We are very happy to announce the next talk in the Semantic Colloquium, which will take place on Thursday, June 27, 4 – 6 pm in IG 4.301.
Bartosz Wieckowski will present „Modes of assumptions and moods of implications“.
We define a natural deduction system for factual and counterfactual implication IFC on top of an intuitionistic natural deduction system S which serves as a reference system for making assumptions in IFC. Intuitively, the set of formulae canonically derived in S comprises what is counted as a fact in the IFC-system based on it. In IFC-systems one may distinguish three modes of making assumptions.
A formula can be assumed factually in case it is contained in the set of facts, it can be assumed counterfactually in case it is not so contained, and it can be assumed in an independent mode, that is, regardless of whether it is a fact or not. Factual (counterfactual, standard) implications are derived by appeal to factual (counterfactual, independent) assumptions. We show, using standard methods, that derivations in IFC-systems normalize and that normal derivations possess the subformula property. As a corollary to this result we obtain a separation theorem. Based on the normalization result we formulate a proof-theoretic semantics for factual and counterfactual implication which explains the meaning of these implications entirely in terms of the structure of derivations. The semantics is in agreement with a BHK- or proof interpretation for these operators. Moreover, it is foundationally autarkic, since it is not defined on the basis of a formal semantics of a different kind (e.g., a possible worlds similarity semantics).
You are cordially invited!