{"type":"ScholarlyArticle","title":"The Complexity of Nested Counterfactuals and Iterated Knowledge Base Revisions","authors":[{"name":"Thomas Eiter","slug":"thomas-eiter","given":"Thomas","family":"Eiter","affiliation":""},{"name":"Georg Gottlob","slug":"georg-gottlob","given":"Georg","family":"Gottlob","affiliation":""}],"abstract":"We consider the computational complexity of evaluating nested counterfactuals over a propositional knowledge base. Counterfactual implication p > q models a statement \"if p, then q,\" where pis known or expected to be false, and is different from material implication p =:} q. A nested counterfactual is a counterfactual statement where the conclusion q is a (possibly negated) counterfactual. Statements of the form p 1 > (p 2 > · · · (Pn > q) · · ·) intuitively correspond to hypothetical queries involving a sequence of revisions. We show that evaluating such statements is IIf-complete, and that this task becomes PSPACE-complete if negation is allowed in the nesting. We also consider nesting a counterfactual in the premise, i.e. (p > q) > r and show that evaluating such statements is most likely much harder than evaluating p > (q > r).","doi":null,"url":"https://ijcai.org/proceedings/1993/74","pdf":"https://ijcai.org/proceedings/1993/0074.pdf","markdown":"https://ijcai.org/proceedings/1993/74.md","bibtex":"https://ijcai.org/proceedings/1993/bibtex/74","volume":{"slug":"1993","title":"Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1993","url":"https://ijcai.org/proceedings/1993/","year":1993,"location":"Chambéry, France","dates":"","editors":"Ruzena Bajcsy","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Knowledge Representation","track":"Knowledge Representation","number":74,"pages":{"first":526,"last":532},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}