JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE) ›› 2013, Vol. 43 ›› Issue (3): 13-18.

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The algebraic structure of α-resolution fields based on lattice-valued logic systems LP(X)

LIU Yi1,2, JIA Hai-rui2, QIN Xiao-yan2, XU Yang2 *   

  1. 1.College of Mathematics and Information Sciences, Neijiang Normal University, Neijiang 641112, China;
    2. Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, China
  • Received:2012-12-05 Online:2013-06-20 Published:2012-12-05

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Abstract:

First, the generalized literals set D*α (g), which couldn′t be α-resolved with a fixed generalized literal g, was a ∨-semigroup and an order filter. Second, a new algebraic structure Df  determined by D*α(g) was a lattice filter, and the properties of Df  were investigated. Finally, the algebraic structure κ(D)  was determined by Df, the fact that  κ(D) was a filter was obtained and the structure of κ(D) was studied.

Key words: filter, α-resolution, lattice-valued logic systems, resolution field, lattice implication algebras

CLC Number: 

  • TP18
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