The Complexity of Nested Counterfactuals and Iterated Knowledge Base Revisions

We consider the computational complexity of evaluating nested counterfactuals over a propositional knowledge base. Counterfactual implication models a statement "if p, then q," where p is known or expected to be false, and is different from material implication A nested counterfactual is a counterfactual statement where the conclusion q is a (possibly negated) counterfactual. Statements of the form intuitively correspond to hypothetical queries involving a sequence of revisions. We show that evaluating such statements is complete, and that this task becomes PSPACE-cornplete if negation is allowed in the nesting. We also consider nesting a counterfactual in the premise, i.e. and show that evaluating such statements is most likely much harder than evaluating

• Type: Conference
• Year: 1993
• Where: IJCAI
• Authors: Thomas Eiter, Georg Gottlob
• Keywords: Counterfactual Implication Models, IJCAI 1993, IJCAI 2007, Nested Counterfactual, Propositional Knowledge Base