Benchmark based Vitality of Axioms and Preconditions for Datalog Theory Repair

In general, axioms a logical theory are not equal in terms of their informational value (IV), and neither are the preconditions in a logical rule. Measuring IV is crucial, particularly in automated repair systems, e.g., the Abduction, Belief Revision and Conceptual Change (ABC) repair system \citep{li2022overview}, because when there are multiple repairs, the one that changes the item of least IV is preferred. However, quantifying IV is challenging. Given a benchmark, we
evaluate the IV from the perspective of how much an axiom/precondition supports the benchmark, which is quantitatively defined as the {\em vitality} of axioms and preconditions. The bigger contribution of an axiom/precondition in supporting the benchmark, the more information it conveys, so the bigger its vitality is. Our evaluation shows that the ABC repair system finds the best-repaired theories with smaller search space by only changing the least vital axioms/preconditions, as shown by our evaluation.