Coalgebraic completeness-via-canonicity for distributive substructural logics

TL;DR

This paper establishes strong completeness results for various substructural logics using a coalgebraic approach, linking resource semantics with logical syntax in a modular framework.

Contribution

It introduces a coalgebraic method for proving completeness-via-canonicity for substructural logics, enabling a unified and extensible analysis.

Findings

Proves strong completeness for multiple substructural logics.

Develops a modular coalgebraic framework for semantics and syntax.

Facilitates future extensions and systematic study of resource models.

Abstract

We prove strong completeness of a range of substructural logics with respect to a natural poset-based relational semantics using a coalgebraic version of completeness-via-canonicity. By formalizing the problem in the language of coalgebraic logics, we develop a modular theory which covers a wide variety of different logics under a single framework, and lends itself to further extensions. Moreover, we believe that the coalgebraic framework provides a systematic and principled way to study the relationship between resource models on the semantics side, and substructural logics on the syntactic side.