Abstract:

The problem of decidability of global admissibility of GL logic rules, i.e. admissibility of an inference rule in all finitely approximable (tabular) extensions of GL logic at once, is investigated. For rules whose model satisfies certain natural properties, a necessary and sufficient condition for global admissibility in GL logic is obtained. Based on the obtained description, an algorithm for checking the global admissibility of an arbitrary rule in reduced form is constructed. Thus, the problem of global admissibility in GL logic is decidable.