Category Theoretic Semantics for Theorem Proving in Logic Programming: Embracing the Laxness

Abstract : A propositional logic program P may be identified with a $P_fP_f$-coalgebra on the set of atomic propositions in the program. The corresponding $C(P_fP_f)$-coalgebra, where $C(P_fP_f)$ is the cofree comonad on $P_fP_f$, 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.
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Ekaterina Komendantskaya, John Power. Category Theoretic Semantics for Theorem Proving in Logic Programming: Embracing the Laxness. 13th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2016, Eindhoven, Netherlands. pp.94-113, ⟨10.1007/978-3-319-40370-0_7⟩. ⟨hal-01446035⟩

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