Axiomatizations of team logics |
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Authors: | Martin Lück |
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Institution: | Leibniz Universität Hannover, Institut für Theoretische Informatik, Appelstraße 4, 30167 Hannover, Germany |
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Abstract: | In a modular approach, we lift Hilbert-style proof systems for propositional, modal and first-order logic to generalized systems for their respective team-based extensions. We obtain sound and complete axiomatizations for the dependence-free fragment FO(~) of Väänänen's first-order team logic TL, for propositional team logic PTL, quantified propositional team logic QPTL, modal team logic MTL, and for the corresponding logics of dependence, independence, inclusion and exclusion.As a crucial step in the completeness proof, we show that the above logics admit, in a particular sense, a semantics-preserving elimination of modalities and quantifiers from formulas. |
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Keywords: | 03B45 03B60 03F03 Dependence logic Team logic Axiomatization Completeness Propositional team logic Modal team logic |
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