Coalgebraic Semantics for Derivations in Logic Programming

Reference:

Komendantskaya, E. and Power, J., 2011. Coalgebraic Semantics for Derivations in Logic Programming. In: Algebra and Coalgebra in Computer Science - 4th International Conference, CALCO 2011, Proceedings. Vol. 6859. Heidelberg: Springer, pp. 268-282.

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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

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