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Complexity and Expressive Power of Logic Programming
, 1997
"... This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results ..."
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Cited by 362 (57 self)
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This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.
Logic Programming and Negation: A Survey
 JOURNAL OF LOGIC PROGRAMMING
, 1994
"... We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them. ..."
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Cited by 280 (8 self)
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We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the prooftheoretic and modeltheoretic issues and the relationships between them.
Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
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Cited by 242 (20 self)
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In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
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 195 (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.
An Algorithm to Evaluate Quantified Boolean Formulae and its Experimental Evaluation
 Journal of Automated Reasoning
, 1999
"... The high computational complexity of advanced reasoning tasks such as reasoning about knowledge and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating Quantified Boolean Formulae, a language that ..."
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Cited by 155 (4 self)
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The high computational complexity of advanced reasoning tasks such as reasoning about knowledge and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating Quantified Boolean Formulae, a language that extends propositional logic in a way such that many advanced forms of propositional reasoning, e.g., circumscription, can be easily formulated as evaluation of a QBF. Algorithms for evaluation of QBFs are suitable for the experimental analysis on a wide range of complexity classes, a property not easily found in other formalisms. Evaluate is based on a generalization of the DavisPutnam procedure for SAT, and is guaranteed to work in polynomial space. Before presenting the algorithm, we discuss several abstract properties of QBFs that we singled out to make it more efficient. We also discuss various options that were investigated about heuristics and data structures, and report the main res...
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 140 (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
A Survey on Knowledge Compilation
, 1998
"... this paper we survey recent results in knowledge compilation of propositional knowledge bases. We first define and limit the scope of such a technique, then we survey exact and approximate knowledge compilation methods. We include a discussion of compilation for nonmonotonic knowledge bases. Keywor ..."
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Cited by 121 (4 self)
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this paper we survey recent results in knowledge compilation of propositional knowledge bases. We first define and limit the scope of such a technique, then we survey exact and approximate knowledge compilation methods. We include a discussion of compilation for nonmonotonic knowledge bases. Keywords: Knowledge Representation, Efficiency of Reasoning
Sound and efficient closedworld reasoning for planning
 Artificial Intelligence
, 1997
"... Closedworld inference is the process of determining that a logical sentence is false based on its absence from a knowledge base, or the inability to derive it. This process is essential for planning with incomplete information. We describe a novel method for closedworld inference and update over t ..."
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Cited by 88 (12 self)
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Closedworld inference is the process of determining that a logical sentence is false based on its absence from a knowledge base, or the inability to derive it. This process is essential for planning with incomplete information. We describe a novel method for closedworld inference and update over the firstorder theories of action used by planning algorithms such as NONLIN, TWEAK, and UCPOP. We show the method to be sound and efficient, but incomplete. In our experiments, closedworld inference consistently averaged about 2 milliseconds, while updates averaged approximately 1.2 milliseconds. We incorporated the method into the XII planner, which supports our Internet Softbot (software robot). The method cut the number of actions executed by the Softbot bya factor of one hundred, and resulted in a corresponding speedup to XII. 1
Propositional Defeasible Logic has Linear Complexity
 of Logic Programming
, 2001
"... Defeasible logic is a rulebased nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts markedly with most other propositional nonmonotonic logics, i ..."
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Cited by 82 (6 self)
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Defeasible logic is a rulebased nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts markedly with most other propositional nonmonotonic logics, in which inference is intractable. 1 Introduction Mostwork in nonmonotonicreasoning has focussed on languages for whichpropositional inference is not tractable. Sceptical default reasoning is \Pi p 2 hard, even for very simple classes of default rules, as is sceptical autoepistemic reasoning and propositional circumscription. The complexity of sceptical inference from logic programs with negationasfailure varies according to the semantics of negation. For both the stable model semantics and the Clark completion, sceptical inference is coNPhard. See [13, 9] for more details. Although such languages are very expressive, and this expressiveness has been exploited in answerset progra...