Proof-Theoretic Considerations on the Structure of Reasoning with Counterfactuals and Knowledge

Taking an intuitionistic stance and regarding proof theory as methodologically basic for semantics and logic, we develop, building on previous work (J. Log. Comput. 31(3): 704-770, 2021; Bull. Symb. Log. 32(1): 136-196, 2026), a proof-theoretic framework for the study of the inferential interaction between counterfactuals and belief/knowledge. Relying on the technical results obtained for this framework (preservation, normalization, the subexpression property), we give a proof-theoretic semantics for elementary constructions which combine (counter)factuals, belief, knowledge, disbelief, and ignorance.