京都大学数理解析研究所の佐藤です。
10月13日11:00から、チェコ科学アカデミーのAdam Prenosil氏に 以下の講演をしていただくことになりましたので、 ご連絡いたします。どうぞお気軽にお越しください。
========== Time: 11:00-12:00, 13 Oct, 2016 Place: Rm 478, Research Building 2, Main Campus, Kyoto University 京都大学 本部構内 総合研究2号館 4階478号室 http://www.kyoto-u.ac.jp/en/access/yoshida/main.html (Building 34) http://www.kyoto-u.ac.jp/ja/access/campus/map6r_y.htm (34番の建物)
Speaker: Adam Prenosil (Czech Academy of Sciences)
Title: Classical proof theory, non-classically
Abstract: We present an approach to cut elimination in classical logic which appeals to elimination rules.rather than to induction on cut rank and which works equally well for proofs from a non-empty set of sequential premises. As an illustration of the benefits of accepting elimination rules as an integral part of the sequent calculus for classical logic, we use the calculus with elimination rules to provide a particularly simple syntactic proof of a recent non-classical refinement of Craig's interpolation theorem due to Milne. This approach, while non-standard, is in fact natural when we view classical logic as part of the family of super-Belnap logics, that is, extensions of the four-valued Belnap-Dunn logic. We shall therefore start by introducing this family proof-theoretically as the logics which retain the structural and logical rules of classical logic, but relax Identity and Cut (as opposed to substructural logics, which retain Identity and Cut but relax the structural rules of classical logic).