Propositional union closed team logics

TL;DR

This paper investigates propositional team logics closed under unions, establishing their expressive completeness, developing natural deduction systems, and exploring properties like locality and interpolation.

Contribution

It proves the expressive completeness of union-closed propositional team logics and introduces sound and complete natural deduction systems.

Findings

All studied logics are expressively complete.

Sound and complete natural deduction systems are developed.

Discussion of locality and interpolation properties.

Abstract

In this paper, we study several propositional team logics that are closed under unions, including propositional inclusion logic. We prove that all these logics are expressively complete, and we introduce sound and complete systems of natural deduction for these logics. We also discuss the locality property and its connection with interpolation in these logics.