Logic Seminar: Elena Wüllhorst

A central problem for Kripke’s theory of truth is the availability of a mathematically strong conditional. This talk presents a consistent Kripke-style theory of truth with an added intuitionistic conditional. First, it constructs the semantic theory of truth in two-steps using order-theoretic fixed-point results. The resulting fixed-point model successfully formulates the T-schema A ↔ T ⌜A⌝ for Kripke's original language with the conditional. Next, it presents an axiomatization based on Thomason's logic. Following criteria outlined by Fischer et al. (2015), it analyses whether the axiomatization can meaningfully capture the semantic construction: it shows soundness with respect to the fixed-point model and analyses the proof-theoretic strength, which coincides with that of KF. And even though there are the expected computational complexity issues for the fixed-points of the jump with the conditional, there is a relativised N-categoricity result for the axiomatic theory. Thus, both the semantic and the axiomatic theory can be said to capture Kripke's original construction, while adding the expressive resources of the conditional. 

Aula 1, Palazzetto Gorresio

https://www.llc-philosophy.unito.it/logicllc/logicllc-seminars#h.qaugrsqvbjk2