A Model-based Completeness Proof of Extended Narrowing And Resolution
Identifieur interne : 000324 ( Hal/Curation ); précédent : 000323; suivant : 000325A Model-based Completeness Proof of Extended Narrowing And Resolution
Auteurs : Jürgen Stuber [France]Source :
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Abstract
We give a proof of refutational completeness for Extended Narrowing And Resolution (ENAR), a calculus introduced by Dowek, Hardin and Kirchner in the context of Theorem Proving Modulo. ENAR integrates narrowing with respect to a set of rewrite rules on propositions into automated first-order theorem proving by resolution. Our proof allows to impose ordering restrictions on ENAR and provides general redundancy criteria, which are crucial for finding nontrivial proofs. On the other hand, it requires confluence and termination of the rewrite system, and in addition the existence of a well-founded ordering on propositions that is compatible with rewriting, compatible with ground inferences, total on ground clauses, and has some additional technical properties. Such orderings exist for hierarchical definitions of predicates. As an exampe we provide such an ordering for a fragment of set theory.
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automatique</term><term>rewriting</term><term>résolution</term><term>réécriture</term><term>skolemization</term><term>surréduction</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We give a proof of refutational completeness for Extended Narrowing And Resolution (ENAR), a calculus introduced by Dowek, Hardin and Kirchner in the context of Theorem Proving Modulo. ENAR integrates narrowing with respect to a set of rewrite rules on propositions into automated first-order theorem proving by resolution. Our proof allows to impose ordering restrictions on ENAR and provides general redundancy criteria, which are crucial for finding nontrivial proofs. On the other hand, it requires confluence and termination of the rewrite system, and in addition the existence of a well-founded ordering on propositions that is compatible with rewriting, compatible with ground inferences, total on ground clauses, and has some additional technical properties. Such orderings exist for hierarchical definitions of predicates. As an exampe we provide such an ordering for a fragment of set theory.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">A Model-based Completeness Proof of Extended Narrowing And Resolution</title><author role="aut"><persName><forename type="first">Jürgen</forename><surname>Stuber</surname></persName><email>stuber@loria.fr</email><idno type="halauthor">130380</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2360"></affiliation></author><editor role="depositor"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2006-09-26 14:45:25</date><date type="whenModified">2016-05-19 01:09:06</date><date type="whenReleased">2006-09-28 15:22:47</date><date type="whenProduced">2001</date></edition><respStmt><resp>contributor</resp><name key="108626"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00100440</idno><idno type="halUri">https://hal.inria.fr/inria-00100440</idno><idno type="halBibtex">stuber:inria-00100440</idno><idno type="halRefHtml">R. Gore, A. Leitsch, T. Nipkow. First International Joint Conference on Automated Reasoning - IJCAR'2001, 2001, Siena, Italy, Springer, 2083, pp.195-210, 2001, Lecture notes in Computer Science</idno><idno type="halRef">R. Gore, A. Leitsch, T. Nipkow. First International Joint Conference on Automated Reasoning - IJCAR'2001, 2001, Siena, Italy, Springer, 2083, pp.195-210, 2001, Lecture notes in Computer Science</idno></publicationStmt><seriesStmt><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="LORIA-FM" p="LORIA">Méthodes formelles</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno></seriesStmt><notesStmt><note type="commentary">Colloque avec actes et comité de lecture. internationale.</note><note type="audience" n="2">International</note><note type="invited" n="0">No</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note><note type="proceedings" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">A Model-based Completeness Proof of Extended Narrowing And Resolution</title><author role="aut"><persName><forename type="first">Jürgen</forename><surname>Stuber</surname></persName><email>stuber@loria.fr</email><idno type="halAuthorId">130380</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2360"></affiliation></author></analytic><monogr><idno type="localRef">A01-R-068 || stuber01a</idno><meeting><title>First International Joint Conference on Automated Reasoning - IJCAR'2001</title><date type="start">2001</date><settlement>Siena, Italy</settlement></meeting><editor>R. Gore, A. Leitsch, T. Nipkow</editor><imprint><publisher>Springer</publisher><biblScope unit="serie">Lecture notes in Computer Science</biblScope><biblScope unit="volume">2083</biblScope><biblScope unit="pp">195-210</biblScope><date type="datePub">2001</date></imprint></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="fr">constraints</term><term xml:lang="fr">automated reasoning</term><term xml:lang="fr">automated theorem proving</term><term xml:lang="fr">rewriting</term><term xml:lang="fr">narrowing</term><term xml:lang="fr">skolemization</term><term xml:lang="fr">preuve automatique</term><term xml:lang="fr">résolution</term><term xml:lang="fr">réécriture</term><term xml:lang="fr">surréduction</term><term xml:lang="fr">contraintes</term><term xml:lang="fr">raisonnement automatique</term></keywords><classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode><classCode scheme="halTypology" n="COMM">Conference papers</classCode></textClass><abstract xml:lang="en">We give a proof of refutational completeness for Extended Narrowing And Resolution (ENAR), a calculus introduced by Dowek, Hardin and Kirchner in the context of Theorem Proving Modulo. ENAR integrates narrowing with respect to a set of rewrite rules on propositions into automated first-order theorem proving by resolution. Our proof allows to impose ordering restrictions on ENAR and provides general redundancy criteria, which are crucial for finding nontrivial proofs. On the other hand, it requires confluence and termination of the rewrite system, and in addition the existence of a well-founded ordering on propositions that is compatible with rewriting, compatible with ground inferences, total on ground clauses, and has some additional technical properties. Such orderings exist for hierarchical definitions of predicates. As an exampe we provide such an ordering for a fragment of set theory.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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