Artificial Intelligence
Reasoning about action I: a possible worlds approach
Artificial Intelligence
On the complexity of epistemic reasoning
Proceedings of the Fourth Annual Symposium on Logic in computer science
Updating logical databases
Complexity classification of truth maintenance systems
STACS 91 Proceedings of the 8th annual symposium on Theoretical aspects of computer science
Hard problems for simple default logics
Artificial Intelligence - Special issue on knowledge representation
On the complexity of propositional knowledge base revision, updates, and counterfactuals
Artificial Intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the semantics of updates in databases
PODS '83 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems
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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 p is 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 p1 (p2 ...(pn q)...) intuitively correspond to hypothetical queries involving a sequence of revisions. We show that evaluating such statements is Π2p 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.(p q) r and show that evaluating such statements is most likely much harder than evaluating p (q r).