The power of the filtration technique for modal logics with team semantics

Modal Team Logic (MTL) extends Väänänen's Modal Dependence Logic (MDL) by Boolean negation. Its satisfiability problem is decidable, but the exact complexity is not yet understood very well. We investigate a model-theoretical approach and generalize the successful filtration technique to work in team semantics. We identify an "existential" fragment of MTL that enjoys the exponential model property and is therefore, like Propositional Team Logic (PTL), complete for the class AEXP(poly). Moreover, superexponential filtration lower bounds for different fragments of MTL are proven, up to the full logic having no filtration for any elementary size bound. As a corollary, superexponential gaps of succinctness between MTL fragments of equal expressive power are shown

Canonical Models and the Complexity of Modal Team Logic

We study modal team logic MTL, the team-semantical extension of classical modal logic closed under Boolean negation. Its fragments, such as modal dependence, independence, and inclusion logic, are well-understood. However, due to the unrestricted Boolean negation, the satisfiability problem of full MTL has been notoriously resistant to a complexity theoretical classification. In our approach, we adapt the notion of canonical models for team semantics. By construction of such a model, we reduce the satisfiability problem of MTL to simple model checking. Afterwards, we show that this method is optimal in the sense that MTL-formulas can efficiently enforce canonicity. Furthermore, to capture these results in terms of computational complexity, we introduce a non-elementary complexity class, TOWER(poly), and prove that the satisfiability and validity problem of MTL are complete for it. We also show that the fragments of MTL with bounded modal depth are complete for the levels of the elementary hierarchy (with polynomially many alternations)