Algebraic semantics of many-valued modal logics

MANUELA BUSANICHE

Denver

Congreso; Spring Western Virtual Sectional Meeting, Special Session on Algebraic Logic; 2022

American Mathematical Society and University of Denver

Historically, modal logics and many-valued logics have run by separated roads, because different semantics are usually used to study these systems: relational semantics for modal logics and algebraic semantics for the case of many-valued systems. It?s crucial to choose one of these approaches when dealing with many-valued modal logics. Although the relational approach is the one most considered, many auhors have recently opted for an algebraic approach to these systems.For each natural number n , let Ln be the MV-chain with n elements. Our goal is to present an algebraic semantics for the minimum many-valued modal logic over Ln and an algebraic semantics for the possilistic modal system over Ln . We analize complex algebras of these quasivarieties and show the relationship with the corresponding Kripke semantics and possibilistic semantics.