InforLorV4, PascalFrancis, Corpus, bibRecord, 000415

Modular proof systems for partial functions with Evans equality

Identifieur interne : 000415 ( PascalFrancis/Corpus ); précédent : 000414; suivant : 000416

Modular proof systems for partial functions with Evans equality

Auteurs : Harald Ganzinger ; Viorica Sofronie-Stokkermans ; Uwe Waldmann

Source :

Information and computation : (Print) [ 0890-5401 ] ; 2006.

RBID : Pascal:06-0527635

Descripteurs français

Pascal (Inist)
- Système modulaire, Fonction Evans, Superposition, Ordre 1, Alphabet, Intersection, Contrainte, Sémantique, Informatique théorique, Proof systems, Système preuve, Preuve, Fonction partielle, Modularité, 68Q55.

English descriptors

KwdEn :
- Alphabet, Computer theory, Constraint, Evans function, First order, Intersection, Modular system, Semantics, Superposition.

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.

Notice en format standard (ISO 2709)

Pour connaître la documentation sur le format Inist Standard.

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A11	`01`	`1`		`@1 GANZINGER (Harald)`
A11	`02`	`1`		`@1 SOFRONIE-STOKKERMANS (Viorica)`
A11	`03`	`1`		`@1 WALDMANN (Uwe)`
A12	`01`	`1`		`@1 ARMANDO (Alessandro) @9 ed.`
A12	`02`	`1`		`@1 RINGEISSEN (Christophe) @9 ed.`
A14	`01`			`@1 Max-Planck-Institut für Informatik, Stuhtsatzenhausweg 85 @2 66123 Saarbrücken @3 DEU @Z 1 aut. @Z 2 aut. @Z 3 aut.`
A15	`01`			`@1 DIST, University of Genova @3 ITA @Z 1 aut.`
A15	`02`			`@1 LORIA & INRIA-Lorraine @2 54500 Vandoeuvre-les-Nancy @3 FRA @Z 2 aut.`
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A44				`@0 0000 @1 © 2006 INIST-CNRS. All rights reserved.`
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A64	`01`	`1`		`@0 Information and computation : (Print)`
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C01	`01`		`ENG`	@0 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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C03	`09`	`X`	`FRE`	`@0 Informatique théorique @5 25`
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C03	`10`	`X`	`FRE`	`@0 Proof systems @4 INC @5 70`
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Format Inist (serveur)

NO :	PASCAL 06-0527635 INIST
ET :	Modular proof systems for partial functions with Evans equality
AU :	GANZINGER (Harald); SOFRONIE-STOKKERMANS (Viorica); WALDMANN (Uwe); ARMANDO (Alessandro); RINGEISSEN (Christophe)
AF :	Max-Planck-Institut für Informatik, Stuhtsatzenhausweg 85/66123 Saarbrücken/Allemagne (1 aut., 2 aut., 3 aut.); DIST, University of Genova/Italie (1 aut.); LORIA & INRIA-Lorraine/54500 Vandoeuvre-les-Nancy/France (2 aut.)
DT :	Publication en série; Niveau analytique
SO :	Information and computation : (Print); ISSN 0890-5401; Coden INFCEC; Etats-Unis; Da. 2006; Vol. 204; No. 10; Pp. 1453-1492; Bibl. 28 ref.
LA :	Anglais
EA :	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.
CC :	001D02A08; 001D02A02
FD :	Système modulaire; Fonction Evans; Superposition; Ordre 1; Alphabet; Intersection; Contrainte; Sémantique; Informatique théorique; Proof systems; Système preuve; Preuve; Fonction partielle; Modularité; 68Q55
ED :	Modular system; Evans function; Superposition; First order; Alphabet; Intersection; Constraint; Semantics; Computer theory
SD :	Sistema modular; Función Evans; Superposición; Orden 1; Alfabeto; Intersección; Coacción; Semántica; Informática teórica
LO :	INIST-8341.354000157254510020
ID :	06-0527635

Links to Exploration step

Pascal:06-0527635

Le document en format XML

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<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>
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<fC01 i1="01" l="ENG"><s0>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.</s0>
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<s5>19</s5>
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<s5>20</s5>
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<s5>20</s5>
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<s5>21</s5>
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<s5>21</s5>
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<s5>23</s5>
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<s5>24</s5>
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<s5>24</s5>
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<s5>75</s5>
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<fN44 i1="01"><s1>OTO</s1>
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<fN82><s1>OTO</s1>
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<server><NO>PASCAL 06-0527635 INIST</NO>
<ET>Modular proof systems for partial functions with Evans equality</ET>
<AU>GANZINGER (Harald); SOFRONIE-STOKKERMANS (Viorica); WALDMANN (Uwe); ARMANDO (Alessandro); RINGEISSEN (Christophe)</AU>
<AF>Max-Planck-Institut für Informatik, Stuhtsatzenhausweg 85/66123 Saarbrücken/Allemagne (1 aut., 2 aut., 3 aut.); DIST, University of Genova/Italie (1 aut.); LORIA & INRIA-Lorraine/54500 Vandoeuvre-les-Nancy/France (2 aut.)</AF>
<DT>Publication en série; Niveau analytique</DT>
<SO>Information and computation : (Print); ISSN 0890-5401; Coden INFCEC; Etats-Unis; Da. 2006; Vol. 204; No. 10; Pp. 1453-1492; Bibl. 28 ref.</SO>
<LA>Anglais</LA>
<EA>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.</EA>
<CC>001D02A08; 001D02A02</CC>
<FD>Système modulaire; Fonction Evans; Superposition; Ordre 1; Alphabet; Intersection; Contrainte; Sémantique; Informatique théorique; Proof systems; Système preuve; Preuve; Fonction partielle; Modularité; 68Q55</FD>
<ED>Modular system; Evans function; Superposition; First order; Alphabet; Intersection; Constraint; Semantics; Computer theory</ED>
<SD>Sistema modular; Función Evans; Superposición; Orden 1; Alfabeto; Intersección; Coacción; Semántica; Informática teórica</SD>
<LO>INIST-8341.354000157254510020</LO>
<ID>06-0527635</ID>
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Modular proof systems for partial functions with Evans equality

Modular proof systems for partial functions with Evans equality

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