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The complexity of circumscriptive inference in Post’s lattice
 Proceedings 10th International Conference om Logic Programming and Nonmonotonic Reasoning (LPNMR 2009
, 2009
"... Abstract. Circumscription is one of the most important formalisms for reasoning with incomplete information. It is equivalent to reasoning under the extended closed world assumption, which allows to conclude that the facts derivable from a given knowledge base are all facts that satisfy a given pro ..."
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Cited by 9 (5 self)
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Abstract. Circumscription is one of the most important formalisms for reasoning with incomplete information. It is equivalent to reasoning under the extended closed world assumption, which allows to conclude that the facts derivable from a given knowledge base are all facts that satisfy a given property. In this paper, we study the computational complexity of several formalizations of inference in propositional circumscription for the case that the knowledge base is described by a propositional theory using only a restricted set of Boolean functions. To systematically cover all possible sets of Boolean functions, we use Post’s lattice. With its help, we determine the complexity of circumscriptive inference for all but two possible classes of Boolean functions. Each of these problems is shown to be either Πp2complete, coNPcomplete, or contained in L. In particular, we show that in the general case, unless P = NP, only literal theories admit polynomialtime algorithms, while for some restricted variants the tractability border is the same as for classical propositional inference. 1
The Complexity of Propositional Implication
, 2008
"... The question whether a set of formulae Γ implies a formula ϕ is fundamental. The present paper studies the complexity of the above implication problem for propositional formulae that are built from a systematically restricted set of Boolean connectives. We give a complete complexity classification f ..."
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Cited by 8 (8 self)
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The question whether a set of formulae Γ implies a formula ϕ is fundamental. The present paper studies the complexity of the above implication problem for propositional formulae that are built from a systematically restricted set of Boolean connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post’s lattice and show that the implication problem is efficientily solvable only if the connectives are definable using the constants{0, 1} and only one of{∧,∨,⊕}. The problem remains coNPcomplete in all other cases. We also consider the restriction of Γ to singletons.
The complexity of reasoning for fragments of autoepistemic logic
 In Circuits, Logic, and Games, volume 10061 of Dagstuhl Seminar Proceedings
, 2010
"... Autoepistemic logic extends propositional logic by the modal operator L. A formula ϕ 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 f ..."
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Cited by 5 (4 self)
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Autoepistemic logic extends propositional logic by the modal operator L. A formula ϕ 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. 1.
Complexity of propositional abduction for restricted sets of boolean functions
 In Proc. KR’10
, 2010
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Complexity Classifications for Propositional Abduction in Post’s Framework∗
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On the Parameterized Complexity of Default Logic and Autoepistemic Logic∗
"... Abstract. We investigate the application of Courcelle’s Theorem and the logspace version of Elberfeld et al. 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 ..."
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Abstract. We investigate the application of Courcelle’s Theorem and the logspace version of Elberfeld et al. 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 fixedparameter 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 fixedparameter algorithms (even in the sense of the large class XPnu), unless P = NP. 1
Generalized Complexity of ALC Subsumption
"... The subsumption problem with respect to terminologies in the description logic ALC is EXPcomplete. 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 ..."
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The subsumption problem with respect to terminologies in the description logic ALC is EXPcomplete. 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. 1