Automated Synthesis of a Finite Complexity Ordering for Saturation
Identifieur interne : 001C23 ( Main/Exploration ); précédent : 001C22; suivant : 001C24Automated Synthesis of a Finite Complexity Ordering for Saturation
Auteurs : Yannick Chevalier [France] ; Mounira Kourjieh [France]Source :
Descripteurs français
- Wicri :
- topic : Résolution.
English descriptors
Abstract
We present in this paper a new procedure to saturate a set of clauses with respect to a well-founded ordering on ground atoms such that A < B implies Var(A) ⊆ Var(B) for every atoms A and B. This condition is satisfied by any atom ordering compatible with a lexicographic, recursive, or multiset path ordering on terms. Our saturation procedure is based on a priori ordered resolution and its main novelty is the on-the-fly construction of a finite complexity atom ordering. In contrast with the usual redundancy, we give a new redundancy notion and we prove that during the saturation a non-redundant inference by a priori ordered resolution is also an inference by a posteriori ordered resolution. We also prove that if a set S of clauses is saturated with respect to an atom ordering as described above then the problem of whether a clause C is entailed from S is decidable.
Url:
Affiliations:
- France
- Franche-Comté, Grand Est, Lorraine (région)
- Belfort, Besançon, Metz, Nancy
- Université de Bourgogne Franche-Comté, Université de Franche-Comté, Université de Lorraine, Université de technologie de Belfort-Montbéliard
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Le document en format XML
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type="url">http://www.cnrs.fr/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><settlement type="city">Metz</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université de Lorraine</orgName><placeName><settlement type="city" wicri:auto="siege">Besançon</settlement><region type="region" nuts="2">Franche-Comté</region></placeName><orgName type="university">Université de Franche-Comté</orgName><orgName type="institution" wicri:auto="newGroup">Université de Bourgogne Franche-Comté</orgName><placeName><settlement type="city" wicri:auto="siege">Belfort</settlement><region type="region" nuts="2">Franche-Comté</region></placeName><orgName type="university">Université de technologie de Belfort-Montbéliard</orgName></affiliation></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Ground entailment problem</term><term>Resolution</term><term>decidability</term><term>first order logic</term></keywords><keywords scheme="Wicri" type="topic" xml:lang="fr"><term>Résolution</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We present in this paper a new procedure to saturate a set of clauses with respect to a well-founded ordering on ground atoms such that A < B implies Var(A) ⊆ Var(B) for every atoms A and B. This condition is satisfied by any atom ordering compatible with a lexicographic, recursive, or multiset path ordering on terms. Our saturation procedure is based on a priori ordered resolution and its main novelty is the on-the-fly construction of a finite complexity atom ordering. In contrast with the usual redundancy, we give a new redundancy notion and we prove that during the saturation a non-redundant inference by a priori ordered resolution is also an inference by a posteriori ordered resolution. We also prove that if a set S of clauses is saturated with respect to an atom ordering as described above then the problem of whether a clause C is entailed from S is decidable.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Franche-Comté</li><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Belfort</li><li>Besançon</li><li>Metz</li><li>Nancy</li></settlement><orgName><li>Université de Bourgogne Franche-Comté</li><li>Université de Franche-Comté</li><li>Université de Lorraine</li><li>Université de technologie de Belfort-Montbéliard</li></orgName></list><tree><country name="France"><noRegion><name sortKey="Chevalier, Yannick" sort="Chevalier, Yannick" uniqKey="Chevalier Y" first="Yannick" last="Chevalier">Yannick Chevalier</name></noRegion><name sortKey="Kourjieh, Mounira" sort="Kourjieh, Mounira" uniqKey="Kourjieh M" first="Mounira" last="Kourjieh">Mounira Kourjieh</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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