The interpolation problem over Johansson’s minimal logic J is considered. We introduce a series of Johansson algebras, which will be used to prove a number of necessary conditions for a J-logic to possess Craig’s interpolation property (CIP). As a consequence, we deduce that there exist only finitely many finite-layered pre-Heyting algebras with CIP.
- Craig’s interpolation property
- finite-layered pre-Heyting logic
- Johansson algebra
- MINIMAL LOGIC
- Craig's interpolation property