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

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...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Charalambidis, Angelos, Ésik, Zoltán, Rondogiannis, Panos
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 15.05.2014
Subjects:	Logic programming Logic programs Semantics
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	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.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1405.3792