### Abstract

We extend logic programming's semantics with the semantic dual of traditional Herbrand semantics by using greatest fixed-points in place of least fixed-points. Executing a logic program then involves using coinduction to check inclusion in the greatest fixed-point. The resulting coinductive logic programming language is syntactically identical to, yet semantically subsumes logic programming with rational terms and lazy evaluation. We present a novel formal operational semantics that is based on synthesizing a coinductive hypothesis for this coinductive logic programming language. We prove that this new operational semantics is equivalent to the declarative semantics. Our operational semantics lends itself to an elegant and efficient goal directed proof search in the presence of rational terms and proofs. We describe a prototype implementation of this operational semantics along with applications of coinductive logic programming.

Original language | English (US) |
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Title of host publication | Logic Programming - 22nd International Conference, ICLP 2006, Proceedings |

Publisher | Springer Verlag |

Pages | 330-345 |

Number of pages | 16 |

ISBN (Print) | 9783540366355 |

State | Published - Jan 1 2006 |

Externally published | Yes |

Event | 22nd International Conference on Logic Programming, ICLP 2006 - Seattle, WA, United States Duration: Aug 17 2006 → Aug 20 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4079 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 22nd International Conference on Logic Programming, ICLP 2006 |
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Country | United States |

City | Seattle, WA |

Period | 8/17/06 → 8/20/06 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Logic Programming - 22nd International Conference, ICLP 2006, Proceedings*(pp. 330-345). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4079 LNCS). Springer Verlag.

**Coinductive logic programming.** / Simon, Luke; Mallya, Ajay; Bansal, Ajay; Gupta, Gopal.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Logic Programming - 22nd International Conference, ICLP 2006, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4079 LNCS, Springer Verlag, pp. 330-345, 22nd International Conference on Logic Programming, ICLP 2006, Seattle, WA, United States, 8/17/06.

}

TY - GEN

T1 - Coinductive logic programming

AU - Simon, Luke

AU - Mallya, Ajay

AU - Bansal, Ajay

AU - Gupta, Gopal

PY - 2006/1/1

Y1 - 2006/1/1

N2 - We extend logic programming's semantics with the semantic dual of traditional Herbrand semantics by using greatest fixed-points in place of least fixed-points. Executing a logic program then involves using coinduction to check inclusion in the greatest fixed-point. The resulting coinductive logic programming language is syntactically identical to, yet semantically subsumes logic programming with rational terms and lazy evaluation. We present a novel formal operational semantics that is based on synthesizing a coinductive hypothesis for this coinductive logic programming language. We prove that this new operational semantics is equivalent to the declarative semantics. Our operational semantics lends itself to an elegant and efficient goal directed proof search in the presence of rational terms and proofs. We describe a prototype implementation of this operational semantics along with applications of coinductive logic programming.

AB - We extend logic programming's semantics with the semantic dual of traditional Herbrand semantics by using greatest fixed-points in place of least fixed-points. Executing a logic program then involves using coinduction to check inclusion in the greatest fixed-point. The resulting coinductive logic programming language is syntactically identical to, yet semantically subsumes logic programming with rational terms and lazy evaluation. We present a novel formal operational semantics that is based on synthesizing a coinductive hypothesis for this coinductive logic programming language. We prove that this new operational semantics is equivalent to the declarative semantics. Our operational semantics lends itself to an elegant and efficient goal directed proof search in the presence of rational terms and proofs. We describe a prototype implementation of this operational semantics along with applications of coinductive logic programming.

UR - http://www.scopus.com/inward/record.url?scp=33749319976&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749319976&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33749319976

SN - 9783540366355

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 330

EP - 345

BT - Logic Programming - 22nd International Conference, ICLP 2006, Proceedings

PB - Springer Verlag

ER -