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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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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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Trichotomy in the complexity of minimal inference
 IN PROC. 24TH LICS
, 2009
"... We study the complexity of the propositional minimal inference problem. Its complexity has been extensively studied before because of its fundamental importance in artificial intelligence and nonmonotonic logics. We prove that the complexity of the minimal inference problem with unbounded queries ha ..."
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We study the complexity of the propositional minimal inference problem. Its complexity has been extensively studied before because of its fundamental importance in artificial intelligence and nonmonotonic logics. We prove that the complexity of the minimal inference problem with unbounded queries has a trichotomy (between P, coNPcomplete, and Π2Pcomplete). This result finally settles with a positive answer the trichotomy conjecture of Kirousis and Kolaitis [A dichotomy in the complexity of propositional circumscription, LICS’01] in the unbounded case. We also present simple and efficiently computable criteria separating the different cases.
Complexity Classifications for Propositional Abduction in Post’s Framework∗
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Checking the Size of Circumscribed Formulae
"... Abstract—The circumscription of a propositional formula T may not be representable in polynomial space, unless the polynomial hierarchy collapses. This depends on the specific formula T, as some can be circumscribed in little space and others cannot. The problem considered in this article is whether ..."
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Abstract—The circumscription of a propositional formula T may not be representable in polynomial space, unless the polynomial hierarchy collapses. This depends on the specific formula T, as some can be circumscribed in little space and others cannot. The problem considered in this article is whether this happens for a given formula or not. In particular, the complexity of deciding whether CIRC(T) is equivalent to a formula of size bounded by k is studied. This theoretical question is relevant as circumscription has applications in temporal logics, diagnosis, default logic and belief revision. Keywords—Circumscription; computational complexity; belief revision. I.