Complexity of Propositional Logics in Team Semantic

We classify the computational complexity of the satisfiability, validity, and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for propositional team logic are complete for alternating exponential-time with polynomially many alternations.Peer reviewe

Parameterized complexity of weighted team definability

In this article, we study the complexity of weighted team definability for logics with team semantics. This problem is a natural analog of one of the most studied problems in parameterized complexity, the notion of weighted Fagin-definability, which is formulated in terms of satisfaction of first-order formulas with free relation variables. We focus on the parameterized complexity of weighted team definability for a fixed formula ϕ of central team-based logics. Given a first-order structure A and the parameter value k ∈ N as input, the question is to determine whether A, T |= ϕ for some team T of size k. We show several results on the complexity of this problem for dependence, independence, and inclusion logic formulas. Moreover, we also relate the complexity of weighted team definability to the complexity classes in the well-known W-hierarchy as well as paraNP

Facets of Distribution Identities in Probabilistic Team Semantics

We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different probabilistic atoms such as conditional independence and different variants of marginal distribution equivalences. We also relate the framework to the first-order theory of the reals and apply our methods to the open question on the complexity of the implication problem of conditional independence.Peer reviewe

Tractability Frontier of Data Complexity in Team Semantics

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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

Complexity thresholds in inclusion logic

Inclusion logic differs from many other logics of dependence and independence in that it can only describe polynomial-time properties. In this article we examine more closely connections between syntactic fragments of inclusion logic and different complexity classes. Our focus is on two computational problems: maximal subteam membership and the model checking problem for a fixed inclusion logic formula. We show that very simple quantifier-free formulae with one or two inclusion atoms generate instances of these problems that are complete for (non-deterministic) logarithmic space and polynomial time. We also present a safety game for the maximal subteam membership problem and use it to investigate this problem over teams in which one variable is a key. Furthermore, we relate our findings to consistent query answering over inclusion dependencies, and present a fragment of inclusion logic that captures non-deterministic logarithmic space in ordered models. (C) 2021 The Author(s). Published by Elsevier Inc.Peer reviewe