Construction of an Explicit Basis for Rules Admissible in Modal System S4

TLDR: In this article, an explicit basis for all admissible rules of the modal logic S4 is given, consisting of an infinite sequence of rules which have compact and simple, readable form and depend on increasing set of variables.

Abstract: We find an explicit basis for all admissible rules of the modal logic S4. Our basis consists of an infinite sequence of rules which have compact and simple, readable form and depend on increasing set of variables. This gives a basis for all quasi-identities valid in the free modal algebra ℱS4(ω) of countable rank.