JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (11): 65-70.doi: 10.6040/j.issn.1671-9352.0.2017.058

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Properties of residuated lattice of deduction systems set algebra in BL system

LIANG Ying, CUI Yan-li, WU Hong-bo   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Received:2017-02-20 Online:2017-11-20 Published:2017-11-17

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Abstract: Firstly, the concept of deduction system of the basic propositional logic system BL is defined, and the method generating deduction system from a subset of formula set F(S)is obtained, and the identity of deduction system and conclusions set is proved. Secondly, in propositional logic system BL the existence of supremum and infimum is proved in family D(F )consisting of all deductive systems with partial order relation of ⊆; Moreover, binary operations *,→ are defined in family D(F ), and it is proved that set algebra(D(F ),∧,∨,*,→,⊥, F(S))is a complete residuated lattice satisfying divisibility.

Key words: propositional logic system BL, deduction system, residuated lattice, fuzzy logic, divisibility

CLC Number: 

  • O141
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