There are (other) ways to negate in propositional team semantics

TL;DR

This paper investigates propositional team semantics with full intuitionistic negation, showing it doesn't complicate axiomatization and establishing expressive completeness for extended propositional logic with dependence and inclusion atoms.

Contribution

It demonstrates that full intuitionistic negation can be incorporated without complicating axiomatization and proves expressive completeness of propositional logic with dependence and inclusion atoms.

Findings

Full intuitionistic negation does not complicate axiomatization.

Expressive completeness of propositional logic with dependence and inclusion atoms.

Revealed how complemented properties are expressed without negation.

Abstract

The languages of logics based on team semantics typically only allow atomic negation or restricted negation. In this paper, we explore propositional team-based logics with full (intuitionistic) negation. We demonstrate that including full intutionistic negation does not complicate the axiomatization of propositional team-based logics with the downward closure property. We also review known expressive completeness results for these logics, highlighting how relevant complemented properties are expressed in propositional dependence logic without directly using negation. Building on these insights, we also prove a new result: propositional logic extended with both dependence and inclusion atoms is expressively complete.