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A propositional logic program P may be identified with a P f P f -coalgebra on the set of atomic propositions in the program. The corresponding C(P f P f )-coalgebra, where C(P f P f ) is the cofree comonad on P f P f , 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 categories and right Kan extensions respectively. We unify the two approaches, exhibiting them as complementary rather than competing, reflecting the theorem-proving and proof-search aspects of logic programming. While maintaining that unity, we further refine lax semantics to give finitary models of logic programs with existential variables, and to develop a precise semantic relationship between variables in logic programming and worlds in local state.
|Number of pages||21|
|Journal||Journal of Logical and Algebraic Methods in Programming|
|Early online date||19 Jul 2018|
|Publication status||Published - 1 Dec 2018|
- Logic programming, coalgebra, coinductive derivation tree, Lawvere theories, lax transformations, saturation