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Uniform proofs as a foundation for logic programming
 ANNALS OF PURE AND APPLIED LOGIC
, 1991
"... A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its ..."
Abstract

Cited by 374 (108 self)
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A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its operational meaning, provided by interpreting logical connectives as simple and fixed search instructions. The operational semantics is formalized by the identification of a class of cutfree sequent proofs called uniform proofs. A uniform proof is one that can be found by a goaldirected search that respects the interpretation of the logical connectives as search instructions. The concept of a uniform proof is used to define the notion of an abstract logic programming language, and it is shown that firstorder and higherorder Horn clauses with classical provability are examples of such a language. Horn clauses are then generalized to hereditary Harrop formulas and it is shown that firstorder and higherorder versions of this new class of formulas are also abstract logic programming languages if the inference rules are those of either intuitionistic or minimal logic. The programming language significance of the various generalizations to firstorder Horn clauses is briefly discussed.
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 ..."
Abstract

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.