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Construction of an Explicit Basis for Rules Admissible in Modal System S4
Author(s) -
Rybakov Vladimir V.
Publication year - 2001
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200111)47:4<441::aid-malq441>3.0.co;2-j
Subject(s) - mathematics , modal , basis (linear algebra) , calculus (dental) , mathematical economics , algebra over a field , pure mathematics , geometry , chemistry , medicine , dentistry , polymer chemistry
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 ℱ S4 ( ω ) of countable rank.