Category Theoretic Semantics for Theorem Proving in Logic Programming: Embracing the Laxness
نویسندگان
چکیده
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. Using lax semantics, that correspondence may be extended to a class of first-order logic programs without existential variables. The resulting extension captures the proofs by term-matching resolution in logic programming. Refining the lax approach, we further extend it to arbitrary logic programs. We also exhibit a refinement of Bonchi and Zanasi’s saturation semantics for logic programming that complements lax semantics.
منابع مشابه
Logic programming: laxness and saturation
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 ca...
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