by Tom Costello and John McCarthy, Stanford University,
appeared in ETAI (Electronic Transactions on Artificial Intelligence), ETAI, Vol 3 (1999), Section A.

Counterfactual conditional sentences are useful to people and can be useful in artificial intelligence. In particular, they allow reasoners to learn from experiences that they did not quite have. The truth of a counterfactual and the conclusions that can be drawn from a counterfactual are theory dependent, and different theories are useful in different circumstances.

A simple class of useful counterfactuals involves a change of one component of a point in a space provided with a cartesian product structure. We call these cartesian counterfactuals. Cartesian counterfactuals can be modeled by assignment and contents functions as in program semantics. We also study the more general tree-structured counterfactuals.

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Neal Roese maintains a site Counterfactual Research News. There is extensive psychological research on what counterfactuals people come up with. Counterfactual Thought Experiments in World Politics by Phillip E. Tetlock and Aaron Belkin, 1996 contains examples relevant to this paper. Uchronia lists literature involving alternate histories. We thank Neal Roese for informing us about these sites, which we didn't know about when preparing the paper. We are fortunate that, so far as we can see, our present paper is orthogonal to everything to which the Roese site links. In particular, our emphasis on useful counterfactuals, counterfactuals in AI, cartesian counterfactuals and counterfactuals as inhabitants of approximate theories all seem to be new.

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