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The Complexity of LogicBased Abduction
, 1993
"... Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logicbased abduction. Candidates for abductive explanations are usually subjected to minima ..."
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Cited by 171 (28 self)
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Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logicbased abduction. Candidates for abductive explanations are usually subjected to minimality criteria such as subsetminimality, minimal cardinality, minimal weight, or minimality under prioritization of individual hypotheses. This paper presents a comprehensive complexity analysis of relevant decision and search problems related to abduction on propositional theories. Our results indicate that abduction is harder than deduction. In particular, we show that with the most basic forms of abduction the relevant decision problems are complete for complexity classes at the second level of the polynomial hierarchy, while the use of prioritization raises the complexity to the third level in certain cases.
On the Computational Cost of Disjunctive Logic Programming: Propositional Case
, 1995
"... This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whethe ..."
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Cited by 116 (26 self)
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This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is P 2 complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is P 2 complete; analogous results are derived for the an
Default Logic as a Query Language
, 1997
"...  Research in nonmonotonic reasoning has focused largely on the idea of representing knowledge about the world via rules that are generally true but can be defeated. Even if relational databases are nowadays the main tool for storing very large sets of data, the approach of using nonmonotonic AI f ..."
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Cited by 42 (10 self)
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 Research in nonmonotonic reasoning has focused largely on the idea of representing knowledge about the world via rules that are generally true but can be defeated. Even if relational databases are nowadays the main tool for storing very large sets of data, the approach of using nonmonotonic AI formalisms as relational database query languages has been investigated to a much smaller extent. In this work we propose a novel application of Reiter's default logic by introducing a default query language (DQL) for nite relational databases, which is based on default rules. The main result of this paper is that DQL is as expressive as SO 98 , the existentialuniversal fragment of secondorder logic. This result is not only of theoretical importance: We exhibit queries {which are useful in practice{ that can be expressed with DQL and can not with other query languages based on nonmonotonic logics such as DATALOG with negation under the stable model semantics. In particular, we show that DQ...
On the Computational Complexity of AssumptionBased Argumentation For Default Reasoning
 Artificial Intelligence
, 2002
"... Bondarenko et al. have recently proposed an abstract framework for default reasoning. Besides capturing most existing formalisms and proving that their standard semantics all coincide, the framework extends these formalisms by generalising the semantics of admissible and preferred arguments, ori ..."
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Cited by 40 (7 self)
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Bondarenko et al. have recently proposed an abstract framework for default reasoning. Besides capturing most existing formalisms and proving that their standard semantics all coincide, the framework extends these formalisms by generalising the semantics of admissible and preferred arguments, originally proposed for logic programming only.
Computing With Default Logic
, 1999
"... Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default l ..."
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Cited by 38 (5 self)
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Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default logic, as a source of largescale problems needed for experimentation and as a source of intuitions needed for a systematic methodology of encoding problems as default theories we use here the domain of combinatorial problems. To experimentally study the performance of DeReS we developed a benchmarking system, the TheoryBase. The TheoryBase is designed to support experimental investigations of nonmonotonic reasoning systems based on the language of default logic or logic programming. It allows the user to create parameterized collections of default theories having similar properties and growing sizes and, consequently, to study the asymptotic performance of nonmonotonic systems under i...
Experimenting with Nonmonotonic Reasoning
 IN PROCEEDINGS OF THE 12TH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING
, 1995
"... In this paper, we describe a system, called TheoryBase, whose goal is to facilitate experimental studies of nonmonotonic reasoning systems. TheoryBase generates test default theories and logic programs. It has an identification system for generated theories, which allows us to reconstruct a logic pr ..."
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Cited by 36 (6 self)
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In this paper, we describe a system, called TheoryBase, whose goal is to facilitate experimental studies of nonmonotonic reasoning systems. TheoryBase generates test default theories and logic programs. It has an identification system for generated theories, which allows us to reconstruct a logic program or a default theory from its identifier. Hence, exchanging test cases requires only exchanging identifiers. TheoryBase can generate a large variety of examples of default theories and logic programs. We believe that its universal adoption may significantly advance experimental studies of nonmonotonic reasoning systems.
