Ground Nonmonotonic Modal Logics

In this paper we address ground logics, a family of nonmonotonic modal logics, and their usage in knowledge representation. In such a setting non-modal sentences are used to represent the knowledge of an agent about the world, while an epistemic operator provides the agent with autoepistemic or introspective knowledge. Ground logics are based on the idea of characterizing the knowledge of the agent by allowing it to make nonmonotonic assumptions only with respect to the knowledge about the world, i.e. expressed by nonmodal formulae. They are characterized by a fix-point equation which determines the set of formulae derivable from the agent’s initial knowledge and which can be applied to different normal modal systems to obtain a variety of nonmonotonic modal logics. In the paper we address the semantical, computational and epistemological properties of ground logics. We provide a semantic characterization of ground logics by defining a preference relation on possible-world models based on the minimization of the knowledge expressed by nonmodal formulae. We analyze the computational complexity of reasoning in ground logics, providing both a lower bound through a reduction from quantified boolean formulae and an upper bound through an algorithm for computing logical entailment. We discuss the representational features of ground logics, in particular defaults, and provide a thorough comparison with McDermott and Doyle’s logics.