On the Numbers of Minimal Tautologies and Properties of Their Proofs in Classical and Nonclassical Logic - Aмбарцумян Aрсен A.; Гаспарян, Гайк А.; Ованнисян, Саркис А.; Чубарян, Анаит А. (Mathematical Problems of Computer Science, 2021)
It is proved in this paper that the number of minimal tautologies for any given logic tautology of size п can be an exponential function in п, and it is also proved that for every tautology of the given logic there is some minimal tautology such that the number of its sequential form proof steps is equal to minimal steps in the proof of sequential form for the given tautology in cut-free sequent systems for classical, intuitionistic, Joganssons and monotone logics.