Verification of Locally Tight Programs
This work is incremental, as it relaxes an existing condition to extend verification capabilities in answer set programming.
The paper tackles the problem of verifying equivalence between logic programs by showing that the tightness condition in a known theorem can be replaced with a less restrictive 'local tightness' requirement, enabling the use of the proof assistant anthem-p2p for such verification.
Program completion is a translation from the language of logic programs into the language of first-order theories. Its original definition has been extended to programs that include integer arithmetic, accept input, and distinguish between output predicates and auxiliary predicates. For tight programs, that generalization of completion is known to match the stable model semantics, which is the basis of answer set programming. We show that the tightness condition in this theorem can be replaced by a less restrictive "local tightness" requirement. From this fact we conclude that the proof assistant anthem-p2p can be used to verify equivalence between locally tight programs. Under consideration for publication in Theory and Practice of Logic Programming