🤖 AI Summary
Existing “counting-based” ceteris paribus (CP) counterfactual evaluation methods often yield counterintuitive results by neglecting the differential importance of antecedents. This paper proposes a significance-aware dynamic logical framework: it formalizes CP conditionals for the first time as iterative dynamic operators; defines model-update semantics based on (weak) center-sphere models; and introduces a formula significance weighting mechanism that enables multi-step counterfactual reasoning while preserving key antecedents invariant. The framework uniformly integrates Lewis’s VC (centered) and VW (weakly centered) axiom systems, and we rigorously establish its formal completeness with respect to both. By grounding counterfactual reasoning in a semantics that respects intuitive priority among antecedents, the framework delivers enhanced intuitiveness, expressivity, and computational tractability—providing a more principled foundation for CP reasoning in formal epistemology and AI.
📝 Abstract
Counterfactuals are conditional statements describing consequences of states of affairs that might not have occurred. Ceteris paribus counterfactuals take into account specific conditions which hold at the actual state of affairs, and which ought to be kept unchanged throughout the evaluation. Inspired by the approach of Girard and Triplett, we define ceteris paribus conditionals as dynamic operators over (weakly) centered sphere models. We introduce three ways of evaluating the operators, by updating sphere models based on ceteris paribus sets of formulas. Our approach features two main novelties: on the one hand, we define our ceteris paribus conditionals as proper dynamic operators, thus allowing for iterated evaluations. On the other hand, when updating the worlds within a system of sphere we additionally take into account a notion of 'significance' of the formulas that ought to be kept unchanged. We discuss the relations of our model updates with other prioritisations introduced in the literature, and show completeness of the set of valid formulas in the updated centered (resp. weakly centered) sphere models with respect to Lewis' axiomatization of the conditional logic VC (resp. VW).
