Dr. Yoriyuki Yamagata (AIST)
Date: July 6 (Thursday) 2017
Time: 16:30 – 18:00
Venue: Large conference room in the basement, Faculty of Letters Main Building, Yoshida Campus, Kyoto University.
Title: Validity of bilateral classical logic and its application
In this talk, we report an ongoing work to define a notion of validity on Rumfitt’s bilateral classical logic. In particular, we define validity over the implicational fragment of the propositional bilateral classical logic, following Prawitz’s article “Ideas and Results in Proof Theory”. As an application, we prove strong normalization of such system under normalization rules, which reduce all introduction/elimination, reductio-ad-absurdum/elimination and reduction-ad-absurdum/contradiction-rules pairs on main branches of derivations. Further, we discuss the relation of our notion of validity and Dummett’s verificationist semantics. Although our definition of validity is hopelessly non-constructive, we argue that there is a way in which verificationists accept our notion of validity, by showing that the notion of decidability can be multiply interpreted.