When Logic meets Algebra: interpolation in Substructural Logics

Abstract: Substructural logics form a broad family of non-classical logics that includes many-valued, intuitionistic, paraconsistent, and relevance logics just to name a few. These systems are designed to model reasoning in different settings, such as those involving incomplete, partial, or inconsistent information.

The algebraic framework for the study of these logics is the class residuated lattices, highlighting how algebraic methods provide powerful tools for investigating their logical properties. In particular, we will focus on the interpolation property, exploring its algebraic counterpart, the amalgamation property, and discussing how algebraic techniques can be used to study it. In particular, we will show that the monoidal t-norm based logic, MTL for short, introduced by Esteva and Godo fails to have the interpolation property.

logic in computer sciencecomputer science theorylogic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic