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Workshop on Proof Theory, Modal Logic and Reflection Principles
October 18, 2017 11:10–11:45, Moscow, Steklov Mathematical Institute

Instantial Neighborhood Logic — tableau, sequent calculus, and interpolation

J. Yu
 Video records: MP4 1,030.3 Mb MP4 282.4 Mb

Abstract: Instantial Neighborhood Logic (INL) employs a two-sorted operator $\square$. In INL, formula $\square(\alpha_1,…,\alpha_j;\alpha_0)$ means, the current point has a neighborhood in which $\alpha_0$ universally holds, and none of $\alpha_1,…,\alpha_j$ universally fails. In my talk last year at Tbilisi State University, a tableau system for INL was presented. To continue, in this talk we convert that tableau system to a hyper-sequent calculus, and then to a (normal) sequent calculus G3inl. Based on a splitting version of G3inl, we will explain how Lyndon interpolation theorem of INL is constructively established.