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中文摘要：
首先,在范数的条件下将格H蕴涵代数进行了扩充（即赋范格H蕴涵代数）,并讨论了它的性质.其次,在赋范格H蕴涵代数中定义了蕴涵距离d→,∨-距离d_∨,∧-距离d_∧,讨论了它们之间的性质,并通过两个赋范格H蕴涵代数L_1和L_2定义了赋范蕴涵满射、赋范格H蕴涵同态、赋范格H蕴涵同构以及赋范同构,随后研究了它的性质.最后,探讨了收敛数列的有界性,得到了数列运算（即,,∨,∧,→）对于蕴涵距离是有界的结论.
英文摘要：
Firstly,in this paper,under a norm situation,the notion of lattice H implication algebra L~（[15]） is extended（i.e.,normed lattice H implication algebras）,and some properties are discussed.Secondly,with the properties of implication distance d_→,∨-distance d_∨and∧-distance d_∧in normed lattice H implication algebras L investigated,the authors also define norned implication epimorphism、normed lattice H implication homomorphism、normed lattice H implication isomorphism and normed isomorphism by using of a mapping f which has two normed lattice H implication algebras L_1 and L_2 together with its properties studied.Finally, the authors further probe into the boundedness of convergence sequence,showing that sequences operations（i.e.,,⊕,∨,∧,→） to implication distance is bounded.
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