On the complexity of propositional knowledge base revision, updates, and counterfactuals

Abstract

We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T, an update p, and a formula q, decide whether q is derivable from Tp, the updated (or revised) knowledge base. This problem amounts to evaluating the counterfactual p>q over T. Besides the general case, also subcases are considered, in particular where T is a conjunction of Horn clauses, or where the size of p is bounded by a constant.