Publications (22)0 Total impact
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Dataset: 1103.0853v1
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Article: Generalized Complexity of ALC Subsumption
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ABSTRACT: The subsumption problem with respect to terminologies in the description logic ALC is EXPTIME-complete. We investigate the computational complexity of fragments of this problem by means of allowed Boolean operators. Hereto we make use of the notion of clones in the context of Post's lattice. Furthermore we consider all four possible quantifier combinations for each fragment parameterized by a clone. We will see that depending on what quantifiers are available the classification will be either tripartite or a quartering.05/2012; -
Article: The Complexity of Monotone Hybrid Logics over Linear Frames and theNatural Numbers
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ABSTRACT: Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of non-elementary complexity. In this paper, we consider monotone hybrid logics (i.e., the Boolean connectives are conjunction and disjunction only) over N and general linear orders. We show that the satisfiability problem remains non-elementary over linear orders, but its complexity drops to PSPACE-completeness over N. We categorize the strict fragments arising from different combinations of modal and hybrid operators into NP-complete and tractable (i.e. complete for NC1or LOGSPACE). Interestingly, NP-completeness depends only on the fragment and not on the frame. For the cases above NP, satisfiability over linear orders is harder than over N, while below NP it is at most as hard. In addition we examine model-theoretic properties of the fragments in question.Technical Report, arXiv. 04/2012; -
Article: On the Parameterized Complexity of Default Logic and Autoepistemic Logic
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ABSTRACT: We investigate the application of Courcelle's Theorem and the logspace version of Elberfeld etal. in the context of the implication problem for propositional sets of formulae, the extension existence problem for default logic, as well as the expansion existence problem for autoepistemic logic and obtain fixed-parameter time and space efficient algorithms for these problems. On the other hand, we exhibit, for each of the above problems, families of instances of a very simple structure that, for a wide range of different parameterizations, do not have efficient fixed-parameter algorithms (even in the sense of the large class XPnu), unless P=NP.10/2011; -
Chapter: Generalized Satisfiability for the Description Logic
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ABSTRACT: The standard reasoning problem, concept satisfiability, in the basic description logic ALC\mathcal{ALC} is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC\mathcal{ALC}, notably logics in the FL\mathcal{FL}, EL\mathcal{EL}, and DL-Lite families, have an easier satisfiability problem; sometimes it is even tractable. We classify the complexity of the standard satisfiability problems for all possible Boolean and quantifier fragments of ALC\mathcal{ALC} in the presence of general axioms.04/2011: pages 552-562; -
Article: Model Checking CTL is Almost Always Inherently Sequential
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ABSTRACT: The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations---restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that, in cases where the combined complexity is of relevance, approaching CTL model checking by parallelism cannot be expected to result in any significant speedup. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL+, and ECTL+.03/2011; -
Article: Generalized Satisfiability for the Description Logic ALC
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ABSTRACT: The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and DL-Lite families, have an easier satisfiability problem; sometimes it is even tractable. We classify the complexity of the standard satisfiability problems for all possible Boolean and quantifier fragments of ALC in the presence of general axioms.03/2011; -
Conference Proceeding: Generalized Satisfiability for the Description Logic
Theory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Tokyo, Japan, May 23-25, 2011. Proceedings; 01/2011 -
Article: Proof complexity of propositional default logic.
