C. Tinelli and M.T. Harandi. Constraint logic programming over unions of constraint theories. The Journal of Functional and Logic Programming, Article 6, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....are then propagated to the second, in the hope that it can be simplified. Examples are Prolog III and CLP(R) 21] in which the linear part of a constraint problem on reals is solved first, while the nonlinear part is delayed. Another approach employing several constraint solvers is proposed in ([30, 37]) First, each solver is applied to the appropriate numeric Y y 2 I I I Lx X Y (c) Figure 6. Search in numeric CSPs. a) interval method, b) backU ack search instantiating the midvalue of an interval, c) backU ack search in which instantiated midvalues of intervals are propagated using ....

Tinelli, C., & Hat'andi, M. (1996). Constraint logic programming over unions of constraint theories. Lecture Notes in Computer Science, 1118: 436-450.

....3.3 is to show that if 1 is also universal and 2 have the same function symbols and contain only finitary formulas, then # is a ground finitary formula. The only research we are aware of that focuses on the cooperation of background reasoners in theory reasoning is that reported in [KZ90, TH98, BR99, Pet00] Except for [Pet00] all of these works embed a well known combination method by Nelson and Oppen [NO79] into a specific theory reasoning calculus: analytic tableaux in [KZ90] a variant of the CLP scheme in [TH98] and constrained resolution in [BR99] In essence, the approach in ....

.... of background reasoners in theory reasoning is that reported in [KZ90, TH98, BR99, Pet00] Except for [Pet00] all of these works embed a well known combination method by Nelson and Oppen [NO79] into a specific theory reasoning calculus: analytic tableaux in [KZ90] a variant of the CLP scheme in [TH98] and constrained resolution in [BR99] In essence, the approach in each of these papers is a specialization of the one presented here. One major di#erence is that the background reasoners return only residues of the form ##, which basically means that they treat key sets as if they were ....

Cesare Tinelli and Mehdi T. Harandi. Constraint logic programming over unions of constraint theories. The Journal of Functional and Logic Programming, 1998(6), December 1998.

....in pruning power to existing methods [Faltings, 1994] Gelle, 1998] A new search method embedding local consistency for discrete and numeric variables is proposed. In contrast to most existing approaches for solving mixed CSPs, which are based on a cooperation between constraint solvers [Tinelli and Harandi, 1996], it integrates the local consistency methods for discrete and numeric variables into the search process and also makes use of the mixed constraints to prune the search space. Finally, a new algorithm is introduced for solving conditional constraint problems with numeric constraints. From the ....

Tinelli, C. and Harandi, M. (1996). Constraint logic programming over unions of constraint theories. Lecture Notes in Computer Science, 1118:436{ 450.

....unify either by another unification strategy like unifyC, unifyAC or unifyBool, or by a strategy for handling Constraint Satisfaction Problems [14] CSPs) The computation domain could also be a union of equational theories (Section 4. 1) and more generally a union of non equational theories like in [49]. Moreover, additional transformation rules are also convenient to take into account the specificity of the computation domain, like the success rule for the Herbrand Universe. The strategy for applying CLP rules can be modified as well and enriched by possible new rules. 5 Programming with ....

C. Tinelli and M. Harandi. Constraint logic programming over unions of constraint theories. In E. C. Freuder, editor, Proceedings of the 2nd International Conference on Principles and Practice of Constraint Programming, Cambridge, MA, USA, volume 1118 of Lecture Notes in Computer Science, pages 436--450. Springer-Verlag, August 1996.

....adoption of different integration schemes and methodologies. While it is important to develop constraint solving techniques in the domain of interest, it is equally important to compare solutions developed in different settings and to look for opportunities of cross fertilisation. For instance, [19] describes how Nelson and Oppen s approach to combining decision procedures [16] developed in the context of Automated Deduction can be lifted to a technique for building composite constraint solvers to be used in Constraint Logic Programming (CLP) In this paper we compare the CLP scheme with a ....

Cesare Tinelli and Mehdi Harandi. Constraint logic programming over unions of constraint theories. Journal of Logic and Functional Programming, 1998. (to appear).

....as part of a second, empty theory and the usual inference steps identifying complementary literals as a background reasoner returning only residues. 5 Related Work The only research we are aware of that focuses on the cooperation of background reasoners in theory reasoning is that reported in [4, 9, 1, 7]. Except for [7] all of these works embed a well known combination method by Nelson and Oppen [5] into a specific theory reasoning calculus: analytic tableaux in [4] a variant of the CLP scheme in [9] and constrained resolution in [1] Although it is not entirely accurate, we could say that ....

.... on the cooperation of background reasoners in theory reasoning is that reported in [4, 9, 1, 7] Except for [7] all of these works embed a well known combination method by Nelson and Oppen [5] into a specific theory reasoning calculus: analytic tableaux in [4] a variant of the CLP scheme in [9], and constrained resolution in [1] Although it is not entirely accurate, we could say that the approach in each of these papers is a specialization of the one presented here. One essential di#erence is that the signatures of the two background theories share at most the equality and the ....

C. Tinelli and M. T. Harandi. Constraint logic programming over unions of constraint theories. The Journal of Functional and Logic Programming, 1998(6).

