Canonical models and the complexity of modal team logic

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Lück, M.: Canonical models and the complexity of modal team logic. In: Leibniz International Proceedings in Informatics, LIPIcs 119 (2018), 30. DOI: https://doi.org/10.4230/LIPIcs.CSL.2018.30

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We study modal team logic MTL, the team-semantical extension of classical modal logic closed under Boolean negation. Its fragments, such as modal dependence, independence, and inclusion logic, are well-understood. However, due to the unrestricted Boolean negation, the satisfiability problem of full MTL has been notoriously resistant to a complexity theoretical classification. In our approach, we adapt the notion of canonical models for team semantics. By construction of such a model, we reduce the satisfiability problem of MTL to simple model checking. Afterwards, we show that this method is optimal in the sense that MTL-formulas can efficiently enforce canonicity. Furthermore, to capture these results in terms of computational complexity, we introduce a non-elementary complexity class, TOWER(poly), and prove that the satisfiability and validity problem of MTL are complete for it. We also show that the fragments of MTL with bounded modal depth are complete for the levels of the elementary hierarchy (with polynomially many alternations).
License of this version: CC BY 4.0 Unported
Document Type: article
Publishing status: publishedVersion
Issue Date: 2018
Appears in Collections:Fakultät für Elektrotechnik und Informatik

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1 image of flag of Germany Germany 44 93.62%
2 image of flag of United States United States 1 2.13%
3 image of flag of United Kingdom United Kingdom 1 2.13%
4 image of flag of Canada Canada 1 2.13%

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