Extensional higher-order logic programming

Authors:
Angelos Charalambidis;Konstantinos Handjopoulos;Panos Rondogiannis;William W. Wadge
Affiliations:
Department of Informatics & Telecommunications, University of Athens, Greece;Department of Informatics & Telecommunications, University of Athens, Greece;Department of Informatics & Telecommunications, University of Athens, Greece;Department of Computer Science, University of Victoria, Canada
Venue:
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
Year:
2010

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Abstract

We propose a purely extensional semantics for higher-order logic programming. Under this semantics, 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 the immediate consequence operator of the program. We also propose an SLD-resolution proof procedure which is 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.