Abstract: Based on the BR0 algebra，Boolean algebra，Basic system L* and propositional calculus system L，the relations between
BR0 algebra and Boolean algebra have been discussed.Particularly，two extension of BL* are obtained by adding axioms(A →B) →¬A ∨ B(A →(B → C)) →(A ∧ B → C) to basic system L*.Then the equivalence between them and system L is
proved.

摘要： 对BR₀代数，Boole 代数以及BL*系统，命题演算形式系统L进行了研究。首先讨论了BR₀代数与Boole 代数间的相互关系，随后在BL*系统中分别添加公理模式(A →B) →¬A ∨ B或(A →(B → C)) →(A ∧ B → C)得到BL*系统的两种扩张，并证明了BL*系统的这两种扩张与命题演算形式系统L之间是等价的。