at the same time avoids some of their drawbacks. In addition to a semantic definition of our system, we provide its equivalent syntactic characterization which relates our logic with the nonmonotonic modal logic S4F and allows us to use in our investigations standard modal logic techniques.