### Abstract

For each first-order language L with a nonempty Herbrand universe, we construct an algebra C interpreting the function symbols of L that is a model of the Clark equality theory with language L and is canonical in the sense that for every definite clause program P in the language L, T_{P}^{C} ↓ ω is the greatest fixed point of T_{P}^{C}. The universe of individuals in C is a quotient of the set of terms of L and is, a fortiori, countable if L is countable. If ℒ contains at least one function symbol of arity at least 2, then the graphs of partial recursive functions on C, suitably defined, are representable in a natural way as individuals in C.

Original language | English (US) |
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Pages (from-to) | 1-19 |

Number of pages | 19 |

Journal | Annals of Mathematics and Artificial Intelligence |

Volume | 1 |

Issue number | 1-4 |

DOIs | |

State | Published - Sep 1 1990 |

### Keywords

- Clause programs
- partial recursive functions
- semantics

### ASJC Scopus subject areas

- Artificial Intelligence
- Applied Mathematics

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## Cite this

Blair, H. A., & Brown, A. L. (1990). Definite clause programs are canonical (over a suitable domain).

*Annals of Mathematics and Artificial Intelligence*,*1*(1-4), 1-19. https://doi.org/10.1007/BF01531067