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arXiv:1106.3457cs.PL

Extensional Higher-Order Logic Programming

A. Charalambidis, K. Handjopoulos, P. Rondogiannis, W. W. Wadge

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Abstract

We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique minimum Herbrand model which is the greatest lower bound of all Herbrand models of the program and the least fixed-point of an immediate consequence operator. We also propose an SLD-resolution proof procedure which is proven sound and complete with respect to the minimum model semantics. In other words, we provide a purely extensional theoretical framework for higher-order logic programming which generalizes the familiar theory of classical (first-order) logic programming.

arXiv comments
45 pages
Journal reference
DOI
Subjects
cs.PLProgramming Languages cs.AIArtificial Intelligence cs.LOLogic in Computer Science

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  1. Extensional Higher Order Prolog 1 comment

    • I've just published a draft paper on an entirely different approach to the same problem: instead of creating a higher-order Prolog, we've discovered a functional (and so higher-order) analogue of Datalog, a more limited language (http://www.rntz.net/files/datafun.pdf, on github…

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