Counterfactual Evaluation by Reopening Information States

Abstract

We develop a counterfactual semantics based on reopening partial information states. Evaluation first removes enough stated content to leave the antecedent’s attributes unresolved, retaining what the chosen scope protects, then asserts the antecedent and considers the surviving consistent refinements. Would and might quantify over the admissible alternatives; a weighted extension supplies graded evaluations. The principal result concerns finite models with fully supported residues. When a conjunctive antecedent reopens each constituent attribute, adding a supported conjunct can remove the grounds of another conclusion. A four-attribute countermodel therefore violates Cautious Monotony, excluding any smooth preferential representation that preserves the evaluable verdicts. We also establish a sufficient nesting condition for Cut and exhibit its failure without that condition. The conjunctive reopening rule is an explicit interpretive commitment; its suitability for ordinary-language counterfactuals remains an empirical question. The account uses declared dependencies, scope restrictions, and priorities, while the quantitative extension assumes a weight kernel. Comparisons with belief revision, premise semantics, update semantics, and causal intervention identify the consequences of reopening an attribute rather than merely making its proposed value consistent with retained information.