PhD Defense - Quentin BLOMET. "Mixed Consequence Logics"

Date/time : Wednesday, December 18, 9:00 a.m.

Location : Salle Madeleine Rebérioux (R2-02), École normale supérieure - Campus Jourdan, 48 boulevard Jourdan, 75014 Paris (or contact quentin.blomet@ens.psl.eu for a Zoom link)

Committee

• Rhys Borchert (University of Greifswald) - Examiner
• Emmanuel Chemla (LSCP, CNRS - ENS-PSL) - Examiner
• Paul Égré (IRL Crossing, CNRS - IJN, ENS-PSL) - Co-supervisor
• Sabine Frittella (INSA - Université d’Orléans) - Reviewer
• Francesca Poggiolesi (IHPST, CNRS - Université Paris 1) - Examiner
• Damian Szmuc (IIF-SADAF - CONICET) - Examiner
• Allard Tamminga (University of Greifswald) - Co-supervisor
• David Ripley (Monash University) - Reviewer

Abstract

We investigate three-valued mixed consequence logics, such as the strict-tolerant logic ST and the tolerant-strict logic TS, where the values for evaluating premises and conclusions of arguments may differ. We characterize these logics in terms of their pure counterparts, such as the well-known logics K3 and LP, and provide several refinements of Craig’s interpolation theorem. We discuss the role played by the properties of Transitivity and Reflexivity in the characterization of these logics. Duality is central to our analysis, we examine various forms from the literature, guiding us toward a broader concept that extends beyond three-valued frameworks.