Minimum model semantics for extensional higher-order logic programming with negation

Angelos Charalambidis, Z. Ésik, Panos Rondogiannis

Research output: Contribution to journalArticle

13 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)725-737
Number of pages13
JournalTheory and Practice of Logic Programming
Volume14
Issue number4-5
DOIs
Publication statusPublished - 2014

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Higher-order Logic
Logic programming
Logic Programming
Semantics
Paradigm
Model
Fixed Point Theory
Classical Logic
Paradox
Logic Programs
Demonstrate
Resolve

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Hardware and Architecture
  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

Minimum model semantics for extensional higher-order logic programming with negation. / Charalambidis, Angelos; Ésik, Z.; Rondogiannis, Panos.

In: Theory and Practice of Logic Programming, Vol. 14, No. 4-5, 2014, p. 725-737.

Research output: Contribution to journalArticle

Charalambidis, Angelos ; Ésik, Z. ; Rondogiannis, Panos. / Minimum model semantics for extensional higher-order logic programming with negation. In: Theory and Practice of Logic Programming. 2014 ; Vol. 14, No. 4-5. pp. 725-737.
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