JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

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A schematic extension of IMTL-logic algebras#br#

ZHOU Jian-ren1,2, WU Hong-bo2*   

  1. 1. College of Mathematics and Statistics, Hexi University, Zhangye 734000, Gansu, China;
    2. College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an   710062, Shaanxi, China
  • Received:2013-06-18 Online:2014-04-20 Published:2014-06-03

Abstract: 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 complementarity to the methods and contents of logic algebras.

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