Propositional Logics of Dependence

TL;DR

This paper explores propositional dependence logics, establishing their expressive completeness, normal forms, and providing complete deduction systems, thereby advancing the formal understanding of dependence in propositional logic.

Contribution

It introduces and analyzes propositional dependence logics, proving their expressiveness, normal forms, and completeness of deduction systems, which are novel contributions in the field.

Findings

Propositional dependence logic is expressively complete.

These logics have disjunctive and conjunctive normal forms.

Complete deduction systems are established for these logics.

Abstract

In this paper, we study logics of dependence on the propositional level. We prove that several interesting propositional logics of dependence, including propositional dependence logic, propositional intuitionistic dependence logic as well as propositional inquisitive logic, are expressively complete and have disjunctive or conjunctive normal forms. We provide deduction systems and prove the completeness theorems for these logics.