On Possibilistic Modal Logics Defined Over MTL-Chains

TLDR: In this article, a modal logic over a finitely-valued Łukasiewicz logic is defined to capture possibilistic reasoning, and a completeness proof is provided.

Abstract: In this chapter we revisit a 1994 chapter by Hajek et al. where a modal logic over a finitely-valued Łukasiewicz logic is defined to capture possibilistic reasoning. In this chapter we go further in two aspects: first, we generalize the approach in the sense of considering modal logics over an arbitrary finite MTL-chain, and second, we consider a different possibilistic semantics for the necessity and possibility modal operators. The main result is a completeness proof that exploits similar techniques to the ones involved in Hajek et al.’s previous work.