18 research outputs found
A Team Based Variant of CTL
We introduce two variants of computation tree logic CTL based on team
semantics: an asynchronous one and a synchronous one. For both variants we
investigate the computational complexity of the satisfiability as well as the
model checking problem. The satisfiability problem is shown to be
EXPTIME-complete. Here it does not matter which of the two semantics are
considered. For model checking we prove a PSPACE-completeness for the
synchronous case, and show P-completeness for the asynchronous case.
Furthermore we prove several interesting fundamental properties of both
semantics.Comment: TIME 2015 conference version, modified title and motiviatio
Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic
In this paper, we initiate a systematic study of the parametrised complexity
in the field of Dependence Logics which finds its origin in the Dependence
Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this
logic (PDL) and investigate a variety of parametrisations with respect to the
central decision problems. The model checking problem (MC) of PDL is
NP-complete. The subject of this research is to identify a list of
parametrisations (formula-size, treewidth, treedepth, team-size, number of
variables) under which MC becomes fixed-parameter tractable. Furthermore, we
show that the number of disjunctions or the arity of dependence atoms
(dep-arity) as a parameter both yield a paraNP-completeness result. Then, we
consider the satisfiability problem (SAT) showing a different picture: under
team-size, or dep-arity SAT is paraNP-complete whereas under all other
mentioned parameters the problem is in FPT. Finally, we introduce a variant of
the satisfiability problem, asking for teams of a given size, and show for this
problem an almost complete picture.Comment: Update includes refined result
Set Semantics for Asynchronous TeamLTL: Expressivity and Complexity
We introduce and develop a set-based semantics for asynchronous TeamLTL. We consider two canonical logics in this setting: the extensions of TeamLTL by the Boolean disjunction and by the Boolean negation. We relate the new semantics with the original semantics based on multisets and establish one of the first positive complexity theoretic results in the temporal team semantics setting. In particular we show that both logics enjoy normal forms that can be utilised to obtain results related to expressivity and complexity (decidability) of the new logics
Validity and Entailment in Modal and Propositional Dependence Logics
The computational properties of modal and propositional dependence logics have been extensively studied over the past few years, starting from a result by Sevenster showing NEXPTIME-completeness of the satisfiability problem for modal dependence logic. Thus far, however, the validity and entailment properties of these logics have remained uncharacterised to a great extent. This paper establishes a complete classification of the complexity of validity and entailment in modal and propositional dependence logics. In particular, we address the question of the complexity of validity in modal dependence logic. By showing that it is NEXPTIME-complete we refute an earlier conjecture proposing a higher complexity for the problem
Linear-Time Temporal Logic with Team Semantics: Expressivity and Complexity
We study the expressivity and complexity of model checking of linear temporal logic with team semantics (TeamLTL). TeamLTL, despite being a purely modal logic, is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. TeamLTL has been introduced quite recently and only few results are known regarding its expressivity and its model checking problem. We relate the expressivity of TeamLTL to logics for hyperproperties obtained by extending LTL with trace and propositional quantifiers (HyperLTL and HyperQPTL). By doing so, we obtain a number of model checking results for TeamLTL and identify its undecidability frontier. In particular, we show decidability of model checking of the so-called left-flat fragment of any downward closed TeamLTL-extension. Moreover, we establish that the model checking problem of TeamLTL with Boolean disjunction and inclusion atoms is undecidable
Parameterised Complexity of Propositional Inclusion and Independence Logic
In this work we analyse the parameterised complexity of propositional
inclusion (PINC) and independence logic (PIND). The problems of interest are
model checking (MC) and satisfiability (SAT). The complexity of these problems
is well understood in the classical (non-parameterised) setting. Mahmood and
Meier (FoIKS 2020) recently studied the parameterised complexity of
propositional dependence logic (PDL). As a continuation of their work, we
classify inclusion and independence logic and thereby come closer to completing
the picture with respect to the parametrised complexity for the three most
studied logics in the propositional team semantics setting. We present results
for each problem with respect to 8 different parameterisations. It turns out
that for a team-based logic L such that L-atoms can be evaluated in polynomial
time, then MC parameterised by teamsize is FPT. As a corollary, we get an FPT
membership under the following parameterisations: formula-size, formula-depth,
treewidth, and number of variables. The parameter teamsize shows interesting
behavior for SAT. For PINC, the parameter teamsize is not meaningful, whereas
for PDL and PIND the satisfiability is paraNP-complete. Finally, we prove that
when parameterised by arity, both MC and SAT are paraNP-complete for each of
the considered logics.Comment: A revised versio
Approximation and dependence via multiteam semantics
A journal version of the FoIKS 2016 conference publication.We define a variant of team semantics called multiteam semantics based on multisets and study the properties of various logics in this framework. In particular, we define natural probabilistic versions of inclusion and independence atoms and certain approximation operators motivated by approximate dependence atoms of Vaananen.Peer reviewe
Set Semantics for Asynchronous TeamLTL: Expressivity and Complexity
We introduce and develop a set-based semantics for asynchronous TeamLTL. We
consider two canonical logics in this setting: the extensions of TeamLTL by the
Boolean disjunction and by the Boolean negation. We establish fascinating
connections between the original semantics based on multisets and the new
set-based semantics as well as show one of the first positive complexity
theoretic results in the temporal team semantics setting. In particular we show
that both logics enjoy normal forms that can be utilised to obtain results
related to expressivity and complexity (decidability) of the new logics. We
also relate and apply our results to recently defined logics whose
asynchronicity is formalized via time evaluation functions