Logic Programming with Bounded Quantifiers

This paper describes an extension of Horn clause logic programs by bounded quantifiers. Bounded quantifiers had been extensively used in a part of mathematical logic called theory of admissible sets [2]. Later some variants of bounded quantifiers had been introduced in logic programming languages [12, 19, 21, 9, 6, 7]. We show that an extension of logic programs by bounded quantifiers has several equivalent logical semantics and is efficiently implementable using a variant of SLD-resolution, which we call SLDB-resolution. We give examples showing that introduction of bounded quantifiers results in a high level logical specification language. An expressive power of subsets of Horn clauses and subsets of logic programs with bounded quantifiers is compared. We also show that the use of bounded quantifiers sheds new light on classical negation in logic programming.

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