Decidability of predicate logics with team semantics

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-Sch\"onfinkel-Ramsey prefix classes of dependence logic.Comment: Extended version of a MFCS 2016 article. Changes on the earlier arXiv version: title changed, added the result on validity of two-variable dependence logic, restructurin

Dependencies Between Quantifiers Vs. Dependencies Between Variables

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Boolean Dependence Logic and Partially-Ordered Connectives

We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\alpha), where \alpha is a Boolean variable. Intuitively, with Boolean dependence atoms one can express quantification of relations, while standard dependence atoms express quantification over functions. We compare the expressive power of Boolean dependence logic to dependence logic and first-order logic enriched by partially-ordered connectives. We show that the expressive power of Boolean dependence logic and dependence logic coincide. We define natural syntactic fragments of Boolean dependence logic and show that they coincide with the corresponding fragments of first-order logic enriched by partially-ordered connectives with respect to expressive power. We then show that the fragments form a strict hierarchy.Comment: 41 page

Defining a Double Team Semantics for Generalized Quantifiers

In this brief technical report we sketch a semantics for fi rst-order logic with generalized quantifiers based on double teams. We also define the notion of a generalized atom. Such atoms can be used in order to define extensions of first-order logic with a team-based semantics. We then briefly discuss how our double team semantics relates to game semantics based approaches to extensions of first-order logic with generalized quantifiers

Defining a Double Team Semantics for Generalized Quantifiers

In this brief technical report we sketch a semantics for fi rst-order logic with generalized quantifiers based on double teams. We also define the notion of a generalized atom. Such atoms can be used in order to define extensions of first-order logic with a team-based semantics. We then briefly discuss how our double team semantics relates to game semantics based approaches to extensions of first-order logic with generalized quantifiers

On the Complexity of Team Logic and Its Two-Variable Fragment

We study the logic FO(~), the extension of first-order logic with team semantics by unrestricted Boolean negation. It was recently shown to be axiomatizable, but otherwise has not yet received much attention in questions of computational complexity. In this paper, we consider its two-variable fragment FO^2(~) and prove that its satisfiability problem is decidable, and in fact complete for the recently introduced non-elementary class TOWER(poly). Moreover, we classify the complexity of model checking of FO(~) with respect to the number of variables and the quantifier rank, and prove a dichotomy between PSPACE- and ATIME-ALT(exp, poly)-complete fragments. For the lower bounds, we propose a translation from modal team logic MTL to FO^2(~) that extends the well-known standard translation from modal logic ML to FO^2. For the upper bounds, we translate FO(~) to fragments of second-order logic with PSPACE-complete and ATIME-ALT(exp, poly)-complete model checking, respectively

On the Complexity of Team Logic and its Two-Variable Fragment

We study the logic FO(~), the extension of first-order logic with team semantics by unrestricted Boolean negation. It was recently shown axiomatizable, but otherwise has not yet received much attention in questions of computational complexity. In this paper, we consider its two-variable fragment FO2(~) and prove that its satisfiability problem is decidable, and in fact complete for the recently introduced non-elementary class TOWER(poly). Moreover, we classify the complexity of model checking of FO(~) with respect to the number of variables and the quantifier rank, and prove a dichotomy between PSPACE- and ATIME-ALT(exp, poly)-completeness. To achieve the lower bounds, we propose a translation from modal team logic MTL to FO2(~) that extends the well-known standard translation from modal logic ML to FO2. For the upper bounds, we translate to a fragment of second-order logic

Tractability Frontier of Data Complexity in Team Semantics

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