Vincent J. Digricoli and Malcolm C. Harrison. Equality-Based binary Resolution. Journal of the Association for Computing Machinery, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....theorem 3 we obtain an order sorted equational logic programming language. We mentioned only a few applications of theorem 7. Due to its universal nature, we can instantiate it also with any other technique developed for solving sets of equations under equational theories, e.g. RUE resolution [Digricoli and Harrison, 1986] or flattening and SLD resolution [Barbuti et al. 1986; Cox and Pietrzykowski, 1986] Our result can easily be generalized to those constraint logic languages, whose constraint solver is sound, strongly complete, and independent. This implies in particular that the computation of the constraints ....

Digricoli, V. J. and Harrison, M. C. (1986). Equality-based binary resolution. Journal of the ACM, 33:253--289.

....in [Kou 88, Gan 91] Our approach is very different from the cited papers because we succeed in obtaining a finite program more often, using generation of conditional and recursive rules. The idea of suspended resolution has been considered in E resolution [Mor 69, And 70] and RUE resolution [DH 86] and repeated in [Hol 89] as lazy resolution . All these methods are either incomplete, or use special equality axioms. Our system is complete and the transformed program does not use any equality axioms. The use of the basic strategy that we achieve by introducing new predicate names can ....

V.J. Digricoli and M.C. Harrison. Equality-based binary resolution. Journal of the Association for Computing Machinery, 33:253--289, 1986.

....generate another equational program. Also, in [12] we consider a powerful recursive folding optimization that succeeds in obtaining a finite program more often, using generation of recursive rules. The idea of suspended resolution has been considered in E resolution [41, 1] and RUE resolution [15] and repeated in [27] as lazy resolution . All these methods are either incomplete or use special equality axioms. Our system is complete and the transformed program does not use any equality axioms. The use of the basic strategy together with the introduction of new predicate names can ....

V.J. Digricoli and M.C. Harrison. Equality-based binary resolution. Journal of the Association for Computing Machinery, 33:253--289, 1986.

....to the formulas to be proven by the system, the usual inference rules are able to process this theory. A better approach is to supply special inference rules for handling the equality predicate with respect to the equality theory, like e.g. paramodulation (Robinson and Wos, 1969) or RUE resolution (Digricoli and Harrison, 1986). Another very well investigated example for theory handling is the design of calculi and proof procedures, which use many or order sorted logics (Bl asius and B urckert, 1989) Here, the aim is to take care of a sort hierarchy in a direct way, e.g. by using a special unification procedure. This ....

....from, say, f (Y ; Y ) h(Y ; Y ) into f (c(d) c(e) is possible. This inference returns (f g; Y = c(d) Y = c(e) h(c(d) c(e) h(Y ; Y ) as a kind of a residue. All of these additional goals may be solved by use of the equation d = e . This technique is much in the spirit of RUE resolution (Digricoli and Harrison, 1986) with the important restriction that the delayed subgoals (the corresponding concept in RUE resolution is disagreement set ) can be restricted to variableterm pairs. Unfortunately the completeness of relaxed paramodulation with set of support strategy has not been proved yet. As a concluding ....

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Digricoli, V. J. and Harrison, M. C. (1986). Equality-Based binary Resolution. Journal of the Association for Computing Machinery.

....axioms for equality. Nevertheless, we feel this paper is an instructive first step towards a system which provides the complete solution. The equality axioms have been identified as a source of inefficiency or even incapacity for clause resolution deduction oriented refutation provers (see e.g. [3, 5, 6, 9, 12, 13, 17] ) A number of approaches to building in equality , have been offered in the literature of automated deduction. These include paramodulation, hyper paramodulation, and demodulation [13, 17] E Resolution [10] RUE Resolution [5, 6] Z Resolution [7] and the approach suggested by Sibert in ....

