Unions of non-disjoint theories and combinations of satisfiability procedures
Identifieur interne : 000663 ( PascalFrancis/Checkpoint ); précédent : 000662; suivant : 000664Unions of non-disjoint theories and combinations of satisfiability procedures
Auteurs : Cesare Tinelli [États-Unis] ; Christophe Ringeissen [France]Source :
- Theoretical computer science [ 0304-3975 ] ; 2003.
Descripteurs français
- Pascal (Inist)
- Théorie décision, Satisfaisabilité, Raisonnement, Déduction, Consistance, Validité, Décidabilité, Algèbre universelle, Théorie équationnelle, Langage, Théorie langage, Composante, Complet, Résultat, Condition, Théorie contrainte, Procédure, Décision, Contrainte, Méthode, Nombre, Indice conditionnement, Modèle, Logique sous contrainte, Procedure combinaison, Procédure Nelson Oppen.
- Wicri :
English descriptors
- KwdEn :
- Combination procedure, Complete, Component, Condition, Condition number, Consistency, Constrained logic, Constraint, Constraint theory, Decidability, Decision, Decision theory, Deduction, Equational theory, Language, Language theory, Method, Models, Nelson Oppen procedure, Number, Procedure, Reasoning, Result, Satisfiability, Universal algebra, Validity.
Abstract
In this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory T1 and one that decides constraint satisfiability with respect to a constraint theory T2, produces a procedure that (semi-)decides constraint satisfiability with respect to the union of T1 and T2. We provide a number of model-theoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete, with special emphasis on the case in which the signatures of the component theories are non-disjoint. We also describe some general classes of theories to which our combination results apply, and relate our approach to some of the existing combination methods in the field.
Affiliations:
- France, États-Unis
- Grand Est, Iowa, Lorraine (région)
- Iowa City, Villers-lès-Nancy
- Université de l'Iowa
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type="city">Villers-lès-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="2003">2003</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>Combination procedure</term><term>Complete</term><term>Component</term><term>Condition</term><term>Condition number</term><term>Consistency</term><term>Constrained logic</term><term>Constraint</term><term>Constraint theory</term><term>Decidability</term><term>Decision</term><term>Decision theory</term><term>Deduction</term><term>Equational theory</term><term>Language</term><term>Language theory</term><term>Method</term><term>Models</term><term>Nelson Oppen procedure</term><term>Number</term><term>Procedure</term><term>Reasoning</term><term>Result</term><term>Satisfiability</term><term>Universal algebra</term><term>Validity</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Théorie décision</term><term>Satisfaisabilité</term><term>Raisonnement</term><term>Déduction</term><term>Consistance</term><term>Validité</term><term>Décidabilité</term><term>Algèbre universelle</term><term>Théorie équationnelle</term><term>Langage</term><term>Théorie langage</term><term>Composante</term><term>Complet</term><term>Résultat</term><term>Condition</term><term>Théorie contrainte</term><term>Procédure</term><term>Décision</term><term>Contrainte</term><term>Méthode</term><term>Nombre</term><term>Indice conditionnement</term><term>Modèle</term><term>Logique sous contrainte</term><term>Procedure combinaison</term><term>Procédure Nelson Oppen</term></keywords><keywords scheme="Wicri" type="topic" xml:lang="fr"><term>Langage</term><term>Décision</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory T<sub>1</sub> and one that decides constraint satisfiability with respect to a constraint theory T<sub>2</sub>, produces a procedure that (semi-)decides constraint satisfiability with respect to the union of T<sub>1</sub> and T<sub>2</sub>. We provide a number of model-theoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete, with special emphasis on the case in which the signatures of the component theories are non-disjoint. We also describe some general classes of theories to which our combination results apply, and relate our approach to some of the existing combination methods in the field.</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>290</s2></fA05><fA06><s2>1</s2></fA06><fA08 i1="01" i2="1" l="ENG"><s1>Unions of non-disjoint theories and combinations of satisfiability procedures</s1></fA08><fA11 i1="01" i2="1"><s1>TINELLI (Cesare)</s1></fA11><fA11 i1="02" i2="1"><s1>RINGEISSEN (Christophe)</s1></fA11><fA14 i1="01"><s1>Department of Computer Science, University of Iowa</s1><s2>Iowa City, IA 52242</s2><s3>USA</s3><sZ>1 aut.</sZ></fA14><fA14 i1="02"><s1>INRIA Lorraine and LORIA-CNRS, BP 101</s1><s2>54602 Villers-lès-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ></fA14><fA20><s1>291-353</s1></fA20><fA21><s1>2003</s1></fA21><fA23 i1="01"><s0>ENG</s0></fA23><fA43 i1="01"><s1>INIST</s1><s2>17243</s2><s5>354000105390550100</s5></fA43><fA44><s0>0000</s0><s1>© 2003 INIST-CNRS. All rights reserved.</s1></fA44><fA45><s0>51 ref.</s0></fA45><fA47 i1="01" i2="1"><s0>03-0108985</s0></fA47><fA60><s1>P</s1></fA60><fA61><s0>A</s0></fA61><fA64 i1="01" i2="1"><s0>Theoretical computer science</s0></fA64><fA66 i1="01"><s0>NLD</s0></fA66><fC01 i1="01" l="ENG"><s0>In this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory T<sub>1</sub> and one that decides constraint satisfiability with respect to a constraint theory T<sub>2</sub>, produces a procedure that (semi-)decides constraint satisfiability with respect to the union of T<sub>1</sub> and T<sub>2</sub>. We provide a number of model-theoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete, with special emphasis on the case in which the signatures of the component theories are non-disjoint. We also describe some general classes of theories to which our combination results apply, and relate our approach to some of the existing combination methods in the field.</s0></fC01><fC02 i1="01" i2="X"><s0>001D01A07</s0></fC02><fC03 i1="01" i2="X" l="FRE"><s0>Théorie décision</s0><s5>01</s5></fC03><fC03 i1="01" i2="X" l="ENG"><s0>Decision theory</s0><s5>01</s5></fC03><fC03 i1="01" i2="X" l="SPA"><s0>Teoría decisión</s0><s5>01</s5></fC03><fC03 i1="02" i2="X" l="FRE"><s0>Satisfaisabilité</s0><s5>02</s5></fC03><fC03 i1="02" i2="X" l="ENG"><s0>Satisfiability</s0><s5>02</s5></fC03><fC03 i1="02" i2="X" l="SPA"><s0>Satisfactoriabilidad</s0><s5>02</s5></fC03><fC03 i1="03" i2="X" l="FRE"><s0>Raisonnement</s0><s5>03</s5></fC03><fC03 i1="03" i2="X" l="ENG"><s0>Reasoning</s0><s5>03</s5></fC03><fC03 i1="03" i2="X" l="SPA"><s0>Razonamiento</s0><s5>03</s5></fC03><fC03 i1="04" i2="X" l="FRE"><s0>Déduction</s0><s5>04</s5></fC03><fC03 i1="04" i2="X" l="ENG"><s0>Deduction</s0><s5>04</s5></fC03><fC03 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