De Morgan algebra

• de Morgan algebra

Named after British mathematician and logician Augustus De Morgan (1806–1871). The notion was introduced by Grigore Moisil.

De Morgan algebra (plural De Morgan algebras)

1. (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 ${\displaystyle (A,\land ,\lor ,\ ',l)}$ where ${\displaystyle (A,\land ,\lor ,l)}$ 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 ${\displaystyle (L,\leq ,{^{-}})}$ is a bounded distributive lattice with negation function (resp. a De Morgan algebra), then ${\displaystyle (L\langle \!\langle S\rangle \!\rangle ,\leq ,{^{-}})}$ constitutes also a bounded distributive lattice with negation function (resp. a De Morgan algebra); for every ${\displaystyle r\in L\langle \!\langle S\rangle \!\rangle }$ its negation ${\displaystyle {\overline {r}}\in L\langle \!\langle S\rangle \!\rangle }$ is defined by ${\displaystyle ({\overline {r}},s)={\overline {(r,s)}}}$ for every ${\displaystyle s\in S}$.

• Ockham algebra
  • distributive lattice

• Kleene algebra
  • Boolean algebra

• De Morgan's laws on Wikipedia.Wikipedia
• Complemented lattice on Wikipedia.Wikipedia