Speaker: Bartosz Więckowski (Goethe Universität Frankfurt am Main)
Date and Time: Thursday, March 6th 2025, 16:30-18:00
Venue: ILLC Seminar Room F1.15, Science Park 107 and online.
Title: Proof-Theoretic Considerations on the Structure of Reasoning with Counterfactuals and Knowledge.
Abstract. Combined reasoning with counterfactuals and knowledge/belief may involve constructions which:
(i) embed knowledge (relativized to an agent a) in the antecedent (resp. consequent) of a counterfactual (e.g., ‘If a knew that A, a would believe that B’), or
(ii) prefix knowledge to a counterfactual (e.g., ‘a knows that if A were the case, B would be the case’), or
(iii) do both;
where the embedding and prefixing can be iterated. Counterfactual inference is typically studied from a model-theoretic perspective. In this talk, we take a proof-theoretic perspective. We combine components from [1] and [2], so as to obtain intuitionistic subatomic natural deduction systems for combined reasoning with (‘would’- and ‘might’-) counterfactuals and knowledge (resp. belief) which are proof-theoretically well-behaved (normalization, subexpression/subformula property, internal completeness) and which admit the formulation of a semantically autarkic proof-theoretic semantics for elementary combined constructions of the aforementioned kinds.
[1] Więckowski, B. (2021). Intuitionistic multi-agent subatomic natural deduction for belief and knowledge, Journal of Logic and Computation 31(3): 704-770. Special issue on External and Internal Calculi for Non-Classical Logics edited by A. Ciabattoni, D. Galmiche, N. Olivetti, and R. Ramanayake.
https://doi.org/10.1093/logcom/exab013
[2] —. (2024). Counterfactual assumptions and counterfactual implications. In Piecha, T. and Wehmeier, K. F., eds., Peter Schroeder-Heister on Proof-Theoretic Semantics, Outstanding Contributions to Logic, Vol. 29, pp. 399-423. Cham, Switzerland: Springer.
https://doi.org/10.1007/978-3-031-50981-0_15