Modal Dependence Logics: Axiomatizations and Model-theoretic Properties

TL;DR

This paper develops sound and complete deduction systems for modal dependence logics, explores their connection to team and single-world semantics, and interprets them as variants of intuitionistic modal logics.

Contribution

It introduces axiomatizations for modal dependence logics with intuitionistic connectives and links team semantics to single-world semantics.

Findings

Established sound and complete deduction systems.

Connected team semantics with single-world semantics.

Interpreted modal dependence logics as variants of intuitionistic modal logics.

Abstract

Modal dependence logics are modal logics defined on the basis of team semantics and have the downward closure property. In this paper, we introduce sound and complete deduction systems for the major modal dependence logics, especially those with intuitionistic connectives in their languages. We also establish a concrete connection between team semantics and single-world semantics, and show that modal dependence logics can be interpreted as variants of intuitionistic modal logics.