Relating fuzzy autoepistemic logic to fuzzy modal logics of belief
Marjon Blondeel, Tommaso Flaminio, Lluı́s Godo, Martine De Cock · DIGITAL.CSIC (Spanish National Research Council (CSIC)) · 2013
Fuzzy autoepistemic logic is a generalization of autoepistemic logic, an important formalism for nonmonotonic reasoning originally intended to model an ideally rational agent reflecting upon his own beliefs, and allows to represent an agent's rational beliefs on partially true gradable propositions.Fuzzy autoepistemic logic has recently been shown to be a suitable logical framework for fuzzy answer set programming, generalizing a classical result.On the other hand, there are well-known links between autoepistemic logic and several nonmonotonic modal logic systems.In this paper, we introduce generalizations of the main classical propositional modal logics of belief based on finitelyvalued Łukasiewicz calculus.We obtain completeness with respect to appropriate Kripke-style semantics and we prove NP-completeness for the satisfiability problem.Then we show how fuzzy autoepistemic logic can be approached in these manyvalued modal settings.In particular we obtain a generalization of Levesque's result on the relationship between stable expansions, belief sets and "only knowing" operators.