Arch. Math. Log. 01/2011; 50:727-742. -
Chapter: Proof Complexity of Propositional Default Logic
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ABSTRACT: Default logic is one of the most popular and successful formalisms for non-monotonic reasoning. In 2002, Bonatti and Olivetti introduced several sequent calculi for credulous and skeptical reasoning in propositional default logic. In this paper we examine these calculi from a proof-complexity perspective. In particular, we show that the calculus for credulous reasoning obeys almost the same bounds on the proof size as Gentzen’s system LK. Hence proving lower bounds for credulous reasoning will be as hard as proving lower bounds for LK. On the other hand, we show an exponential lower bound to the proof size in Bonatti and Olivetti’s enhanced calculus for skeptical default reasoning.07/2010: pages 30-43; -
Article: The Complexity of Reasoning for Fragments of Autoepistemic Logic
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ABSTRACT: Autoepistemic logic extends propositional logic by the modal operator L. A formula that is preceded by an L is said to be "believed". The logic was introduced by Moore 1985 for modeling an ideally rational agent's behavior and reasoning about his own beliefs. In this paper we analyze all Boolean fragments of autoepistemic logic with respect to the computational complexity of the three most common decision problems expansion existence, brave reasoning and cautious reasoning. As a second contribution we classify the computational complexity of counting the number of stable expansions of a given knowledge base. To the best of our knowledge this is the first paper analyzing the counting problem for autoepistemic logic.06/2010; -
Article: The Complexity of Satisfiability for Sub-Boolean Fragments of ALC
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ABSTRACT: The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and DL-Lite family, have an easier satisfiability problem; sometimes it is even tractable. All these fragments restrict the use of Boolean operators in one way or another. We look at systematic and more general restrictions of the Boolean operators and establish the complexity of the concept satisfiability problem in the presence of axioms. We separate tractable from intractable cases. Comment: 17 pages, accepted (in short version) to Description Logic Workshop 201001/2010; -
Conference Proceeding: The Complexity of Satisfiability for Sub-Boolean Fragments of ALC.
Proceedings of the 23rd International Workshop on Description Logics (DL 2010), Waterloo, Ontario, Canada, May 4-7, 2010; 01/2010 -
Conference Proceeding: Proof Complexity of Propositional Default Logic.
Theory and Applications of Satisfiability Testing - SAT 2010, 13th International Conference, SAT 2010, Edinburgh, UK, July 11-14, 2010. Proceedings; 01/2010 -
Chapter: The Complexity of Satisfiability for Fragments of Hybrid Logic—Part I
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ABSTRACT: The satisfiability problem of hybrid logics with the downarrow binder is known to be undecidable. This initiated a research program on decidable and tractable fragments. In this paper, we investigate the effect of restricting the propositional part of the language on decidability and on the complexity of the satisfiability problem over arbitrary, transitive, total frames, and frames based on equivalence relations. We also consider different sets of modal and hybrid operators. We trace the border of decidability and give the precise complexity of most fragments, in particular for all fragments including negation. For the monotone fragments, we are able to distinguish the easy from the hard cases, depending on the allowed set of operators.08/2009: pages 587-599; -
Article: The Complexity of Satisfiability for Fragments of Hybrid Logic -- Part I
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ABSTRACT: The satisfiability problem of hybrid logics with the downarrow binder is known to be undecidable. This initiated a research program on decidable and tractable fragments. In this paper, we investigate the effect of restricting the propositional part of the language on decidability and on the complexity of the satisfiability problem over arbitrary, transitive, total frames, and frames based on equivalence relations. We also consider different sets of modal and hybrid operators. We trace the border of decidability and give the precise complexity of most fragments, in particular for all fragments including negation. For the monotone fragments, we are able to distinguish the easy from the hard cases, depending on the allowed set of operators.06/2009; -
Conference Proceeding: The Complexity of Satisfiability for Fragments of Hybrid Logic-Part I.
Mathematical Foundations of Computer Science 2009, 34th International Symposium, MFCS 2009, Novy Smokovec, High Tatras, Slovakia, August 24-28, 2009. Proceedings; 01/2009 -
Conference Proceeding: Model Checking CTL is Almost Always Inherently Sequential.
TIME 2009, 16th International Symposium on Temporal Representation and Reasoning, Bressanone-Brixen, Italy, 23-25 July 2009, Proceedings; 01/2009 -
Article: The Complexity of Satisfiability for Fragments of CTL and CTL*.
Int. J. Found. Comput. Sci. 01/2009; 20:901-918. -
Article: The Complexity of Reasoning for Fragments of Default Logic
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ABSTRACT: Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as $\SigmaPtwo$-complete, and the complexity of the credulous and skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete. Additionally, he investigated restrictions on the default rules, i.e., semi-normal default rules. Selman made in 1992 a similar approach with disjunction-free and unary default rules. In this paper we systematically restrict the set of allowed propositional connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-, P-, NL-complete, trivial) for the extension existence problem, while for the credulous and skeptical reasoning problem we obtain similar classifications without trivial cases. Comment: Corrected version08/2008;
Top co-authors
Institutions
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2010–2012
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Leibniz Universität Hannover
- Institute of Theoretical Computer Science
Hannover, Lower Saxony, Germany
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