Possible world semantics and autoepistemic reasoning

Abstract

The possible world semantics of modal logic has been employed to study the nonmonotonic reasoning formalism, Moore's autoepistemic logic. Only Kripke structure, which is also known as a standard model, has been used to represent the autoepistemic expansions of modal theories. Here we argue that the mode of autoepistemic reasoning, which is formalized by autoepistemic logic, is not necessarily associated with a standard model. Another model of the possible world semantics, the minimal model, is helpful in knowledge representation and belief reasoning. In particular, the minimal model can be used as a structure to represent all the autoepistemic expansions of a modal theory. We extend the minimal model with standard model to deal with both knowledge and belief and introduce a null value called unknown to provide a refined model for knowledge and belief. We also present a notion of epistemic base of basic sentences to identify the possible worlds in a minimal model. By reformulating Moore's autoepistemic logic with respect to epistemic base, some reasonable modal theories that do not have any autoepistemic expansion will have generalized autoepistemic expansions.