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:Theory and practice of logic programming Vol. 14; no. 4-5; pp. 725 - 737
Main Authors: CHARALAMBIDIS, ANGELOS, ÉSIK, ZOLTÁN, RONDOGIANNIS, PANOS
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.07.2014
Subjects:
Logic programming
Paradoxes
Preserves
Regular Papers
Semantics
ISSN:1471-0684, 1475-3081
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.
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ISSN:1471-0684
1475-3081
DOI:10.1017/S1471068414000313