Undecidable properties of extensions of provability logic. II
[For part I see Algebra Logika 29, No.3, 350-367 (1990; Zbl 0723.03005).] The aim of this paper is to study questions of effective recognition of properties of modal logics which extend the Gödel-Löb system GL. Using some uniform emulation method for the working of a Minski maschine in modal propositional logic, the author shows that the following properties: a) to be Kripke-complete, b) to be the modal counterpart of Int, c) to be closed with respect to the Gödel normalization rule, d) to be Halldén-complete, are undecidable. By the way, some interesting results of other kinds are obtained. For instance that there are \(2^{\omega}\) maximal logics among the modal counterparts of Int extending the logic S.
modal logics which extend the Gödel-Löb system GL
scientific article; zbMATH DE number 4204314