### 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 language | English |
---|---|

Pages (from-to) | 725-737 |

Number of pages | 13 |

Journal | Theory and Practice of Logic Programming |

Volume | 14 |

Issue number | 4-5 |

DOIs | |

Publication status | Published - 2014 |

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### ASJC Scopus subject areas

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

### Cite this

*Theory and Practice of Logic Programming*,

*14*(4-5), 725-737. https://doi.org/10.1017/S1471068414000313

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

Research output: Contribution to journal › Article

*Theory and Practice of Logic Programming*, vol. 14, no. 4-5, pp. 725-737. https://doi.org/10.1017/S1471068414000313

}

TY - JOUR

T1 - Minimum model semantics for extensional higher-order logic programming with negation

AU - Charalambidis, Angelos

AU - Ésik, Z.

AU - Rondogiannis, Panos

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84904666546&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904666546&partnerID=8YFLogxK

U2 - 10.1017/S1471068414000313

DO - 10.1017/S1471068414000313

M3 - Article

AN - SCOPUS:84904666546

VL - 14

SP - 725

EP - 737

JO - Theory and Practice of Logic Programming

JF - Theory and Practice of Logic Programming

SN - 1471-0684

IS - 4-5

ER -