On weak implication algebra

In this paper, we introduce the notion of implication filter as a generalization of Boolean filter of first kind in Hilbert algebra and study it in detail. Also, we prove that F is an implication filter of a Hilbert algebra H if and only if every implicative filter of quotient algebra H  /  F is an...

Full description

Saved in:
Bibliographic Details
Published inSoft computing (Berlin, Germany) Vol. 23; no. 14; pp. 5393 - 5400
Main Authors Soleimani Nasab, Ali, Borumand Saeid, Arsham
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2019
Springer Nature B.V
Subjects
Algebra
Artificial Intelligence
Boolean
Boolean algebra
Computational Intelligence
Control
Engineering
Foundations
Logic
Mathematical Logic and Foundations
Mechatronics
Quotients
Robotics
Implication filter
Weak implication algebra
Online AccessGet full text

Cover

More Information
Summary:In this paper, we introduce the notion of implication filter as a generalization of Boolean filter of first kind in Hilbert algebra and study it in detail. Also, we prove that F is an implication filter of a Hilbert algebra H if and only if every implicative filter of quotient algebra H  /  F is an implication filter. Finally, we generalized Boolean algebra and introduced a weak implication algebra, we prove that F is an implication filter of a Hilbert algebra H if and only if the quotient algebra H  /  F is a weak implication algebra. By suitable diagrams, we summarize the results of this paper and the previous results in these fields.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-018-3495-0