Hannula, Miika - Validity and Entailment in Modal and Propositional Dependence Logics

lmcs:4215 - Logical Methods in Computer Science, April 26, 2019, Volume 15, Issue 2
Validity and Entailment in Modal and Propositional Dependence Logics

Authors: Hannula, Miika

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.


Source : oai:arXiv.org:1608.04301
Volume: Volume 15, Issue 2
Published on: April 26, 2019
Submitted on: January 17, 2018
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic,F.4.1


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