Authors: Avgerinos Delkos and Marianna Girlando

Counterfactuals, studied in the seminal book by D. Lewis [2], 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, and which ought to be kept unchanged throughout the evaluation.

Inspired by the approach of Girard and Triplett in [3,4], 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 (mainly considering [3,4]). Furthermore, we 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 \(\mathsf{VC}\) (resp. \(\mathsf{VW}\)).
A preprint with full details is available [1].

Bibliography

1. A. Delkos and M. Girlando,A dynamic approach to ceteris paribus counterfactuals,arXiv preprint (2023), arXiv:2312.15209, {https://arxiv.org/abs/2312.15209}
2. D. Lewis,Counterfactuals,Blackwell,Oxford,1973.
3. P. Girard and M.A. Triplett,Ceteris paribus logic in counterfactual reasoning,Proceedings Fifteenth Conference on Theoretical Aspects of Rationality and Knowledge(TARK 2015),(R. Ramanujam, editor),vol. X215EPTCS,2015,pp. 176–193.
4. P. Girard and M.A. Triplett,Prioritised ceteris paribus logic for counterfactual reasoning,Synthese,vol. 195 (2018), no. 4, pp. 1681–1703.