### Abstract

A propositional logic program P may be identiﬁed with a PfPf-coalgebra on the set of atomic propositions in the program. The corresponding C(PfPf)-coalgebra, where C(PfPf) is the cofree comonad on PfPf, describes derivations by resolution. That correspondence has been developed to model ﬁrst-order programs in two ways, with lax semantics and saturated semantics, based on locally ordered categories and right Kan extensions respectively. We unify the two approaches, exhibiting them as complementary rather than competing, reﬂecting the theorem-proving and proof-search aspects of logic programming. While maintaining that unity, we further reﬁne lax semantics to give ﬁnitary models of logic programs with existential variables, and to develop a precise semantic relationship between variables in logic programming and worlds in local state.

Original language | English |
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Pages (from-to) | 1-21 |

Number of pages | 21 |

Journal | Journal of Logical and Algebraic Methods in Programming |

Volume | 101 |

Early online date | 19 Jul 2018 |

DOIs | |

Publication status | Published - Dec 2018 |

### Keywords

- Logic programming
- Coalgebra
- Coinductive Derivation Tree
- Lawvere theories
- Lax transformations
- Saturation

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## Profiles

## Ekaterina Komendantskaya

- School of Mathematical & Computer Sciences - Associate Professor
- School of Mathematical & Computer Sciences, Computer Science - Associate Professor

Person: Academic (Research & Teaching)