A Preference Semantics for Ground Nonmonotonic Modal Logics

In this paper we provide a semantic characterization of ground logics, a family of nonmonotonic modal logics obtained by means of a variant of the well known Mc Dermott and Doyle xed point equation. The term ground logics carries the idea of restricting the negative in-trospection capabilities of the reasoning agent to the objective (i.e. non modal) part of the theory. This intuition was nicely formalized for modal logic S5 by a semantic deenition based on a preference relation on Kripke models, which was obtained as the semantic counterpart to the notion of minimal knowledge initially deened by Halpern and Moses. We have then found a preference relation on Kripke models that both generalizes this notion of minimal knowledge and provides a semantic characterization for a signiicant subset of ground logics.