Modular proof systems for partial functions with Evans equality
Identifieur interne : 005595 ( Main/Exploration ); précédent : 005594; suivant : 005596Modular proof systems for partial functions with Evans equality
Auteurs : Harald Ganzinger [Allemagne] ; Viorica Sofronie-Stokkermans [Allemagne] ; Uwe Waldmann [Allemagne]Source :
- Information and computation : (Print) [ 0890-5401 ] ; 2006.
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- Pascal (Inist)
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- topic : Preuve.
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Abstract
The paper presents a modular superposition calculus for the combination of first-order theories involving both total and partial functions. The modularity of the calculus is a consequence of the fact that all the inferences are pure-only involving clauses over the alphabet of either one, but not both, of the theories-when refuting goals represented by sets of pure formulae. The calculus is shown to be complete provided that functions that are not in the intersection of the component signatures are declared as partial. This result also means that if the unsatisfiability of a goal modulo the combined theory does not depend on the totality of the functions in the extensions, the inconsistency will be effectively found. Moreover, we consider a constraint superposition calculus for the case of hierarchical theories and show that it has a related modularity property. Finally, we identify cases where the partial models can always be made total so that modular superposition is also complete with respect to the standard (total function) semantics of the theories.
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aut.</sZ></inist:fA14><country>Allemagne</country><placeName><region type="land" nuts="2">Sarre (Land)</region><settlement type="city">Sarrebruck</settlement></placeName></affiliation></author><author><name sortKey="Sofronie Stokkermans, Viorica" sort="Sofronie Stokkermans, Viorica" uniqKey="Sofronie Stokkermans V" first="Viorica" last="Sofronie-Stokkermans">Viorica Sofronie-Stokkermans</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Max-Planck-Institut für Informatik, Stuhtsatzenhausweg 85</s1><s2>66123 Saarbrücken</s2><s3>DEU</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>Allemagne</country><placeName><region type="land" nuts="2">Sarre (Land)</region><settlement type="city">Sarrebruck</settlement></placeName></affiliation></author><author><name sortKey="Waldmann, Uwe" sort="Waldmann, Uwe" uniqKey="Waldmann U" first="Uwe" last="Waldmann">Uwe Waldmann</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Max-Planck-Institut für Informatik, Stuhtsatzenhausweg 85</s1><s2>66123 Saarbrücken</s2><s3>DEU</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>Allemagne</country><placeName><region type="land" nuts="2">Sarre (Land)</region><settlement type="city">Sarrebruck</settlement></placeName></affiliation></author></analytic><series><title level="j" type="main">Information and computation : (Print)</title><title level="j" type="abbreviated">Inf. comput. : (Print)</title><idno type="ISSN">0890-5401</idno><imprint><date when="2006">2006</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Information and computation : (Print)</title><title level="j" type="abbreviated">Inf. comput. : (Print)</title><idno type="ISSN">0890-5401</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Alphabet</term><term>Computer theory</term><term>Constraint</term><term>Evans function</term><term>First order</term><term>Intersection</term><term>Modular system</term><term>Semantics</term><term>Superposition</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Système modulaire</term><term>Fonction Evans</term><term>Superposition</term><term>Ordre 1</term><term>Alphabet</term><term>Intersection</term><term>Contrainte</term><term>Sémantique</term><term>Informatique théorique</term><term>Proof systems</term><term>Système preuve</term><term>Preuve</term><term>Fonction partielle</term><term>Modularité</term><term>68Q55</term></keywords><keywords scheme="Wicri" type="topic" xml:lang="fr"><term>Preuve</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The paper presents a modular superposition calculus for the combination of first-order theories involving both total and partial functions. The modularity of the calculus is a consequence of the fact that all the inferences are pure-only involving clauses over the alphabet of either one, but not both, of the theories-when refuting goals represented by sets of pure formulae. The calculus is shown to be complete provided that functions that are not in the intersection of the component signatures are declared as partial. This result also means that if the unsatisfiability of a goal modulo the combined theory does not depend on the totality of the functions in the extensions, the inconsistency will be effectively found. Moreover, we consider a constraint superposition calculus for the case of hierarchical theories and show that it has a related modularity property. Finally, we identify cases where the partial models can always be made total so that modular superposition is also complete with respect to the standard (total function) semantics of the theories.</div></front></TEI><affiliations><list><country><li>Allemagne</li></country><region><li>Sarre (Land)</li></region><settlement><li>Sarrebruck</li></settlement></list><tree><country name="Allemagne"><region name="Sarre (Land)"><name sortKey="Ganzinger, Harald" sort="Ganzinger, Harald" uniqKey="Ganzinger H" first="Harald" last="Ganzinger">Harald Ganzinger</name></region><name sortKey="Sofronie Stokkermans, Viorica" sort="Sofronie Stokkermans, Viorica" uniqKey="Sofronie Stokkermans V" first="Viorica" last="Sofronie-Stokkermans">Viorica Sofronie-Stokkermans</name><name sortKey="Waldmann, Uwe" sort="Waldmann, Uwe" uniqKey="Waldmann U" first="Uwe" last="Waldmann">Uwe Waldmann</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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