Bowen, K. A. Programming with full first-order logic. Machine Intelligence 10, Hayes, J. E., Michie, D. and Pao, Y-H, eds., Halsted Press, 1982, 421 -- 440.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....While surveying other work, this section also discusses the design of our logic language with functions. 4.1 Larger fragments of first order logic If our goal is to program in logic then we should go beyond Horn clauses, aiming ultimately at programming in full first order logic. Bowen [10] proposed a complete theorem prover where programs consist of sequents of the form A 1 , A m B 1 , B n ; a standard Prolog interpreter handles the case where these resemble definite clauses. Many similar proposals have appeared since. Stickel s Prolog Technology Theorem Prover [41] ....

Bowen, K. A., Programming with full first-order logic, In Machine Intelligence 10, J. E. Hayes, D. Michie,, Y.-H. Pao, Eds. Ellis Horwood Ltd, 1982, pp. 421--440

.... The proof development method (PDM) and the proof strategy of KARNAK # are similar to those of KARNAK whicharedescribedindetailin[6,9] It was already noted that PPC and PPC # are natural sequent calculi and not pure sequent calculi for which the backwards PDM can be implemented e#ciently [3, 12, 15] due to the subformula property. The forwards application of introduction rules and the backwards application of elimination rules are explosive. This means that neither the forwards nor the backwards PDM can easily be used with natural calculi. The PDM of KARNAK and KARNAK # is mainly forwards. ....

Bowen K.A., Programming with Full First-Order Logic, MI 10, 421-440 (1982).

....section we describe the higher order logic used in this paper, summarizing several necessary logical notions in the process. The axiomatization presented here for the logic is in the style of Gentzen [9] The use of a sequent calculus, although unusual in the literature on logic programming (see [4] for an exception) has several advantages. One advantage is the simplification of prooftheoretic discussions that we hope this paper demonstrates. In another direction, it is the casting of our arguments within such a calculus that has been instrumental in the discovery of the essential ....

Bowen, K. A. Programming with full first-order logic. Machine Intelligence 10, Hayes, J. E., Michie, D. and Pao, Y-H, eds., Halsted Press, (a subsidiary of John Wiley & Sons, Inc.), New York, 1982, 421 -- 440.

....[14] For the sake of run time efficiency, the logic programming language described in this work does not use SLD resolution, nor even perform run time unification. Departing from this kind of implementation removes much of the motivation for using Horn clause logic. Bowen wrote an early paper [10] on the use of full first order logic for programming. Horn clause logic has also been popular for theoretical reasons. Because Horn clause logic restricts the use of negation, it is easy to assign semantic models to new predicates defined in it [2, 37] Recent developments in semantics [20, 57] ....

Bowen, K. A., Programming with Full First-Order Logic, in Artificial Intelligence 10, 1982, 421-440

....we encourage others not so theoretically oriented to look at the ideas from the opposite point of view. What restrictions on the language will lead to e#ciency without loosing naturalness It should be noted that the use of full first order logic as a programming language is not a new idea. Both [1] and [9] propose versions, with the second explicitly using tableaus. The di#erence here is that clauses are not thought of as simply first order formulas, but as first order formulas plus a recursion mechanism, in which the attempt to close one tableau can cause the creation of further tableaus. ....

Bowen, K. A. Programming with full first-order logic. In Machine Intelligence 10 (1982), Hayes, Michie, and Pao, Eds., Ellis Horwood and John Wiley, pp. 421--440.

....rule. Sometimes the rule has been stated as follows [11, 7] 8 ) Gamma; ff(t 1 ) ff(t k ) 8xff(x) Delta Gamma; 8xff(x) Delta where t 1 ; t k are terms from the language up to a given depth. This allows the mechanization of the calculus to perform validity checking. In [10, 2] it is proposed to delay the choice of the terms until an attempt to unify a pair of formulae occurring in the opposite sides of the same sequent succeeds. The notion of metavariable or dummy is introduced and the following version of the rule is given, that we shall also adopt: 8 ) Gamma; ....

K. A. Bowen. Programming with full first-order logic. In J. E. Hayes, D. Michie, and Y.-H. Pao, editors, Machine Intelligence, volume 10, pages 421--440. Halsted Press, 1982.

....with a computation of instantiations by unification. Skolemization [13] is a well known technique which guarantees that proofs constructed with a lazy handling of instantiations can be validated in general. In the context of sequent calculi, skolemization has been investigated for classical [4] as well as for non classical logics [12, 9] The technique for simultaneous quantifier elimination presented in this article is specific to sequent calculi. It provides an optimization over the usual approach for lazy handling of instantiations. The two justifications of its soundness yield ....

K. A. Bowen. Programming with full first-order logic, In Hayes, Michie, Pao, Eds., Machine Intelligence 10, 1982.

.... logic for logic programming Do more powerful (and useful) logics exist The idea of using arbitrary clauses as opposed to Horn clauses has been championed by [Kow79] In a similar fashion, the use of full firstorder logic as opposed to logic in clausal form has been advocated and explored [Bow82]. In a more conservative direction, extending the structure of Horn clauses by limited uses of connectives and quantifiers has been suggested. The best known extension of pure Horn clause logic within the logic programming paradigm permits negation in goals, using the notion of ....

K. A. Bowen. Programming with full first-order logic. In J. E. Hayes, D. Michie, and Y-H Pao, editors, Machine Intelligence 10, pages 421--440. Halsted Press, 1982.

....with a computation of instantiations by unification. Skolemization [14] is a well known technique which guarantees that proofs constructed with a lazy handling of instantiations can be validated in general. In the context of sequent calculi, skolemization has been investigated for classical [4] as well as for non classical logics [13, 10] The technique for simultaneous quantifier elimination [1] is specific to sequent calculi. It provides an optimization over the usual approach for lazy handling of instantiations. Our algebraic justification of its soundness clarifies the dependencies ....

K. A. Bowen. Programming with full first-order logic, In Hayes, Michie, Pao, Eds., Machine Intelligence 10, 1982.

....be applied to proof search in any sequent calculus with conventional quantifier rules and a cut elimination theorem. The technique is described just for the intuitionistic calculus in order to keep the exposition concrete. Proof search techniques for classical sequent calculi are fairly well known [BB74, Bow82, KW84]. These techniques work by Herbrandizing 1 the goal sequent to eliminate quantifiers and then use propositional reasoning and unification to carry out the proof search on the resulting quantifier free sequent. Consider the attempt to search for a proof of the following sequent which is ....

K. A. Bowen. Programming with full first-order logic. In J. E. Hayes, D. Michie, and Y.-H. Pao, editors, Machine Intelligence 10, pages 421--440. Halsted Press, 1982.

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Bowen, K. A. Programming with full first-order logic. Machine Intelligence 10, Hayes, J. E., Michie, D. and Pao, Y-H, eds., Halsted Press, 1982, 421 -- 440.

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