Extensional Higher-Order Logic Programming

Authors:
Angelos Charalambidis;Konstantinos Handjopoulos;Panagiotis Rondogiannis;William W. Wadge
Affiliations:
University of Athens;University of Athens;University of Athens;University of Victoria
Venue:
ACM Transactions on Computational Logic (TOCL)
Year:
2013

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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 system which is proven sound and complete with respect to the minimum Herbrand 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.