Construction of an explicit basis for rules admissible in modal system S4. (English) Zbl 0992.03027

Rybakov, Vladimir V.

Math. Log. Q. 47, No. 4, 441-446 (2001).

Summary: 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 a compact and simple, readable form and depend on an increasing set of variables. This gives a basis for all quasi-identities valid in the free modal algebra \({\mathcal F}_{\text{S4}}(\omega)\) of countable rank.

MSC:

03B45	Modal logic (including the logic of norms)
03G25	Other algebras related to logic

Keywords:

admissible inference rules; basis for admissible rules; basis for quasi-identities; modal logic S4; free modal algebra