Wagner Sanz
Universidade Federal de Goiás, Brasil

Abstract: The rule of Cut in the sequent calculus is a cornerstone of proof-theory. Its eliminability in a calculus guarantees a series of nice properties of this calculus, like consistency via subformula principle, etc. It has been usually treated as a syntactical property. We defy such an assumption. The points we intend to claim are the following: (i) Cut is a semantical principle; (ii) The notion of hypothesis is intimately related to Cut; (iii) A nice semantics for intuitionistic propositional logic is obtained if we admit the concept of hypothesis as a primary concept; (iv) Kripke semantics is intensionally wrong; (v) the tableaux rules are an immediate reading of the semantical clauses.

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