Speaker: Yanjing Wang (Peking University)
Date and Time: Thursday, November 11th 2021, 15:30-17:00, Amsterdam time.
Venue: online.
Title: Intuitionistic logic as an epistemic logic of knowing how
Abstract.
In this talk, we propose a general method to “decode” (propositional) intuitionistic logic and various intermediate logics as (dynamic) epistemic logics of knowing how. Our approach is inspired by some scattered ideas hidden in the vast literature of math, philosophy, CS, and linguistics about intuitionistic logic in the past 100 years, which echoed Heyting’s initial (but forgotten?) conception about intuitionistic truth as “knowing how to prove”. The core technical idea is to use a bundled know-how modality to unify the formalized Brouwer–Heyting–Kolmogorov interpretation and the Kripke semantics of intuitionistic logic. As we will see, this approach can reveal the hidden complicated dynamic-epistemic information behind the innocent-looking connectives but makes intuitionistic logic intuitive. With the natural but precise epistemic readings of intuitionistic formulas, various technical results about intuitionistic logic and intermediate logics become transparent, if not trivial. If time permits, we show how to decode inquisitive logic and some version of dependence logic as epistemic logics in order to demonstrate the power of this general approach, which could also be a meeting point of various research themes at ILLC.
(The talk is partly based on the joint work with Haoyu Wang and Yunsong Wang)