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On P/NP Dichotomies for EL Subsumption under Relational Constraints
"... Abstract. We consider the problem of characterising relational constraints under which TBox reasoning in EL is tractable. We obtain P vs. coNPhardness dichotomies for tabular constraints and constraints imposed on a single reflexive role. 1 ..."
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Abstract. We consider the problem of characterising relational constraints under which TBox reasoning in EL is tractable. We obtain P vs. coNPhardness dichotomies for tabular constraints and constraints imposed on a single reflexive role. 1
A Does Treewidth Help in Modal Satisfiability?
"... Many tractable algorithms for solving the Constraint Satisfaction Problem (Csp) have been developed using the notion of the treewidth of some graph derived from the input Csp instance. In particular, the incidence graph of the Csp instance is one such graph. We introduce the notion of an incidence g ..."
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Many tractable algorithms for solving the Constraint Satisfaction Problem (Csp) have been developed using the notion of the treewidth of some graph derived from the input Csp instance. In particular, the incidence graph of the Csp instance is one such graph. We introduce the notion of an incidence graph for modal logic formulas in a certain normal form. We investigate the parameterized complexity of modal satisfiability with the modal depth of the formula and the treewidth of the incidence graph as parameters. For various combinations of Euclidean, reflexive, symmetric and transitive models, we show either that modal satisfiability is Fixed Parameter Tractable (Fpt), or that it is W[1]hard. In particular, modal satisfiability in general models is Fpt, while it is W[1]hard in transitive models. As might be expected, modal satisfiability in transitive and Euclidean models is Fpt.
Finite Satisfiability of Modal Logic over Horn Definable Classes of Frames
"... Modal logic plays an important role in various areas of computer science, including verification and knowledge representation. In many practical applications it is natural to consider some restrictions of classes of admissible frames. Traditionally classes of frames are defined by modal axioms. Howe ..."
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Modal logic plays an important role in various areas of computer science, including verification and knowledge representation. In many practical applications it is natural to consider some restrictions of classes of admissible frames. Traditionally classes of frames are defined by modal axioms. However, many important classes of frames, e.g. the class of transitive frames or the class of Euclidean frames, can be defined in a more natural way by firstorder formulas. In a recent paper it was proved that the satisfiability problem for modal logic over the class of frames defined by a universally quantified, firstorder Horn formula is decidable. In this paper we show that also the finite satisfiability problem for modal logic over such classes is decidable. Keywords: modal logic, decidability, finite satisfiability 1