In  the classification of extensions of the minimal logic J using slices was introduced and decidability of the classification was proved. We will consider extensions of the logic Gl = J + (A V ¬A). The logic Gl and its extensions have been studied in [8, 9]. In , it is established that the logic Gl is strongly recognizable over J, and the family of extensions of the logic Gl is strongly decidable over J. In this paper we prove strong decidability of the classification over Gl: for every finite set Rul of axiom schemes and rules of inference, it is possible to efficiently calculate the slice number of the calculus obtained by adding Rul as new axioms and rules to Gl.
- The minimal logic
- Kripke frame
- recognizable logic
- 1.01 MATHEMATICS
State classification of scientific and technological information
- 27.03 Mathematical logic and foundations of mathematics