Reinhard Kahle
CMA and DM, FCT, Universidade Nova de Lisboa

Abstract: Schwichtenberg observed that a naive understanding of the BHK (Brouwer-Heyting-Kolmogorov) interpretation leads to a trivial “proof" of Fermat's last theorem, as its forall clause only requires that one can verify the statement of Fermat's last theorem for all numerical instances. For a formalized version of BHK, Artemov resolved this problem by making use of an idea of Gödel. In this talk, we will show that the corresponding paradox for dialogical logic cannot be resolved in the same, but that it is an intrinsic problem for this framework. As conclusion we will argue that dialogical logic has to be considered as some kind of semantics rather than a framework allowing for derivations.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.