Expressivity and Complexity of Dependence Logic

Approximation and dependence via multiteam semantics

“…From (6) it follows that θ is well-defined, whereas (5) and (7) ensure that every clause of ϕ is satisfied by θ. Hence we have ϕ ∈ 3SAT.…”

“…For example, inclusion atoms give rise to a variant of dependence logic that corresponds to the complexity class PTIME over finite ordered structures [10]. In fact, the complexity theoretic aspects of these atoms in propositional, modal, and first-order setting have been studied extensively during the past few years (see the survey of Durand et al [6] and the references therein).…”

Characterising modal definability of team-based logics via the universal modality

“…Kontinen et al [25] have shown that exactly the properties of teams that are closed under the team k-bisimulation are definable in the so-called modal team logic, whereas Hella and Stumpf established [20] that the so-called extended modal inclusion logic is characterised by the empty team property, union closure, and closure under team k-bisimulation. See the survey [7] for a detailed exposition on the expressive power and computational complexity of related logics. Whereas the expressive powers of the related logics have been well-studied, the closely related topics of model and frame definability have not been addressed before.…”

Complexity of Propositional Logics in Team Semantic

“…The computational aspects of (first-order) dependence logic and its variants have been actively studied, and are now quite well understood (see [5]). On the other hand, the complexity of the propositional versions of these logics have not been systematically studied.…”