Bruno de Backer and Henri Beringer. Intelligent backtracking for CLP languages: An application to CLP(R). In Vijay Saraswat and Kazunori Ueda, editors, ILPS'91: Proceedings International Logic Programming Symposium, pages 405--419, San Diego, CA, October 1991. MIT Press.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....merge and maintain no goods for any combination of nonzero dual values in any infeasible LP node, and can infer primitive and nonprimitive constraints which will strengthen SFD . A related use of the infeasible combination has previously been explored in the context of intelligent backtracking (De Backer Beringer 1991). Figure 2 shows our nogood constraint and the other basic nonprimitive constraints of MLLP. Element FD Fnan Fnan OO Fnan Fnan Element LP Fnan Fnan Fnan Fnan 33 Conditional y i Ax b Fnan Fnan 33 Fnan Fnan FD Store LP Store Nogood W :y i Fnan Fnan [ Fnan Fnan ....

De Backer, B., and Beringer, H. 1991. Intelligent backtracking for CLP languages: An application to CLP(R). In Saraswat, V., and Ueda, K., eds., Logic Programming, Proceedings of the 1991 International Symposium, 405--419.

....is identified. A stronger result is: Theorem 4. Once the solved form algorithm detects unsatisfiability in (5) the constraints identified by the non basic variables with nonzero coefficients constitute a minimal inconsistent subset of the set of constraints. We draw upon a result by deBacker [1], which extended Lassez s Quasi Dual results [11] based on Fourier s theorem. Theorem5 Fourier 1827. A set S of inequalities is inconsistent iff there exists a positive linear combination of inequalities which give 0 k, where k 0. S : 8 : n X j=1 a ij x j b i 9 = iffl1: m (9) ....

Backer B.de, Beringer H.: Intelligent Backtracking for CLP Languages: An Application to CLP(R), in Saraswat V. & Ueda K.(eds.), Symposion on Logic Programming, MIT Press, Cambridge, MA, pp.405-419, 1991.

....subsets of constraints on failure. This algorithm must operate on the same constraint representation which the solver uses during the derivation sequence of a CLP system. ffl and finally compare the failure analysis methods proposed here to the two other methods proposed in the literature [DBB91, Hav92] for the domain of linear constraints over the reals. The rest of this paper is organised as follows. In section 2 the motivations for using intelligent backtracking in a CLP( system are briefly presented. Section 3 illustrates some of the issues a failure analysis procedure must handle, by ....

....arises. In a future report we will examine the application of our failure analysis procedure to incremental user interfaces. To summarise, 1. the prospective wide applicability of intelligent backtracking in CLP( systems in such diverse areas as spatial reasoning [THL91] model based diagnosis [DBB91], disjunctive scheduling and resource allocation [Bak74] electrical enginnering [HMS92] expert systems [Hav92] incremental user interfaces [MS89] 2. as well as the fact that finite domain search algorithms are not easily applicable 3. and the encouraging result that a minimal inconsistent ....

[Article contains additional citation context not shown here]

Bruno De Backer and Henri Beringer. Intelligent backtracking for CLP languages: An application to CLP(R). In Vijay Saraswat and Kazunori Ueda, editors, Logic Programming, Proceedings of the 1991 International Symposium, pages 405--419, San Diego, USA, 1991. The MIT Press.

....prove its completeness in a simple framework of constraints as closure operators. The second requirement concerns the capability of the constraint solver to identify the causes of an inconsistency. This problem has been well studied in the context of intelligent backtracking for Prolog [7] CLP(R) [9] and CLP(FD) 5] For CLP(R) it is shown in [9] that the Quasi Dual algorithm of Lassez [20] provides in fact a minimal conflict. For CLP(FD) we show in the next section how the dependency graph provides also a solution to this requirement. 4. INCREMENTAL CONSTRAINT PROPAGATION ALGORITHMS In ....

....constraints as closure operators. The second requirement concerns the capability of the constraint solver to identify the causes of an inconsistency. This problem has been well studied in the context of intelligent backtracking for Prolog [7] CLP(R) 9] and CLP(FD) 5] For CLP(R) it is shown in [9] that the Quasi Dual algorithm of Lassez [20] provides in fact a minimal conflict. For CLP(FD) we show in the next section how the dependency graph provides also a solution to this requirement. 4. INCREMENTAL CONSTRAINT PROPAGATION ALGORITHMS In this section, we present the dynamic constraint ....

B. De Backer and H. Beringer. Intelligent backtracking for clp languages: an application to clp(r). In ILPS'91. MIT Press, 1991.

....done through backtracking. Considering intelligent backtracking when using constraints has been introduced in the Constraint Programming community: either for Constraint Satisfaction Problems [ Dechter, 1990 ] or for Constraint Logic Programming (Logic Programming with constraint propagation) de Backer and B eringer, 1991 ] In the latter, an intelligent backtracking mechanism is proposed to be used with an incremental simplex algorithm solving sets of linear constraints. All intelligent backtracking techniques involve the computation of explanations (also called nogoods) when encountering a contradiction in the ....

Bruno de Backer and Henri B'eringer. Intelligent backtracking for CLP languages: An application to CLP(R). In Vijay Saraswat and Kazunori Ueda, editors, ILPS'91: Proceedings International Logic Programming Symposium, pages 405--419, San Diego, CA, October 1991. MIT Press.

....done through backtracking. Considering intelligent backtracking when using constraints has been introduced in the Constraint Programming community: either for Constraint Satisfaction Problems [ Dechter, 1990 ] or for Constraint Logic Programming (Logic Programming with constraint propagation) de Backer and B eringer, 1991 ] In the latter, an intelligent backtracking mechanism is proposed to be used with an incremental simplex solving sets of linear constraints. All intelligent backtracking techniques involve the computation of explanations (also called nogoods) when encountering a contradiction in the search ....

Bruno de Backer and Henri B'eringer. Intelligent backtracking for CLP languages: An application to CLP(R). In Vijay Saraswat and Kazunori Ueda, editors, ILPS'91: Proceedings International Logic Programming Symposium, pages 405--419, San Diego, CA, October 1991. MIT Press.

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Bruno de Backer and Henri Beringer. Intelligent backtracking for CLP languages: An application to CLP(R). In Vijay Saraswat and Kazunori Ueda, editors, ILPS'91: Proceedings International Logic Programming Symposium, pages 405--419, San Diego, CA, October 1991. MIT Press.

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