Uniform Interpolation in Provability Logics

Autoři: Mgr. Marta Bílková, Ph.D.
Rok vydání: 2016
Typ publikace: Kapitola v monografii
Periodikum: Liber Amicorum Alberti. A Tribute to Albert Visser
Projekty: Algebraické metody v teorii důkazů
Bibliografická citace: BÍLKOVÁ, Marta. Uniform Interpolation in Provability Logics. In: EIJCK VAN, J., IEMHOFF, R., JOOSTEN, J.J., eds. Liber Amicorum Alberti. A Tribute to Albert Visser. London: College Publications, 2016, S. 57-90. Tributes, 30. ISBN 978-1-84890-204-6.
ID: 471990

Abstrakt

We prove the uniform interpolation theorem in modal provability logics GL and Grz by a proof-theoretical method, using analytical and terminating sequent calculi for the logics. The calculus for Godel-Lob’s logic GL is a multiset based variant of the standard sequent calculus, in the case of Grzegorczyk’s logic Grz, the calculus implements an explicit loop-preventing mechanism inspired by work of Heuerding.