Axioms for a Logic of Consequential Counterfactuals.

The article focuses on the development and analysis of a logic system called CI.0, which formalizes two types of consequential implication: analytical (→) and synthetic (↠). CI.0 is shown to be definitionally equivalent to the modal system KT and is extended with a circumstantial operator (*) to form CI.0*Eq, enabling the formalization of context-dependent (counterfactual) conditionals via ↠. The paper establishes a complete, tableau-decidable system KTw that mediates between CI.0*Eq and CI.0, providing soundness, completeness, and decidability results through translations among their languages and corresponding model classes. It further demonstrates that the ↠ operator satisfies key positive and negative properties expected of synthetic conditionals, including failure of transitivity and contraposition, distinguishing it from classical conditional logics. The study suggests that CI.0 offers a linguistically faithful and computationally manageable framework for consequential implication, with potential for future exploration of its relations to classical conditional logics and extensions to quantificational settings.