Validity and Entailment in Modal and Propositional Dependence Logics

TL;DR

This paper classifies the complexity of validity and entailment in modal and propositional dependence logics, revealing that validity in modal dependence logic is NEXPTIME-complete, correcting previous conjectures.

Contribution

It provides the first comprehensive complexity classification for validity and entailment in various dependence logics, including a key result on modal dependence logic validity.

Findings

Validity in modal dependence logic is NEXPTIME-complete.

The complexity of entailment varies across different dependence logics.

Refutes earlier conjectures about higher complexity for validity.

Abstract

The computational properties of modal and propositional dependence logics have been extensively studied over the past few years, starting from a result by Sevenster showing NEXPTIME-completeness of the satisfiability problem for modal dependence logic. Thus far, however, the validity and entailment properties of these logics have remained mostly unaddressed. This paper provides a comprehensive classification of the complexity of validity and entailment in various modal and propositional dependence logics. The logics examined are obtained by extending the standard modal and propositional logics with notions of dependence, independence, and inclusion in the team semantics context. In particular, we address the question of the complexity of validity in modal dependence logic. By showing that it is NEXPTIME-complete we refute an earlier conjecture proposing a higher complexity for the problem.