De Morgan algebra

plural De Morgan algebras · alternative de Morgan algebra

1. algebraA bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws.

   Finally it is shown that the compact elements in the congruence lattice of a De Morgan algebra form a Boolean sublattice.

   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

   2 more examples

   By a topological de Morgan algebra we shall mean an abstract algebra (A,#92;land,#92;lor,#92;',l) where (A,#92;land,#92;lor,l) is a de Morgan algebra,

   2000, Luo Congwen, Topological De Morgan Algebras and Kleene-Stone Algebras: The Journal of Fuzzy Mathematics, Volume 8, Pages 1-524, page 268

   If (L,#92;le,#123;⁻#125;) is a bounded distributive lattice with negation function (resp. a De Morgan algebra), then (L#92;langle#92;#33;#92;langleS#92;rangle#92;#33;#92;rangle,#92;le,#123;⁻#125;) constitutes also a bounded distributive lattice with negation function (resp. a De Morgan algebra); for every r#92;inL#92;langle#92;#33;#92;langleS#92;rangle#92;#33;#92;rangle its negation #92;overline#123;r#125;#92;inL#92;langle#92;#33;#92;langleS#92;rangle#92;#33;#92;rangle is defined by (#92;overline#123;r#125;,s)#61;#92;overline#123;(r,s)#125; for every s#92;inS.

   2009, George Rahonis, “Chapter 12: Fuzzy Languages”, in Manfred Droste, Werner Kuich, Heiko Vogler, editors, Handbook of Weighted Automata, Springer, page 486