Modal definability based on {\L}ukasiewicz validity relations

TL;DR

This paper explores modal definability within { ext{ extL}}ukasiewicz finitely valued-logics, establishing an analogue of the Goldblatt-Thomason theorem for these modal extensions and their relational structures.

Contribution

It introduces two notions of definability for classes of relational structures based on modal { ext{ extL}}ukasiewicz logics and proves their equivalence to a Goldblatt-Thomason type theorem.

Findings

Established an analogue of the Goldblatt-Thomason theorem for { ext{ extL}}ukasiewicz modal logics.

Defined two notions of definability for classes of relational structures.

Proved the equivalence of these notions to a modal definability theorem.

Abstract

We study two notions of definability for classes of relational structures based on modal extensions of {\L}ukasiewicz finitely valued-logics. The main results of the paper are the equivalent of the Goldblatt - Thomason theorem for these notions of definability.