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We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs P and Q and vocabulary V (set of predicates) the existence of a program R in V such that P R and P Q are strongly equivalent can be expressed as a first-order entailment. Moreover, our result is effective: A program R can be constructed from a Craig interpolant for this entailment, using a known first-order encoding for testing strong equivalence, which we apply in reverse to extract programs from formulas. As a further perspective, this allows transforming logic programs via transforming their first-order encodings. In a prototypical implementation, the Craig interpolation is performed by first-order provers based on clausal tableaux or resolution calculi. Our work shows how definability and interpolation, which underlie modern logic-based approaches to advanced tasks in knowledge representation, transfer to answer set programming.
Heuer et al. (Mon,) studied this question.