On three-valued presentations of classical logic

BRUNO DA RE; DAMIAN SZMUC

Workshop; Logical Connectives Session of the X Workshop on Philosophical Logic; 2021

Cobreros, Égré, Ripley, and van Rooij (2012) have shown that the logic defined using the strict-tolerant consequence relation over the (three-valued) Strong Kleene schema coincides with classical logic (at least inferentially speaking). More recently, Ferguson and Szmuc (2021) have proved that the (three-valued) Weak Kleene schema serves that purpose also. The aim of this talk is twofold. First, we generalize these results and present all of the three-valued schemata such that the strict-tolerant consequence relation over them coincides with classical logic. Secondly, we generalize these results and present all of the three-valued schemata such that the tolerant-strict, strict-strict, tolerant-tolerant, and order-consequence relation over them coincides with classical logic. This is based on joint work with Emmanuel Chemla and Paul Egré.