Artificial Intelligence: A Computational Perspective
 Essentials in Knowledge Representation
, 1994
"... Although the computational perspective on cognitive tasks has always played a major role in Artificial Intelligence, the interest in the precise determination of the computational costs that are required for solving typical AI problems has grown only recently. In this paper, we will describe what in ..."
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Cited by 31 (1 self)
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Although the computational perspective on cognitive tasks has always played a major role in Artificial Intelligence, the interest in the precise determination of the computational costs that are required for solving typical AI problems has grown only recently. In this paper, we will describe what insights a computational complexity analysis can provide and what methods are available to deal with the complexity problem. This work was partially supported by the European Commission as part of DRUMSII, the ESPRIT Basic Research Project P6156. 1 Introduction It is wellknown that typical AI problems, such as natural language understanding, scene interpretation, planning, configuration, or diagnosis are computationally difficult. Hence, it seems to be worthless to analyze the computational complexity of these problems. In fact, some people believe that all AI problems are NPhard or even undecidable. Conceiving AI as a scientific field that has as its goal the analysis and synthesis of...
Default Reasoning Using Classical Logic
 Artificial Intelligence
, 1996
"... In this paper we show how propositional default theories can be characterized by classical propositional theories: for each finite default theory, we show a classical propositional theory such that there is a onetoone correspondence between models for the latter and extensions of the former. T ..."
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Cited by 24 (2 self)
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In this paper we show how propositional default theories can be characterized by classical propositional theories: for each finite default theory, we show a classical propositional theory such that there is a onetoone correspondence between models for the latter and extensions of the former. This means that computing extensions and answering queries about coherence, setmembership and setentailment are reducible to propositional satisfiability. The general transformation is exponential but tractable for a subset which we call 2DT  a superset of network default theories and disjunctionfree default theories. Consequently, coherence and setmembership for the class 2DT is NPcomplete and setentailment is coNPcomplete. This work paves the way for the application of decades of research on efficient algorithms for the satisfiability problem to default reasoning. For example, since propositional satisfiability can be regarded as a constraint satisfaction problem (CSP...
Semantics and complexity of abduction from default theories (Extended Abstract)
 ARTIFICIAL INTELLIGENCE
, 1997
"... Since logical knowledge representation is commonly based on nonclassical formalisms like default logic, autoepistemic logic, or circumscription, it is necessary to perform abductive reasoning from theories of nonclassical logics. In this paper, we investigate how abduction can be performed from theo ..."
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Cited by 23 (2 self)
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Since logical knowledge representation is commonly based on nonclassical formalisms like default logic, autoepistemic logic, or circumscription, it is necessary to perform abductive reasoning from theories of nonclassical logics. In this paper, we investigate how abduction can be performed from theories in default logic. Different modes of abduction are plausible, based on credulous and skeptical default reasoning; they appear useful for different applications such as diagnosis and planning. Moreover, we analyze the complexity of the main abductive reasoning tasks. They are intractable in the general case; we also present known classes of default theories for which abduction is tractable.
Preferred arguments are harder to compute than stable extensions
 Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI99Vol1
, 1999
"... Based on an abstract framework for nonmonotonic reasoning, Bondarenko et at. have extended the logic programming semantics of admissible and preferred arguments to other nonmonotonic formalisms such as circumscription, autoepisternic logic and default logic. Although the new semantics have been taci ..."
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Cited by 21 (2 self)
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Based on an abstract framework for nonmonotonic reasoning, Bondarenko et at. have extended the logic programming semantics of admissible and preferred arguments to other nonmonotonic formalisms such as circumscription, autoepisternic logic and default logic. Although the new semantics have been tacitly assumed to mitigate the computational problems of nonmonotonic reasoning under the standard semantics of stable extensions, it seems questionable whether they improve the worstcase behaviour. As a matter of fact, we show that credulous reasoning under the new semantics in propositional logic programming and prepositional default logic has the same computational complexity as under the standard semantics. Furthermore, sceptical reasoning under the admissibility semantics is easier ~ since it is trivialised to monotonic reasoning. Finally, sceptical reasoning under the preferability semantics is harder than under the standard semantics. 1