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HigherOrder Horn Clauses
 JOURNAL OF THE ACM
, 1990
"... A generalization of Horn clauses to a higherorder logic is described and examined as a basis for logic programming. In qualitative terms, these higherorder Horn clauses are obtained from the firstorder ones by replacing firstorder terms with simply typed #terms and by permitting quantification ..."
Abstract

Cited by 62 (21 self)
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A generalization of Horn clauses to a higherorder logic is described and examined as a basis for logic programming. In qualitative terms, these higherorder Horn clauses are obtained from the firstorder ones by replacing firstorder terms with simply typed #terms and by permitting quantification over all occurrences of function symbols and some occurrences of predicate symbols. Several prooftheoretic results concerning these extended clauses are presented. One result shows that although the substitutions for predicate variables can be quite complex in general, the substitutions necessary in the context of higherorder Horn clauses are tightly constrained. This observation is used to show that these higherorder formulas can specify computations in a fashion similar to firstorder Horn clauses. A complete theorem proving procedure is also described for the extension. This procedure is obtained by interweaving higherorder unification with backchaining and goal reductions, and constitutes a higherorder generalization of SLDresolution. These results have a practical realization in the higherorder logic programming language called λProlog.
HigherOrder Logic as the Basis for Logic Programming
, 1989
"... : A generalization of Horn clauses to a higherorder logic is described and examined as a basis for logic programming. In qualitative terms, these higherorder Horn clauses are obtained from the firstorder ones by replacing firstorder terms with simply typed terms and by permitting quantification ..."
Abstract
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: A generalization of Horn clauses to a higherorder logic is described and examined as a basis for logic programming. In qualitative terms, these higherorder Horn clauses are obtained from the firstorder ones by replacing firstorder terms with simply typed terms and by permitting quantification over all occurrences of function symbols and some occurrences of predicate symbols. Several prooftheoretic results concerning these extended clauses are presented. One result shows that although the substitutions for predicate variables can be quite complex in general, the substitutions necessary in the context of higherorder Horn clauses are tightly constrained. This observation is used to show that these higherorder formulas can specify computations in a fashion similar to firstorder Horn clauses. A complete theorem proving procedure is also described for the extension. This procedure is obtained by interweaving higherorder unification with backchaining and goal reductions, and const...