Non-distributive logics: from semantics to meaning

TL;DR

This paper explores the semantics and conceptual understanding of non-distributive logics, emphasizing dual characterization and correspondence theory to bridge technical and intuitive perspectives.

Contribution

It advances the semantic analysis of non-distributive logics using dual characterization and unified correspondence theory, with implications for their intuitive interpretation.

Findings

Develops dual characterization results for non-distributive logics

Links semantic structures to intuitive meaning of these logics

Provides conceptual insights into non-distributive logic semantics

Abstract

We discuss an ongoing line of research in the relational (non topological) semantics of non-distributive logics. The developments we consider are technically rooted in dual characterization results and insights from unified correspondence theory. However, they also have broader, conceptual ramifications for the intuitive meaning of non-distributive logics, which we explore.