Digricoli, V.J. Resolution by unification and equality. Proceedings of the Fourth Workshop on Automated Deduction, Austin, Texas, February 1979, 43--52.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....such as unit resulting resolution and hyperresolution. Paramodulation [36] can be viewed as an instance of binary partial theory resolution where T is the theory of equality EQ. P (b) is an EQ resolvent (paramodulant) of P (a) and a = b. Digricoli s resolution by unification and equality [13] can be viewed similarly. a 6= b is an EQ resolvent (RUE resolvent) of P (a) and :P (b) Morris s E resolution [21] can be viewed as an instance of total theory resolution. 2 is a total EQ resolvent (E resolvent) of P (a) P (b) and a = b. The difference between these equality reasoning ....

Digricoli, V.J. Resolution by unification and equality. Proceedings of the Fourth Workshop on Automated Deduction, Austin, Texas, February 1979, 43--52.

....a sketch of the 1 This work was partially supported by the BSI (Bundesamt fur Sicherheit in der Informationstechnik) proof and then, to tackle the resulting subproblems [15] Now, the problem arises how to break down a proof in such a hierachical manner. The existing approaches of RUE resolution [10] and the calculus of Blasius [6] do this in a simple syntactical way. In order to equalize two terms first, the top level symbols have to be equalized and then, the corresponding arguments of both terms have to be adapted. While these two general approaches of difference reduction were not ....

Vincent J. Digricoli. Resolution by unification and equality. In William H. Joyner, editor, Proceedings 4 th Workshop on Automated Deduction, pages 43--52, Austin, USA, February 1979.

....Informatik, Universitat des Saarlandes Abstract. This paper presents two approaches to primitive equality treatment in higher order (HO) automated theorem proving: a calculus EP adapting traditional first order (FO) paramodulation [RW69] and a calculus ERUE adapting FO RUE Resolution [Dig79] to classical type theory, i.e. HO logic based on Church s simply typed calculus. EP and ERUE extend the extensional HO resolution approach ER [BK98a] In order to reach Henkin completeness without the need for additional extensionality axioms both calculi employ new, positive extensionality ....

....amount of blind search with ER s primitive substitution rule Prim. Therefore we adapt two well known first order (FO) approaches to primitive equality: the paramodulation approach [RW69] the basis of many successful refinements such as the superposition approach) and the RUE resolution approach [Dig79] (a generalisation of E resolution [Dar68] The main goal thereby is to preserve Henkin completeness. We will show that therefore positive extensionality rules are needed (which operate on positive equation literals) as in contrast to FO logic single positive equations can be contradictory by ....

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V. J. Digricoli. Resolution by unification and equality. In W. H. Joyner, editor, Proc. of the 4th Workshop on Automated Deduction, Austin, 1979.

....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, W.J., Resolution by unification and equality, proceedings of the Fourth Workshop on Automated Deduction, Austin, Texas, (1979), pp. 43-52.

....in a clause set. Numerous calculi and strategies have been developed in order to overcome the complexity problem in connection with the equality predicate. see, for example: Wos et al. 1967, Robinson and Wos, 1969, Sibert, 1969, Morris, 1969, Knuth and Bendix, 1970, Brand, 1975, Shostak, 1978, Digricoli, 1979, Huet and Oppen, 1980, Lim and Henschen, 1985, Blasius, 1986] Using term rewriting techniques and Knuth Bendix completion, for instance, the group problem above can be solved very easily. The purpose of this subsection was just to present paramodulation as an illustration for partial theory ....

Digricoli, V. J. (1979). Resolution by unification and equality. In Proc. of 4 th Workshop on Automated Deduction, Austin, TX.

....equational reasoning is the approach of difference reduction . The general idea is to find a sketch of the proof and then, to tackle the resulting subproblems [NSS59] Now, the problem arises how to break down a proof in such a hierachical manner. The existing approaches of RUE resolution [Dig79] and the calculus of Blasius [Bla86] do this in a simple syntactical way. In order to equalize two terms first, the top level symbols have to be equalized and then, the corresponding arguments of both terms have to be adapted. While these two general approaches of difference reduction were no ....

Vincent J. Digricoli. Resolution by unification and equality. In William H. Joyner, editor, Proceedings 4 th Workshop on Automated Deduction, pages 43--52, Austin, USA, February 1979.

....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, W.J., Resolution by unification and equality, proceedings of the Fourth Workshop on Automated Deduction, Austin, Texas, (1979), pp. 43-52.

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