LTL Fragments are Hard for Standard Parameterisations

We classify the complexity of the LTL satisfiability and model checking problems for several standard parameterisations. The investigated parameters are temporal depth, number of propositional variables and formula treewidth, resp., pathwidth. We show that all operator fragments of LTL under the investigated parameterisations are intractable in the sense of parameterised complexity.Comment: TIME 2015 conference versio

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

Axiomatizations for propositional and modal team logic

A framework is developed that extends Hilbert-style proof systems for propositional and modal logics to comprehend their team-based counterparts. The method is applied to classical propositional logic and the modal logic K. Complete axiomatizations for their team-based extensions, propositional team logic PTL and modal team logic MTL, are presented

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

Team logic : axioms, expressiveness, complexity

Team semantics is an extension of classical logic where statements do not refer to single states of a system, but instead to sets of such states, called teams. This kind of semantics has applications for example in mathematical logic, verification of dynamic systems as well as in database theory. In this thesis, we focus on the propositional, modal and first-order variant of team logic. We study the classical questions of formal logic: Expressiveness (can we formalize sufficiently interesting properties of models?), axiomatizability (can all true statements be deduced in some formal system?) and complexity (can problems such as satisfiability and model checking be solved algorithmically?). Finally, we classify existing team logics and show approaches how team semantics can be defined for arbitrary other logics.Team-Semantik ist eine Erweiterung klassischer Logik, bei der Aussagen nicht über einzelne Zustände eines Systems getroffen werden, sondern über Mengen solcher Zustände, genannt Teams. Diese Art von Semantik besitzt unter anderem Anwendungen in der mathematischen Logik, in der Verifikation dynamischer Systeme sowie in der Datenbanktheorie. In dieser Arbeit liegt der Fokus auf der aussagenlogischen, der modallogischen und der prädikatenlogischen Variante der Team-Logik. Es werden die klassischen Fragestellungen formaler Logik untersucht: Ausdruckskraft (können hinreichend interessante Eigenschaften von Modellen formalisiert werden?), Axiomatisierbarkeit (lassen sich alle wahren Aussagen in einem Kalkül ableiten?) und Komplexität (können Probleme wie Erfüllbarkeit und Modellprüfung algorithmisch gelöst werden?). Schlussendlich werden existierende Team-Logiken klassifiziert und es werden Ansätze aufgezeigt, wie Team-Semantik für beliebige weitere Logiken definiert werden kann