....an extension of the scheme that can include constraint domains built as the combination of a number of independent domains, such as, for instance, the domains of finite trees, real numbers, lists, strings, partial orders, and so on. An earlier, less detailed version of our extension appeared in [TH96a] 1.1 Notation and Conventions We adhere rather closely to the notation and definitions given in [Sho67] for what concerns mathematical logic in general, and [JM94] for what concerns constraint logic programming in particular. We report here the most notable notational conventions followed. ....

Cesare Tinelli and Mehdi Harandi. Constraint logic programming over unions of constraint theories. In E. C. Freuder, editor, Proceedings of the 2nd International Conference on Principles and Practice of Constraint Programming (Cambridge, MA), volume 1118 of Lecture Notes in Computer Science, pages 436--450, Berlin, August 1996. Springer-Verlag.

....as part of a second, empty theory and the usual inference steps identifying complementary literals as a background reasoner returning only residues. 5 Related Work The only research we are aware of that focuses on the cooperation of background reasoners in theory reasoning is that reported in [4, 9, 1, 7]. Except for [7] all of these works embed a well known combination method by Nelson and Oppen [5] into a speci c theory reasoning calculus: analytic tableaux in [4] a variant of the CLP scheme in [9] and constrained resolution in [1] Although it is not entirely accurate, we could say that the ....

.... on the cooperation of background reasoners in theory reasoning is that reported in [4, 9, 1, 7] Except for [7] all of these works embed a well known combination method by Nelson and Oppen [5] into a speci c theory reasoning calculus: analytic tableaux in [4] a variant of the CLP scheme in [9], and constrained resolution in [1] Although it is not entirely accurate, we could say that the approach in each of these papers is a specialization of the one presented here. One essential di erence is that the signatures of the two background theories share at most the equality and the ....

C. Tinelli and M. T. Harandi. Constraint logic programming over unions of constraint theories. The Journal of Functional and Logic Programming, 1998(6). 224

....universal rsal 5 T . Also, we will implicitly assume for all tableaux mentioned below that the signature of their formulas is (included in) sko . 10 We must say in principle here because we are ignoring eciency concerns. 12 De nition 4.1 Let S = V; E) and S 0 be two tableaux. We say that S 0 T derives from S i S 0 is obtained from S in one of the following ways: 1. by applying one of the expansion rules in Fig. 2 to a formula in a branch B of S, i.e. by de ning S 0 as follows for some 2 B: S 0 : 8 : V [ f 1 ; 2 g; E [ fhleaf (B) 1 i; h 1 ; 2 ....

....A (possibly in nite) sequence (S j ) j of tableaux is a (tableau) T derivation i for all j 0, S j derives from S j 1 . We say that a tableau branch B 0 extends a tableau branch B if there is a substitution such that B , as a path, is an initial segment of B 0 (possibly coinciding with B 0 ) It is easy to verify that every branch of a tableau in a T derivation extends one, and only one, branch in each previous tableau in the derivation. De nition 4.3 (Proof) Let be an sentence. A T derivation (S j ) j is a (tableau) T derivation of i S 0 is a tableau whose only node ....

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Cesare Tinelli and Mehdi T. Harandi. Constraint logic programming over unions of constraint theories. The Journal of Functional and Logic Programming,

....part of a second, empty theory and the usual inference steps identifying complementary literals as a background reasoner returning only # residues. 5 Related Work The only research we are aware of that focuses on the cooperation of background reasoners in theory reasoning is that reported in [4, 9, 1, 7]. Except for [7] all of these works embed a well known combination method by Nelson and Oppen [5] into a specific theory reasoning calculus: analytic tableaux in [4] a variant of the CLP scheme in [9] and constrained resolution in [1] Although it is not entirely accurate, we could say that ....

.... on the cooperation of background reasoners in theory reasoning is that reported in [4, 9, 1, 7] Except for [7] all of these works embed a well known combination method by Nelson and Oppen [5] into a specific theory reasoning calculus: analytic tableaux in [4] a variant of the CLP scheme in [9], and constrained resolution in [1] Although it is not entirely accurate, we could say that the approach in each of these papers is a specialization of the one presented here. One essential di#erence is that the signatures of the two background theories share at most the equality and the ....

C. Tinelli and M. T. Harandi. Constraint logic programming over unions of constraint theories. The Journal of Functional and Logic Programming, 1998(6).

....in the way we describe it here 2 . Besides in its relative generality, the Nelson Oppen method s appeal also lies in its easy integrability, in principle, into most Constraint based Reasoning framework. The integration of the method into the Constraint Logic Programming Scheme is described in [TH98] The method s main limitations are its restriction to a quantifierfree language of constraints and, more importantly, to component theories that share no function or predicate symbols besides the equality symbol. 1.2 Our Approach The problem of combining non disjoint theories is of prime ....

Cesare Tinelli and Mehdi Harandi. Constraint logic programming over unions of constraint theories. Journal of Logic and Functional Programming, 1998. (to appear).

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C. Tinelli and M.T. Harandi. Constraint logic programming over unions of constraint theories. The Journal of Functional and Logic Programming, Article 6, 1998.

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C. Tinelli and M.T. Harandi. Constraint logic programming over unions of constraint theories. The Journal of Functional and Logic Programming, Article 6, 1998.

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