Abstract canonical presentations
Identifieur interne : 005816 ( Main/Merge ); précédent : 005815; suivant : 005817Abstract canonical presentations
Auteurs : Nachum Dershowitz [Israël] ; Claude Kirchner [France]Source :
- Theoretical computer science [ 0304-3975 ] ; 2006.
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
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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Pascal:06-0371738Le document en format XML
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<series><title level="j" type="main">Theoretical computer science</title>
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<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>
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<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>
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