An algebraic semantics for possibilistic finite-valued Łukasiewicz logic

Abstract

In this paper we present an axiomatization for the many-valued modal logic semantically defined by Łn-valued possibilistic frames. We provide an algebraic semantics for this logic that generalizes pseudomonadic Boolean algebras (the case when n=2). Consequently, we obtain that the famous modal axioms KD45 are no longer appropriate to model possibilistic systems when the systems are also many-valued. In the first part of the paper, we work in the more general setting of arbitrary commutative bounded residuated lattices, paving the way for future research for other non-classical possibilistic modal systems.