Results 1 
8 of
8
THE COMPLEXITY OF REASONING FOR FRAGMENTS OF DEFAULT LOGIC
, 2008
"... Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as Σ p 2complete, and the complexity of the credulous and skeptical reasoning problem as Σ p 2complete, resp. Πp2complete. Additionally, ..."
Abstract

Cited by 10 (10 self)
 Add to MetaCart
(Show Context)
Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as Σ p 2complete, and the complexity of the credulous and skeptical reasoning problem as Σ p 2complete, resp. Πp2complete. Additionally, he investigated restrictions on the default rules, i.e., seminormal default rules. Selman made 1992 a similar approach with disjunctionfree 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 trichotomy, NPcomplete, trivial) for the extension existence problem, whereas for the credulous and sceptical reasoning problem we get a finer classification down to NLcomplete cases. (Σ p 2 1.
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 ..."
Abstract

Cited by 9 (5 self)
 Add to MetaCart
(Show Context)
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 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 ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
(Show Context)
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.
Generalized Satisfiability for the Description Logic ALC
"... The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSpacecomplete, and it is ExpTimecomplete in the presence of general concept inclusions. Several fragments of ALC, notably logics in the FL, EL, and DLLite families, have an easier satisfiability problem ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSpacecomplete, and it is ExpTimecomplete in the presence of general concept inclusions. Several fragments of ALC, notably logics in the FL, EL, and DLLite families, have an easier satisfiability problem; for some of these logics, satisfiability can be decided in polynomial time. We classify the complexity of the standard variants of the satisfiability problem for all possible Boolean and quantifier fragments of ALC with and without general concept inclusions.