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Lexical scoping as universal quantification
 In Sixth International Logic Programming Conference
, 1989
"... Abstract: A universally quantified goal can be interpreted intensionally, that is, the goal ∀x.G(x) succeeds if for some new constant c, the goal G(c) succeeds. The constant c is, in a sense, given a scope: it is introduced to solve this goal and is “discharged ” after the goal succeeds or fails. Th ..."
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Cited by 64 (17 self)
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Abstract: A universally quantified goal can be interpreted intensionally, that is, the goal ∀x.G(x) succeeds if for some new constant c, the goal G(c) succeeds. The constant c is, in a sense, given a scope: it is introduced to solve this goal and is “discharged ” after the goal succeeds or fails. This interpretation is similar to the interpretation of implicational goals: the goal D ⊃ G should succeed if when D is assumed, the goal G succeeds. The assumption D is discharged after G succeeds or fails. An interpreter for a logic programming language containing both universal quantifiers and implications in goals and the body of clauses is described. In its nondeterministic form, this interpreter is sound and complete for intuitionistic logic. Universal quantification can provide lexical scoping of individual, function, and predicate constants. Several examples are presented to show how such scoping can be used to provide a Prologlike language with facilities data types, and encapsulation of state.
A ProofTheoretic Analysis of GoalDirected Provability
 Journal of Logic and Computation
, 1992
"... One of the distinguishing features of logic programming seems to be the notion of goaldirected provability, i.e. that the structure of the goal is used to determine the next step in the proof search process. It is known that by restricting the class of formulae it is possible to guarantee that a ..."
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Cited by 14 (7 self)
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One of the distinguishing features of logic programming seems to be the notion of goaldirected provability, i.e. that the structure of the goal is used to determine the next step in the proof search process. It is known that by restricting the class of formulae it is possible to guarantee that a certain class of proofs, known as uniform proofs, are complete with respect to provability in intuitionistic logic. In this paper we explore the relationship between uniform proofs and classes of formulae more deeply. Firstly we show that uniform proofs arise naturally as a normal form for proofs in firstorder intuitionistic sequent calculus. Next we show that the class of formulae known as hereditary Harrop formulae are intimately related to uniform proofs, and that we may extract such formulae from uniform proofs in two different ways. We also give results which may be interpreted as showing that hereditary Harrop formulae are the largest class of formulae for which uniform proo...
Herbrand Methods in Sequent Calculi: Unification in LL
 Proc. of the Joint International Conference and Symposium on Logic Programming
, 1992
"... We propose a reformulation of quantifiers rules in sequent calculi which allows to replace blind existential instantiation with unification, thereby reducing nondeterminism and complexity in proofsearch. Our method, based on some ideas underlying the proof of Herbrand theorem for classical logic, m ..."
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Cited by 5 (2 self)
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We propose a reformulation of quantifiers rules in sequent calculi which allows to replace blind existential instantiation with unification, thereby reducing nondeterminism and complexity in proofsearch. Our method, based on some ideas underlying the proof of Herbrand theorem for classical logic, may be applied to any "reasonable" nonclassical sequent calculus, but here we focus on sequent calculus for linear logic, in view of an application to linear logic programming. We prove that the new linear proofsystem which we propose, the so called system LLH, is equivalent to standard linear sequent calculus LL. 1 Introduction A result in classical logic which has been widely exploited in logic programming is Herbrand theorem. Several versions of this result are present in the literature; we recall here one of them (see [13]). Herbrand Theorem Let F be a prenex formula of the form 9w8x9y8zA[w; x; y; z] with A quantifierfree. F is provable in predicate calculus if and only if a disjun...
A Higher Order Reconstruction of Stepwise Enhancement
 7th international workshop, LOPSTR’97
"... This paper presents two views of stepwise enhancement, one a pragmatic syntaxbased approach and the other a semantic approach based on higher order functions and relating to shape and polytypism. The approaches are outlined, and the perhaps surprisingly close relationship between the two described. ..."
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Cited by 1 (0 self)
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This paper presents two views of stepwise enhancement, one a pragmatic syntaxbased approach and the other a semantic approach based on higher order functions and relating to shape and polytypism. The approaches are outlined, and the perhaps surprisingly close relationship between the two described. By combining the advantages of both approaches, it is shown how more code in both functional and logic programming languages can be constructed in a systematic and partially automated way.