AC-superposition with constraints: No AC-unifiers needed
Identifieur interne : 002432 ( Istex/Corpus ); précédent : 002431; suivant : 002433AC-superposition with constraints: No AC-unifiers needed
Auteurs : Robert Nieuwenhuis ; Albert RubioSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: We prove the completeness of (basic) deduction strategies with constrained clauses modulo associativity and commutativity (AC). Here each inference generates one single conclusion with an additional equality s=AC t in its constraint (instead of one conclusion for each minimal AC-unifier, i.e. exponentially many). Furthermore, computing AC-unifiers is not needed at all. A clause C〚 T〛 is redundant if the constraint T is not AC-unifiable. If C is the empty clause this has to be decided to know whether C〚 T 〛 denotes an inconsistency. In all other cases any sound method to detect unsatisfiable constraints can be used.
Url:
DOI: 10.1007/3-540-58156-1_40
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Here each inference generates one single conclusion with an additional equality s=AC t in its constraint (instead of one conclusion for each minimal AC-unifier, i.e. exponentially many). Furthermore, computing AC-unifiers is not needed at all. A clause C〚 T〛 is redundant if the constraint T is not AC-unifiable. If C is the empty clause this has to be decided to know whether C〚 T 〛 denotes an inconsistency. 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Here each inference generates one single conclusion with an additional equality s=AC t in its constraint (instead of one conclusion for each minimal AC-unifier, i.e. exponentially many). Furthermore, computing AC-unifiers is not needed at all. A clause C〚 T〛 is redundant if the constraint T is not AC-unifiable. If C is the empty clause this has to be decided to know whether C〚 T 〛 denotes an inconsistency. 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Here each inference generates <hi rend="italic">one single conclusion</hi> with an additional equality <hi rend="italic">s</hi>=<hi rend="subscript">A<hi rend="italic">C</hi></hi><hi rend="italic">t</hi> in its constraint (instead of one conclusion for each minimal AC-unifier, i.e. exponentially many). Furthermore, <hi rend="italic">computing AC-unifiers is not needed at all</hi>. A clause <hi rend="italic">C</hi>〚 <hi rend="italic">T</hi>〛 is redundant if the constraint <hi rend="italic">T</hi> is not AC-unifiable. If <hi rend="italic">C</hi> is the empty clause this has to be decided to know whether <hi rend="italic">C</hi>〚 <hi rend="italic">T</hi> 〛 denotes an inconsistency. In all other cases any sound method to detect unsatisfiable constraints can be used.</p></abstract><textClass ana="subject"><keywords scheme="book-subject-collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass ana="subject"><keywords scheme="book-subject"><list><label>I</label><item><term type="Primary">Computer Science</term></item><label>I21017</label><item><term type="Secondary" subtype="priority-1">Artificial Intelligence (incl. 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Here each inference generates <Emphasis Type="Italic">one single conclusion</Emphasis> with an additional equality <Emphasis Type="Italic">s</Emphasis>=<Subscript>A<Emphasis Type="Italic">C</Emphasis></Subscript><Emphasis Type="Italic">t</Emphasis> in its constraint (instead of one conclusion for each minimal AC-unifier, i.e. exponentially many). Furthermore, <Emphasis Type="Italic">computing AC-unifiers is not needed at all</Emphasis>. A clause <Emphasis Type="Italic">C</Emphasis>〚 <Emphasis Type="Italic">T</Emphasis>〛 is redundant if the constraint <Emphasis Type="Italic">T</Emphasis> is not AC-unifiable. If <Emphasis Type="Italic">C</Emphasis> is the empty clause this has to be decided to know whether <Emphasis Type="Italic">C</Emphasis>〚 <Emphasis Type="Italic">T</Emphasis> 〛 denotes an inconsistency. In all other cases any sound method to detect unsatisfiable constraints can be used.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>Both authors upported by the Esprit Working Group CCL, ref. 6028</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>AC-superposition with constraints: No AC-unifiers needed</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>AC-superposition with constraints: No AC-unifiers needed</title></titleInfo><name type="personal"><namePart type="given">Robert</namePart><namePart type="family">Nieuwenhuis</namePart><affiliation>Technical University of Catalonia, Pau Gargallo 5, 08028, Barcelona, Spain</affiliation><affiliation>E-mail: roberto@lsi.upc.es</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Albert</namePart><namePart type="family">Rubio</namePart><affiliation>Technical University of Catalonia, Pau Gargallo 5, 08028, Barcelona, Spain</affiliation><affiliation>E-mail: rubio@lsi.upc.es</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="ReviewPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">1994</dateIssued><copyrightDate encoding="w3cdtf">1994</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: We prove the completeness of (basic) deduction strategies with constrained clauses modulo associativity and commutativity (AC). Here each inference generates one single conclusion with an additional equality s=AC t in its constraint (instead of one conclusion for each minimal AC-unifier, i.e. exponentially many). Furthermore, computing AC-unifiers is not needed at all. A clause C〚 T〛 is redundant if the constraint T is not AC-unifiable. If C is the empty clause this has to be decided to know whether C〚 T 〛 denotes an inconsistency. In all other cases any sound method to detect unsatisfiable constraints can be used.</abstract><relatedItem type="host"><titleInfo><title>Automated Deduction — CADE-12</title><subTitle>12th International Conference on Automated Deduction Nancy, France, June 26 – July 1, 1994 Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Alan</namePart><namePart type="family">Bundy</namePart><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1994</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I21017">Artificial Intelligence (incl. 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