# Coalgebraic semantics for derivations in logic programming

### Reference:

Komendantskaya, E. and Power, J., 2011. Coalgebraic semantics for derivations in logic programming. *In*: Corradini, A., Kin, B. and Cirstea, C., eds. *Algebra and Coalgebra in Computer Science: 4th International Conference, CALCO 2011, Winchetser, UK, August 30 - September 2, 2011. Proceedings.* Heidelberg: Springer, pp. 268-282. (Lecture Notes in Computer Science; 6859)

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### Official URL:

http://dx.doi.org/10.1007/978-3-642-22944-2_19

### Abstract

Every variable-free logic program induces a Pf P f -coalgebra on the set of atomic formulae in the program. The coalgebra p sends an atomic formula A to the set of the sets of atomic formulae in the antecedent of each clause for which A is the head. In an earlier paper, we identified a variable-free logic program with a Pf P f -coalgebra on Set and showed that, if C(Pf P f ) is the cofree comonad on Pf P f , then given a logic program P qua Pf P f -coalgebra, the corresponding C(Pf P f )-coalgebra structure describes the parallel and-or derivation trees of P. In this paper, we extend that analysis to arbitrary logic programs. That requires a subtle analysis of lax natural transformations between Poset-valued functors on a Lawvere theory, of locally ordered endofunctors and comonads on locally ordered categories, and of coalgebras, oplax maps of coalgebras, and the relationships between such for locally ordered endofunctors and the cofree comonads on them

### Details

Item Type | Book Sections |

Creators | Komendantskaya, E.and Power, J. |

Editors | Corradini, A., Kin, B. and Cirstea, C. |

DOI | 10.1007/978-3-642-22944-2_19 |

Departments | Faculty of Science > Computer Science |

Publisher Statement | Power_CALCO_2011_268.pdf: The original publication is available at www.springerlink.com |

Refereed | No |

Status | Published |

ID Code | 26422 |

Additional Information | 4th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2011. 30 August - 2 September 2011. Winchester, United Kingdom. |

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