@MISC{Pinto_cutformulae, author = {Luis Pinto}, title = {Cut Formulae and Logic Programming}, year = {} }

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Abstract

. In this paper we present a mechanism to define names for proof-witnesses of formulae and thus to use Gentzen's cut-rule in logic programming. We consider a program to be a set of logical formulae together with a list of such definitions. Occurrences of the defined names guide the proof-search by indicating when an instance of the cut-rule should be attempted. By using the cut-rule there are proofs that can be made dramatically shorter. We explain how this idea of using the cut-rule can be applied to the logic of hereditary Harrop formulae. 1 Introduction The computation mechanisms both for logic and for functional programming are searches for cut-free proofs. First, in pure logic programming the achievement of a goal G w.r.t. a program P can be seen 1 as the search for a proof in Gentzen's intuitionistic sequent calculus LJ [Gen69], of the sequent P ) G, that by Gentzen's cut-elimination theorem can be cut-free [Bee89], [Mil90]; a -term found as a witness to a proof contains among...