×

zbMATH — the first resource for mathematics

Independent bases of admissible rules. (English) Zbl 1146.03008
In their study of admissibility of rules in the intuitionistic propositional logic IPC and normal modal logics, Rybakov and others showed among others that there exists a tabular logic without independent basis of admissible rules and all pretabular extensions of S4 or IPC have an independent basis of addimissible rules, leaving open the problem to ask whether the basic transitive logics (K4, S4, IPC) enjoy independent bases of admissible rules.
In this paper the author gives an affirmative answer to the question in an extended form. For the logics IPC, K4, GL, S4, and for any extension to inherit the admissible rules of one of them, the author and Iemhoff have already given explicit (non-independent) bases of admissible rules, which then are reconstructed here so as to be independent.

MSC:
03B45 Modal logic (including the logic of norms)
03B55 Intermediate logics
PDF BibTeX Cite
Full Text: DOI