an:06581390
Zbl 1397.03016
Bezhanishvili, Nick; Gabelaia, David; Ghilardi, Silvio; Jibladze, Mamuka
Admissible bases via stable canonical rules
EN
Stud. Log. 104, No. 2, 317-341 (2016).
0039-3215 1572-8730
2016
j
03B20 03B25 03B45
admissible rules; admissible bases; modal logic; intuitionistic logic; modal algebras; Heyting algebras; canonical rules; decidability.
The dichotomy property means that a canonical multi-conclusion rule is either admissible or equivalent to an assumption-free rule. The authors establish the same property for stable multi-conclusion canonical rules for the intuitionistic propositional calculus (IPC), and the modal systems K4 and S4 (see [\textit{V. V. Rybakov}, Admissibility of logical inference rules. Amsterdam: Elsevier (1997; Zbl 0872.03002)]). An immediate consequence of the main result is decidability of the admissibility problem for IPC, K4 and S4, while the admissibility for the basic modal logic K remains a long standing open problem.
Branislav Boričić (Beograd)
0872.03002