Abstract canonical presentations
Identifieur interne : 000411 ( PascalFrancis/Checkpoint ); précédent : 000410; suivant : 000412Abstract canonical presentations
Auteurs : Nachum Dershowitz [Israël] ; Claude Kirchner [France]Source :
- Theoretical computer science [ 0304-3975 ] ; 2006.
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Abstract
Solving goals-like proving properties, deciding word problems or resolving constraints-is much easier with some presentations of the underlying theory than with others. Typically, what have been called "completion processes", in particular in the study of equational logic, involve finding appropriate presentations of a given theory to more easily solve a given class of problems. We provide a general proof-theoretic setting that relies directly on the fundamental concept of "good", that is, normal-form, proofs, itself defined using well-founded orderings on proof objects. This foundational framework allows for abstract definitions of canonical presentations and very general characterizations of saturation and redundancy criteria.
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Box 39040, RamatAviv</s1><s2>Tel Aviv 69978</s2><s3>ISR</s3><sZ>1 aut.</sZ></inist:fA14><country>Israël</country><wicri:noRegion>Tel Aviv 69978</wicri:noRegion></affiliation></author><author><name sortKey="Kirchner, Claude" sort="Kirchner, Claude" uniqKey="Kirchner C" first="Claude" last="Kirchner">Claude Kirchner</name><affiliation wicri:level="3"><inist:fA14 i1="02"><s1>JNRJA & LORIA, 615, rue du Jardin Botanique, B.P 101</s1><s2>54602 WIers-les-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">WIers-les-Nancy</settlement></placeName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">06-0371738</idno><date when="2006">2006</date><idno type="stanalyst">PASCAL 06-0371738 INIST</idno><idno type="RBID">Pascal:06-0371738</idno><idno type="wicri:Area/PascalFrancis/Corpus">000434</idno><idno type="wicri:Area/PascalFrancis/Curation">000599</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000411</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000411</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Abstract canonical presentations</title><author><name sortKey="Dershowitz, Nachum" sort="Dershowitz, Nachum" uniqKey="Dershowitz N" first="Nachum" last="Dershowitz">Nachum Dershowitz</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>School of Computer Science, Tel Aviv University, P.O. Box 39040, RamatAviv</s1><s2>Tel Aviv 69978</s2><s3>ISR</s3><sZ>1 aut.</sZ></inist:fA14><country>Israël</country><wicri:noRegion>Tel Aviv 69978</wicri:noRegion></affiliation></author><author><name sortKey="Kirchner, Claude" sort="Kirchner, Claude" uniqKey="Kirchner C" first="Claude" last="Kirchner">Claude Kirchner</name><affiliation wicri:level="3"><inist:fA14 i1="02"><s1>JNRJA & LORIA, 615, rue du Jardin Botanique, B.P 101</s1><s2>54602 WIers-les-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">WIers-les-Nancy</settlement></placeName></affiliation></author></analytic><series><title level="j" type="main">Theoretical computer science</title><title level="j" type="abbreviated">Theor. comput. sci.</title><idno type="ISSN">0304-3975</idno><imprint><date when="2006">2006</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Theoretical computer science</title><title level="j" type="abbreviated">Theor. comput. sci.</title><idno type="ISSN">0304-3975</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Canonical rewriting</term><term>Canonicity</term><term>Completion</term><term>Computer theory</term><term>Equational logic</term><term>Normal form</term><term>Proof ordering</term><term>Redundancy</term><term>Rewriting</term><term>Saturation</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Complétion</term><term>Forme normale</term><term>Saturation</term><term>Redondance</term><term>Réécriture</term><term>Informatique théorique</term><term>Problème mot</term><term>Logique équationnelle</term><term>Réécriture canonique</term><term>Canonicité</term><term>Relation ordre preuve</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Solving goals-like proving properties, deciding word problems or resolving constraints-is much easier with some presentations of the underlying theory than with others. Typically, what have been called "completion processes", in particular in the study of equational logic, involve finding appropriate presentations of a given theory to more easily solve a given class of problems. We provide a general proof-theoretic setting that relies directly on the fundamental concept of "good", that is, normal-form, proofs, itself defined using well-founded orderings on proof objects. This foundational framework allows for abstract definitions of canonical presentations and very general characterizations of saturation and redundancy criteria.</div></front></TEI><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0304-3975</s0></fA01><fA02 i1="01"><s0>TCSCDI</s0></fA02><fA03 i2="1"><s0>Theor. comput. sci.</s0></fA03><fA05><s2>357</s2></fA05><fA06><s2>1-3</s2></fA06><fA08 i1="01" i2="1" l="ENG"><s1>Abstract canonical presentations</s1></fA08><fA09 i1="01" i2="1" l="ENG"><s1>Clifford lectures and the mathematical foundations of programmming semantics, New Orleans, March 20-26, 2002</s1></fA09><fA11 i1="01" i2="1"><s1>DERSHOWITZ (Nachum)</s1></fA11><fA11 i1="02" i2="1"><s1>KIRCHNER (Claude)</s1></fA11><fA12 i1="01" i2="1"><s1>ARTEMOV (Sergei)</s1><s9>ed.</s9></fA12><fA12 i1="02" i2="1"><s1>MISLOVE (Michael)</s1><s9>ed.</s9></fA12><fA14 i1="01"><s1>School of Computer Science, Tel Aviv University, P.O. Box 39040, RamatAviv</s1><s2>Tel Aviv 69978</s2><s3>ISR</s3><sZ>1 aut.</sZ></fA14><fA14 i1="02"><s1>JNRJA & LORIA, 615, rue du Jardin Botanique, B.P 101</s1><s2>54602 WIers-les-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ></fA14><fA15 i1="01"><s1>Computer Science, CUNY Graduate Center, 365 Fifth Avenue</s1><s2>New York, NY 10016</s2><s3>USA</s3><sZ>1 aut.</sZ></fA15><fA15 i1="02"><s1>Department of Mathematics, Tulane University</s1><s2>New Orleans, LA 70118</s2><s3>USA</s3><sZ>2 aut.</sZ></fA15><fA20><s1>53-69</s1></fA20><fA21><s1>2006</s1></fA21><fA23 i1="01"><s0>ENG</s0></fA23><fA43 i1="01"><s1>INIST</s1><s2>17243</s2><s5>354000138873780040</s5></fA43><fA44><s0>0000</s0><s1>© 2006 INIST-CNRS. 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