Validity and entailment in modal and propositional dependence logics

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
Article number24
JournalLogical Methods in Computer Science
Volume15
Issue number2
Pages (from-to)4:1–4:24
Number of pages24
ISSN1860-5974
DOIs
Publication statusPublished - 26 Apr 2019
MoE publication typeA1 Journal article-refereed

Fields of Science

  • dependence logic
  • inclusion logic
  • independenc logic
  • modal logic
  • propositional logic
  • complexity
  • validity
  • entailment
  • COMPLEXITY
  • INCLUSION
  • 113 Computer and information sciences

Cite this

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title = "Validity and entailment in modal and propositional dependence logics",
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.",
keywords = "dependence logic, inclusion logic, independenc logic, modal logic, propositional logic, complexity, validity, entailment, COMPLEXITY, INCLUSION, 113 Computer and information sciences",
author = "Miika Hannula",
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Validity and entailment in modal and propositional dependence logics. / Hannula, Miika.

In: Logical Methods in Computer Science, Vol. 15, No. 2, 24, 26.04.2019, p. 4:1–4:24.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Validity and entailment in modal and propositional dependence logics

AU - Hannula, Miika

PY - 2019/4/26

Y1 - 2019/4/26

N2 - 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.

AB - 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.

KW - dependence logic

KW - inclusion logic

KW - independenc logic

KW - modal logic

KW - propositional logic

KW - complexity

KW - validity

KW - entailment

KW - COMPLEXITY

KW - INCLUSION

KW - 113 Computer and information sciences

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