IMTL逻辑代数的一种新强化形式

A schematic extension of IM TL-logic algebras

对IMTL-代数及其相关逻辑代数进行了进一步的研究,通过加强IMTL-代数条件的方法建立了IMTL*-代数,并通过实例证明了IMTL*-代数结构的存在性;其次,构造了一个非IMTL*-代数的IMTL-代数,说明了IMTL*-代数是IMTL-代数的真的强化形式,并基于IMTL-代数给出了IMTL*-代数的一些等价刻画;最后,给出了IMTL*-代数的蕴涵表示形式。本文的结果是对逻辑代数的研究内容和方法的有益补充。

IMTL and its related logic algebras are investigated in depth again and some new useful results are obtained. Firstly, the IMTL-algebras are introduced by strengthening the conditions of IMTL-algebra, and the existence of IMTL-algebras is explained by establishing structures of IMTL＊-algebra.Secondly, an algebra structure is established that is IMTL-algebra and not IMTL＊-algebra, which explains that IMTL＊-algebras are truely strengthened form of IMTL-algebras, and based on IMTL-algebras some equivalent characterization of IMTL＊-algebras are given.At last, the pure implication representation of IMTL＊-algebras is obtained.The results of this paper are necessary complemen-tarity to the methods and contents of logic algebras.