Por Joaquim Waddington (UERJ/UCL).

The separation property states that given a system S, S has the separation property if, whenever Π is a Normal Deduction of A from Γ in S, then the only inference rules that are applied in Π are the inference rules for the logical constants that occur in A or in some formula of Γ. The separation property is closely related to the subformula property. In fact, the separation property is a corollary of the subformula property, but the converse is not the case. There are systems for propositional classical logic in natural deduction that have the separation property but don’t have the subformula property. The purpose of this talk is to share some of the results obtained during my Master’s dissertation, specifically (I) the development of the NH system, (II) the development of a normalization procedure for the NH system, and (III) the classification of different classical natural deduction systems into three grades of analyticity: (i) non analytical systems (systems that have neither the subformula nor the separation property), (ii) strictly analytical systems (systems that have the separation property but don’t have the subformula property) and (iii) Ultra Strictly Analytical systems (systems that have the separation property and the subformula property). The NH system is a natural deduction system for propositional classical logic obtained through the addition of Hosoi’s rule ((A → B) → B), (A → C), (B → C) ⊢ C to the propositional fragment of Gentzen’s NJ system.

Transmissão via Zoom (pw: 919 4789 5133).