Complexity Thresholds in Inclusion Logic

Abstract

Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in these logics are relatively well understood. Inclusion logic is similar to these team-based logical formalisms with the exception that it corresponds to deterministic polynomial time in ordered models. In this article we examine connections between syntactical fragments of inclusion logic and different complexity classes in terms of 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. Furthermore, we present a fragment of inclusion logic that captures non-deterministic logarithmic space in ordered models.

Axiomatizing first order consequences in inclusion logic

“…Building on these results, Grädel defined model-checking games for inclusion logic [9], which then found applications in [10]. There also emerged some studies [13,14,16,27] on the computational complexity and syntactical fragments of inclusion logic. Embedding the semantics of inclusion atoms into the semantics of the quantifiers, Rönnholm [28] introduced the interesting inclusion quantifiers that generalize the idea of the slashed quantifiers of independence-friendly logic [20] (a close relative to dependence logic).…”