We study the complexity of predicate logics based on team semantics. We show that the satisfiability problems of two-variable independence logic and inclusion logic are both NEXPTIME-complete. Furthermore, we show that the validity problem of two-variable dependence logic is undecidable, thereby solving an open problem from the team semantics literature. We also briefly analyse the complexity of the Bernays-Schoenfinkel-Ramsey prefix classes of dependence logic.
@InProceedings{kontinen_et_al:LIPIcs.MFCS.2016.60, author = {Kontinen, Juha and Kuusisto, Antti and Virtema, Jonni}, title = {{Decidability of Predicate Logics with Team Semantics}}, booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)}, pages = {60:1--60:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-016-3}, ISSN = {1868-8969}, year = {2016}, volume = {58}, editor = {Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.60}, URN = {urn:nbn:de:0030-drops-64726}, doi = {10.4230/LIPIcs.MFCS.2016.60}, annote = {Keywords: team semantics, dependence logic, complexity, two-variable logic} }
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