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Complexity of computing with extended propositional logic programs

Complexity of computing with extended propositional logic programs In this paper we introduce the notion of anF-program, whereF is a collection of formulas. We then study the complexity of computing withF-programs.F-programs can be regarded as a generalization of standard logic programs. Clauses (or rules) ofF-programs are built of formulas fromF. In particular, formulas other than atoms are allowed as “building blocks” ofF-program rules. Typical examples ofF are the set of all atoms (in which case the class of ordinary logic programs is obtained), the set of all literals (in this case, we get the class of logic programs with classical negation [9]), the set of all Horn clauses, the set of all clauses, the set of all clauses with at most two literals, the set of all clauses with at least three literals, etc. The notions of minimal and stable models [16, 1, 7] of a logic program have natural generalizations to the case ofF-programs. The resulting notions are called in this paperminimal andstable answer sets. We study the complexity of reasoning involving these notions. In particular, we establish the complexity of determining the existence of a stable answer set, and the complexity of determining the membership of a formula in some (or all) stable answer sets. We study the complexity of the existence of minimal answer sets, and that of determining the membership of a formula in all minimal answer sets. We also list several open problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Complexity of computing with extended propositional logic programs

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References (35)

Publisher
Springer Journals
Copyright
Copyright
Subject
Computer Science; Artificial Intelligence; Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/BF01536401
Publisher site
See Article on Publisher Site

Abstract

In this paper we introduce the notion of anF-program, whereF is a collection of formulas. We then study the complexity of computing withF-programs.F-programs can be regarded as a generalization of standard logic programs. Clauses (or rules) ofF-programs are built of formulas fromF. In particular, formulas other than atoms are allowed as “building blocks” ofF-program rules. Typical examples ofF are the set of all atoms (in which case the class of ordinary logic programs is obtained), the set of all literals (in this case, we get the class of logic programs with classical negation [9]), the set of all Horn clauses, the set of all clauses, the set of all clauses with at most two literals, the set of all clauses with at least three literals, etc. The notions of minimal and stable models [16, 1, 7] of a logic program have natural generalizations to the case ofF-programs. The resulting notions are called in this paperminimal andstable answer sets. We study the complexity of reasoning involving these notions. In particular, we establish the complexity of determining the existence of a stable answer set, and the complexity of determining the membership of a formula in some (or all) stable answer sets. We study the complexity of the existence of minimal answer sets, and that of determining the membership of a formula in all minimal answer sets. We also list several open problems.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: Apr 6, 2005

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