H'el`ene Kirchner. On the use of constraints in automated deduction. In A. Podelski, editor, Constraint Programming: Basics and Trends,  Home/Search   Document Details and Download   Summary   Related Articles   Check

....admits an incremental version. All of these characteristics enable its easy integration in the CLP paradigm [1] Theorem proving and constraints We have further investigated the concept of deduction with constraints. Previous results already described in previous reports have also been publihed [57, 63]. We have shown the completeness of an extension of SLD resolution to the equational setting [64] This proves a conjecture of Laurent Fribourg and shows the completeness of an implementation of his. It is the first completeness result for superposition of equational horn clauses which reduces ....

H'el`ene Kirchner. On the use of constraints in automated deduction. In A. Podelski, editor, Constraint Programming: Basics and Trends, volume 910 of Lecture Notes in Computer Science, pages 128--146. SpringerVerlag, 1995.

....botanique BP 101 54602 Villers l es Nancy Cedex, France email: fFarid.Ajili,Claude.Kirchnerg loria.fr In less than a decade, Deduction with Constraints (DwC) has opened a new universe in computer science. DwC can be viewed from two perspectives: one related to the automated deduction framework [17, 19], the other to the development and usage of programming languages based on logic [7, 14] Within the automated deduction framework, constraints on the generic data structure terms have become a popular tool because they allow to express and encode strategies and to modularise deduction ....

.... the other to the development and usage of programming languages based on logic [7, 14] Within the automated deduction framework, constraints on the generic data structure terms have become a popular tool because they allow to express and encode strategies and to modularise deduction processes [19]. We call symbolic, constraints over terms [11] There are plenty of symbolic constraint systems, some examples are unification (see [16] for a survey) disunification [10] ordering [5] membership [9, 13] and feature constraints [1] The most well known example is equational unification. ....

H'el`ene Kirchner. On the use of constraints in automated deduction. In A. Podelski, editor, Constraint Programming: Basics and Trends, volume 910 of Lecture Notes in Computer Science, pages 128--146. Springer-Verlag, 1995.

....provers RRL [12] SPIKE [2] and STeP [15] Here we focus on constraint contextual rewriting (CCR) which generalises contextual rewriting by incorporating the functionalities provided by a decision procedure. For a different approach to integrating constraint solving with term rewriting see, e.g. [13]. In what follows E and E 0 are ground clauses, i.e. finite sets of ( Sigma j ; Pi j ) literals. 1 The disjointness of Sigma p and Sigma c is not required, instead it is assumed that Sigma c Sigma p = Sigma j . C, C 0 , and C 00 are constraint stores, i.e. sets of ( Sigma j ; Pi ....

H. Kirchner. On the use of constraints in automated deduction. Lecture Notes in Computer Science, 910:128--??, 1995.

....CSP solving. Section 4 presents c fl 1996 Elsevier Science B. V. C. Castro in details the computational system we have developed. Finally, Section 5 concludes the paper. 2 Basic De nitions and Notation In this section we formalise CSP. The basic concepts and de nitions that we use are based on [10,11,24]. De nition 2.1 [CSP] An elementary constraint c is an atomic formula built on a signature Sigma = F ; P) where F is a set of ranked function symbols and P a set of ranked predicate symbols, and a denumerable set X of variable symbols. Elementary constraints can be combined with usual ....

H. Kirchner. On the Use of Constraints in Automated Deduction. In A. Podelski, editor, Constraint Programming: Basics and Trends, volume 910 of Lecture Notes in Computer Science, pages 128146. Springer-Verlag, 1995.

.... theorem proving system based on the sequent calculus for classical logic (Anufriev and Aselderov [1] Degtyarev, Zhezherun and Lyaletski [3] see also the survey by Degtyarev and Voronkov [2] The use of constraints in automated deduction is investigated in many papers (see the survey by Kirchner [11]) In this article, we consider the use of constraints in intuitionistic logic. In particular, we obtain some complexity results for the problem of the instantiation of derivation skeletons and for the prenex fragment of intuitionistic logic. It is generally well known how to design sequent based ....

H. Kirchner. On the use of constraints in automated deduction. In A. Podelski, editor, Constraint Programming: Basics and Tools, volume 910 of Lecture Notes in Computer Science, pages 128--146. Springer Verlag, 1995.

....distinguish two levels of deduction and to use adequate and efficient tools at each level. This idea has been widely studied in the context of programming languages (the class of CLP languages) and knowledge representation. There are several advantages in using constraints in automated deduction [555]. They provide a way to make explicit every symbolic computation step, especially unification, orientation and typing problems to check while applying an inference rule. Moreover they keep track of choices made along a derivation and this is a way to avoid a new choice inconsistent with previous ....

H. Kirchner. On the Use of Constraints in Automated Deduction. In A. Podelski, editor, Constraint Programming: Basics and Trends, pages 128--146. Springer LNCS 910, 1995. \Phi.

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H'el`ene Kirchner. On the use of constraints in automated deduction. In A. Podelski, editor, Constraint Programming: Basics and Trends,

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