Fuzzy autoepistemic logic and its relation to fuzzy answer set programming

Abstract

Autoepistemic logic is an important formalism for nonmonotonic reasoning. It extends propositional logic by offering the ability to reason about an agent's (lack of) beliefs. Moreover, it is well known to generalize the stable model semantics of answer set programming. Fuzzy logics on the other hand are multi-valued logics, which allow to model the intensity to which properties are satisfied. We combine these ideas to a fuzzy autoepistemic logic which can be used to reason about one's beliefs in the degrees to which properties are satisfied. We show that many properties from classical autoepistemic logic, e.g. the equivalence between autoepistemic models and stable expansions, remain valid under this generalization. In this paper, we consider a version of fuzzy answer set programming and show that its answer sets can be equivalently described as models in fuzzy autoepistemic logic. We also define a fuzzy logic of minimal belief and negation-as-failure and use this as a tool to show that fuzzy autoepistemic logic generalizes fuzzy answer set programming.