De Morgan algebra
English
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editEtymology
editNamed after British mathematician and logician Augustus De Morgan (1806–1871). The notion was introduced by Grigore Moisil.
Noun
editDe Morgan algebra (plural De Morgan algebras)
- (algebra, order theory) A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws.
- 1980, H. P. Sankappanavar, “A Characterization of Principal Congruences of De Morgan Algebras and its Applications”, in A. I. Arruda, R. Chuaqui, N. C. A. Da Costa, editors, Mathematical Logic in Latin America: Proceedings of the IV Latin American Symposium on Mathematical Logic, page 341:
- Finally it is shown that the compact elements in the congruence lattice of a De Morgan algebra form a Boolean sublattice.
- 2000, Luo Congwen, Topological De Morgan Algebras and Kleene-Stone Algebras: The Journal of Fuzzy Mathematics, Volume 8, Pages 1-524, page 268:
- By a topological de Morgan algebra we shall mean an abstract algebra where is a de Morgan algebra,
- 2009, George Rahonis, “Chapter 12: Fuzzy Languages”, in Manfred Droste, Werner Kuich, Heiko Vogler, editors, Handbook of Weighted Automata, Springer, page 486:
- If is a bounded distributive lattice with negation function (resp. a De Morgan algebra), then constitutes also a bounded distributive lattice with negation function (resp. a De Morgan algebra); for every its negation is defined by for every .
Hypernyms
editHyponyms
editTranslations
editbounded distributive lattice equipped with an involution satisfying De Morgan's laws
Further reading
edit- De Morgan's laws on Wikipedia.Wikipedia
- Complemented lattice on Wikipedia.Wikipedia