# zbMATH — the first resource for mathematics

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