Negative equivalence over the minimal logic and interpolation

摘要

It is proved that extensions of the minimal Johansson logicJ are negatively equivalent if and only if their centers are equal. It isproved in [1] that the logics with the weak interpolation property WIPare divided into eight intervals with etalon logics on the top. Therefore alogic possesses WIP iff it is negatively equivalent to one of the eight etalonlogics. An axiomatization and a semantic characterization are found forWIP-minimal logics, which are the least elements of all eight intervals oflogics with WIP. The Craig interpolation property CIP is stated for themost of WIP-minimal logics.