Parameterised complexity of model checking and satisfiability in propositional dependence logic

Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) of PDL is NP -complete (Ebbing and Lohmann, SOFSEM 2012). The subj...

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Veröffentlicht in:Annals of mathematics and artificial intelligence Jg. 90; H. 2-3; S. 271 - 296
Hauptverfasser: Mahmood, Yasir, Meier, Arne
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.03.2022
Springer
Springer Nature B.V
Schlagworte:
Artificial Intelligence
Atomic properties
Complex Systems
Computer Science
Logic
Mathematical models
Mathematics
Parameters
Semantics
Teams
Model checking
68Q25
Propositional dependence logic
03B70
Parameterised complexity
Satisfiability
ISSN:1012-2443, 1573-7470
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Zusammenfassung:Dependence Logic was introduced by Jouko Väänänen in 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parameterisations with respect to central decision problems. The model checking problem (MC) of PDL is NP -complete (Ebbing and Lohmann, SOFSEM 2012). The subject of this research is to identify a list of parameterisations (formula-size, formula-depth, treewidth, 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) which classically is known to be NP -complete as well (Lohmann and Vollmer, Studia Logica 2013). There we are presenting a different picture: under team-size, or dep-arity SAT is paraNP -complete whereas under all other mentioned parameters the problem is FPT . Finally, we introduce a variant of the satisfiability problem, asking for a team of a given size, and show for this problem an almost complete picture.
Bibliographie:ObjectType-Article-1
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ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-021-09730-w