Boolean algebra (structure): Difference between revisions

Revision as of 14:42, 23 February 2024

Revision as of 02:25, 17 September 2024

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{{short description|Algebraic structure modeling logical operations}}

{{for -multi|an introduction to the subject|Boolean algebra|an alternative presentation|Boolean algebras canonically defined}}

{{Use dmy dates|date=November 2020}}

In [[abstract algebra]], a '''Boolean algebra''' or '''Boolean lattice''' is a [[complemented lattice|complemented]] [[distributive lattice]]. This type of [[algebraic structure]] captures essential properties of both [[Set (mathematics)|set]] operations and [[logic]] operations. A Boolean algebra can be seen as a generalization of a [[power set]] algebra or a [[field of sets]], or its elements can be viewed as generalized [[truth value]]s. It is also a special case of a [[De Morgan algebra]] and a [[Kleene algebra (with involution)]].

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=== General references ===

{{insufficientmore inlinefootnotes citationsneeded|date=July 2013}}

*{{citation

| last1 = Brown

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* {{springer|title=Boolean algebra|id=p/b016920}}

* [[Stanford Encyclopedia of Philosophy]]: "[http://plato.stanford.edu/entries/boolalg-math/ The Mathematics of Boolean Algebra]", by J. Donald Monk.

* McCune W., 1997. ''[http://www.cs.unm.edu/~mccune/papers/robbins/ Robbins Algebras Are Boolean]'' JAR 19(3), 263—276263–276

* [http://demonstrations.wolfram.com/BooleanAlgebra/ "Boolean Algebra"] by [[Eric W. Weisstein]], [[Wolfram Demonstrations Project]], 2007.

* Burris, Stanley N.; Sankappanavar, H. P., 1981. ''[http://www.thoralf.uwaterloo.ca/htdocs/ualg.html A Course in Universal Algebra.]'' Springer-Verlag. {{ISBN|3-540-90578-2}}.

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{{Order theory}}

{{DEFAULTSORT:Boolean Algebra (Structure)}}

{{DEFAULTSORT:Boolean Algebra (Structure)}}

[[Category:Boolean algebra| ]]

[[Category:Algebraic structures]]