Mercoledì 20 marzo 2024 ore 11.00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
Sala Altana
Gerhard Jaeger (University of Bern)
Gentzen in the 3- and 4-Valued Jungle
Abstract: Starting point is the well known sequent calculus LK for classical propositional logic à la Gentzen. From that we move on to weak and strong 3-valued Schütte valuations and relate them to structural properties of LK. It is then a natural step to look at Kleene’s approach to 3-valued logic. Two central parts of my talk deal with syntactic properties of Kleene’s 3-valued logic and Belnap’s 4-valued logic and sound and complete sequent calculi for both. Belnap’s 4-valued logic is then used as a basis for a formal approach to the Catuskoti, an important principle of reasoning in Indian logic and theology. We end our talk with presenting a corresponding formal framework that also incorporated some ideas due to Graham Priest.