Modality for Free: Notes on Adding the Tarskian M\"{o}glichkeit to Substructural Logics

TL;DR

This paper explores how Tarskian modal operators can be integrated into substructural logics like MALL and compares it with the modal logic K, offering insights into their derivable modal formulas.

Contribution

It introduces a method for adding Tarskian modalities to substructural logics and compares their modal formula derivations with those in modal logic K.

Findings

Derived modal formulas in MALL with Tarskian modalities

Comparison of modal derivations between substructural logic and modal logic K

Insights into the expressive differences of these systems

Abstract

We briefly examine the modal formulae that can be derived in Multiplicative Additive Linear Logic (MALL) and some extensions by using Tarksi's extensional modal operators. We also breifly compare this with a substructural form of the modal logic K.