Certain Method for Generating a Series of Logics
Satoshi Miura, Shûrô Nagata · Nagoya Mathematical Journal · 1968
At first, we define three relations ⊇, =, and ⊃ in connection with a pair of logics L and L* as follows: L ⊇ L*, if and only if every proposition provable in L* is also provable in L; L = L*, if and only if L ⊇ L* and L* ⊇ L; L ⊃ L*, if and only if L, ⊇ L* but not L* ⊇ L.