How logic programming (especially ASP) is related to the reasoning in (first-order) logic?

Question

How logic programming (https://en.wikipedia.org/wiki/Logic_programming, especially answer set programming) is related to the reasoning in the (first-order) logic? Maybe logic programming can be expressed using lambda calculus and then this connection between logic programming and logic and be exspressed as type of Curry-Howard isomorphism?

But maybe this connection can be established without this bypass?

Maybe such connection can not be established, as logical reasoning is monotonic (it just discovers consquences that are implicit in the initial premises), but logic programming is non-monotonic (it asserts new facts and knowledge). If so, then logic programming is generalization of logical reasoning and under what (syntactic) conditions logic program becomes set of logical formulas/logical theory?