....oriented refutation provers (see e.g. 3, 5, 6, 9, 12, 13, 17] A number of approaches to building in equality , have been offered in the literature of automated deduction. These include paramodulation, hyper paramodulation, and demodulation [13, 17] E Resolution [10] RUE Resolution [5, 6], Z Resolution [7] and the approach suggested by Sibert in [14] More recently, restrictions of ordered paramodulation are described in, for example, 1, 2] However, with the exception of [14] and the work described in [1, 2] nothing significant has yet been written on how the notions of ....

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Digricoli, V.J., and Harrison, M.C., Equality-Based Binary Resolution, J. ACM, Vol 33, no.2, (April 1986), pp. 253-289.

....the outermost steps within a subproblem, so an efficient implementation should take care not to repeat work that is required in several different ways. There appears to be some convergence between these ideas based on term rewriting, and recent work on resolution based equational theorem proving [DH86]. The final problem, of avoiding search through many different reduction sequences, is probably solved by a careful application of Paul Chew s directed congruence closure algorithm [Che80] Congruence closure was originally intended to provide decision procedures for theories of finite sets of ....

V. J. Digricoli and M. C. Harrison. Equality-based binary resolution. Journal of the ACM, 33(2):253--289, 1986.

....clausal resolution refutation which build in the reflexivity, symmetry, transitivity and predicate substitutivity axioms for equality. The equality axioms have been identified as a source of inefficiency or even incapacity for clause resolution deduction oriented refutation provers (see e.g. [3, 5, 6, 9, 13, 14, 18] ) A number of approaches to building in equality , have been offered in the literature of automated deduction. These include paramodulation, hyper paramodulation, and demodulation [14, 18] E Resolution [11] RUE Resolution [5, 6] Z Resolution [7] and the approach suggested by Sibert in ....

....oriented refutation provers (see e.g. 3, 5, 6, 9, 13, 14, 18] A number of approaches to building in equality , have been offered in the literature of automated deduction. These include paramodulation, hyper paramodulation, and demodulation [14, 18] E Resolution [11] RUE Resolution [5, 6], Z Resolution [7] and the approach suggested by Sibert in [15] More recently, restrictions of ordered paramodulation are described in, for example, 1, 2] However, with the exception of [15] and the work described in [1, 2] very little has yet been written on how the notions of tautology ....

[Article contains additional citation context not shown here]

Digricoli, V.J., and Harrison, M.C., Equality-Based Binary Resolution, J. ACM, Vol 33, no.2, (April 1986), pp. 253-289.

....solved by a careful application of the directed congruence closure procedure mentioned in Section 3, although the details have never been studied. There appears to be some convergence between these ideas based on term rewriting, and recent work on equational theorem proving based on resolution [DH86]. Beyond proving equalities, it would be very useful to be able to solve equalities between terms with variables. This is precisely the problem of unification modulo a set of equations, and has been studied extensively in the attempt to combine Prolog with Functional Programming, but without ....

V. J. Digricoli and M. C. Harrison. Equality-based binary resolution. Journal of the ACM, 33(2):253--289, 1986.

....E is given by :E = a : b) However, no clause which equationally implies : a : b can be deduced by paramodulation and resolution from fA(a) A(b)g. This is true even in the presence of reflexivity. Another refutation calculus is based on RUE NRF resolution (Digricioli and Harrison [12]) In RUE NRF resolution, equality assumptions required for a given unification to succeed are introduced in each resolution step. For instance, the RUE resolvent of : A(b) and A(a) is : a : b, so that the deduction required in the previous example can be performed. However, suppose that T = ....

V.J. Digricoli and M.C. Harrison, Equality-based binary resolution, J. of the ACM 33 (1986) 253--289.

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Vincent J. Digricoli and Malcolm C. Harrison. Equality-Based binary Resolution. Journal of the Association for Computing Machinery, 1986.

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V.J. Digricoli and M.C. Harrison. Equality-based binary resolution. Journal of the Association for Computing Machinery, 33:253--289, 1986.

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V.J. Digricoli and M.C. Harrison. Equality-based binary resolution. Journal of the Association for Computing Machinery, 33:253--289, 1986.

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