Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation*. Issue 4 (21st July 2014)

• Record Type: Journal Article
• Authors: CHARALAMBIDIS, ANGELOS; ÉSIK, ZOLTÁN; RONDOGIANNIS, PANOS; Leuschel, Michael; Schrijvers, Tom
• Is Part Of: Theory and practice of logic programming. Volume 14:Issue 4/5(2014)
• Page Start: 725
• Page End: 737
• Publication Date: 2014-07-21
• Subjects: Logic programming -- Periodicals; Artificial intelligence -- Computer programs -- Periodicals; Constraint programming (Computer science) -- Periodicals; 005.115
• DOI: 10.1017/S1471068414000313
• Languages: English
• ISSNs: 1471-0684

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>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 <italic>minimum</italic> 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.</p> </abstract>