See De Morgan algebra on Wiktionary
{
"etymology_text": "Named after British mathematician and logician Augustus De Morgan (1806–1871). The notion was introduced by Grigore Moisil.",
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"ref": "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:",
"text": "Finally it is shown that the compact elements in the congruence lattice of a De Morgan algebra form a Boolean sublattice.",
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"ref": "2000, Luo Congwen, Topological De Morgan Algebras and Kleene-Stone Algebras: The Journal of Fuzzy Mathematics, Volume 8, Pages 1-524, page 268:",
"text": "By a topological de Morgan algebra we shall mean an abstract algebra (A,#x5C;land,#x5C;lor,#x5C;',l) where (A,#x5C;land,#x5C;lor,l) is a de Morgan algebra,",
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"ref": "2009, George Rahonis, “Chapter 12: Fuzzy Languages”, in Manfred Droste, Werner Kuich, Heiko Vogler, editors, Handbook of Weighted Automata, Springer, page 486:",
"text": "If (L,#x5C;le,#x7B;⁻#x7D;) is a bounded distributive lattice with negation function (resp. a De Morgan algebra), then (L#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle,#x5C;le,#x7B;⁻#x7D;) constitutes also a bounded distributive lattice with negation function (resp. a De Morgan algebra); for every r#x5C;inL#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle its negation #x5C;overline#x7B;r#x7D;#x5C;inL#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle is defined by (#x5C;overline#x7B;r#x7D;,s)#x3D;#x5C;overline#x7B;(r,s)#x7D; for every s#x5C;inS.",
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"A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws."
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"(algebra, order theory) A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws."
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"ref": "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:",
"text": "Finally it is shown that the compact elements in the congruence lattice of a De Morgan algebra form a Boolean sublattice.",
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{
"ref": "2000, Luo Congwen, Topological De Morgan Algebras and Kleene-Stone Algebras: The Journal of Fuzzy Mathematics, Volume 8, Pages 1-524, page 268:",
"text": "By a topological de Morgan algebra we shall mean an abstract algebra (A,#x5C;land,#x5C;lor,#x5C;',l) where (A,#x5C;land,#x5C;lor,l) is a de Morgan algebra,",
"type": "quote"
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"ref": "2009, George Rahonis, “Chapter 12: Fuzzy Languages”, in Manfred Droste, Werner Kuich, Heiko Vogler, editors, Handbook of Weighted Automata, Springer, page 486:",
"text": "If (L,#x5C;le,#x7B;⁻#x7D;) is a bounded distributive lattice with negation function (resp. a De Morgan algebra), then (L#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle,#x5C;le,#x7B;⁻#x7D;) constitutes also a bounded distributive lattice with negation function (resp. a De Morgan algebra); for every r#x5C;inL#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle its negation #x5C;overline#x7B;r#x7D;#x5C;inL#x5C;langle#x5C;#x21;#x5C;langleS#x5C;rangle#x5C;#x21;#x5C;rangle is defined by (#x5C;overline#x7B;r#x7D;,s)#x3D;#x5C;overline#x7B;(r,s)#x7D; for every s#x5C;inS.",
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"A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws."
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"(algebra, order theory) A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws."
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