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Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation*

Published online by Cambridge University Press:  21 July 2014

ANGELOS CHARALAMBIDIS ,
ZOLTÁN ÉSIK  and
PANOS RONDOGIANNIS
ANGELOS CHARALAMBIDIS
Affiliation:
Department of Informatics & Telecommunications, University of Athens, Greece (e-mail: a.charalambidis@di.uoa.gr)
ZOLTÁN ÉSIK
Affiliation:
Department of Computer Science, University of Szeged, Hungary (e-mail: ze@inf.u-szeged.hu)
PANOS RONDOGIANNIS
Affiliation:
Department of Informatics & Telecommunications, University of Athens, Greece (e-mail: prondo@di.uoa.gr)
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Abstract

Extensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic programming. In this paper we consider the semantics of negation in the context of the new paradigm. Using some recent results from non-monotonic fixed-point theory, we demonstrate that every higher-order logic program with negation has a unique minimum infinite-valued model. In this way we obtain the first purely model-theoretic semantics for negation in extensional higher-order logic programming. Using our approach, we resolve an old paradox that was introduced by W. W. Wadge in order to demonstrate the semantic difficulties of higher-order logic programming.

Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 14 , Special Issue 4-5: 30th International Conference on Logic Programming , July 2014 , pp. 725 - 737
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

*

This research is being supported by the Greek General Secretariat for Research and Technology, the National Development Agency of Hungary, and the European Commission (European Regional Development Fund) under a Greek-Hungarian intergovernmental programme of Scientific and Technological collaboration. Project title: “Extensions and Applications of Fixed Point Theory for Non-Monotonic Formalisms”. It is also supported by grant no. ANN 110883 from the National Foundation of Hungary for Scientific Research.

References

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Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation

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