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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
    CreatorsKomendantskaya, E.and Power, J.
    EditorsCorradini, A., Kin, B. and Cirstea, C.
    DOI10.1007/978-3-642-22944-2_19
    DepartmentsFaculty of Science > Computer Science
    Publisher StatementPower_CALCO_2011_268.pdf: The original publication is available at www.springerlink.com
    StatusPublished
    ID Code26422
    Additional Information4th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2011. 30 August - 2 September 2011. Winchester, United Kingdom.

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