35th International Symposium on Multiple-Valued Logic (ISMVL'05) Partially Ordered Set with Residuated t-norm University of Calgary, Canada May 19-May 21 ISBN: 0-7695-2336-6
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ISMVL.2005.37
We consider properties of partially ordered sets with residuated t-norm and show that1. If (X; T, 0, 1) is a bounded partially ordered set with residuated t-norm T, then (X; *, 0_{x} , 1_{x} ) is a bounded BCK-algebra with condition (S);2. Conversely, if (B; *, 0_{B} , 1_{B} ) is a bounded BCK-algebra with (S), then (B; T, 0, 1) is the bounded partially ordered set with residuated t-norm.This means that the class of all bounded partially ordered sets with residuated t-norm coincides with the class of all bounded BCK-algebras with condition (S). Since the class of these algebras forms a variety, the class of partially ordered sets with residuated t-norm is represented by only equations.
Citation:
Michiro Kondo, Mayuka F. Kawaguchi, "Partially Ordered Set with Residuated t-norm," ismvl, pp.26-29, 35th International Symposium on Multiple-Valued Logic (ISMVL'05), 2005 Usage of this product signifies your acceptance of the Terms of Use. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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