Abstract: It is well known that the distributive law plays a core role in deduction mechanism of classical logic.How-ever,distributive law is abandoned in quantum logic,so that the classic deduction mechanism disappears from quantum,which spontaneously arises the debate whether the quantum logic can be called “logic”? In this paper,we introduced the defects of using closed subspaces of Hilbert space to describe quantum logic and deeply analyzed the deduction mechanism in classical logic.Further,the deduction mechanism can be established in quantum logic by using the orthomodular law instead of distributive law.In particular,the deduction mechanism can be renewed with adjunctions in category,which is a generalization of deduction mechanism in classical logic.

Key words: Distributive law,Deduction mechanism,Orthomodular law,Adjunctions