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Workshop on Proof Theory, Modal Logic and Reflection Principles
October 19, 2017 15:15–15:40, Moscow, Steklov Mathematical Institute

Student session

On axiomatization and polytime decidability of strictly positive fragments of some modal logics

M. Svyatlovsky
 Video records: MP4 845.3 Mb MP4 192.3 Mb

Abstract: We call a formula strictly positive, if it is built of propositional variables, conjunction and modal diamond operators. The strictly positive fragment (SP-fragment) of a logic L is the set of all provable in L implications A$\to$B, where A and B are strictly positive formulas. E. V. Dashkov proved that Gödel–Löb provability logic GL and the logic K4 have the same SP-fragments.