In mathematics, an Ockham algebra is a bounded distributive lattice L {\displaystyle L} with a dual endomorphism, that is, an operation ∼ : L → L {\displaystyle \sim \colon L\to L} satisfying
∼ ( x ∧ y ) =
∼ x ∨
∼ y {\displaystyle \sim (x\wedge y)={}\sim x\vee {}\sim y} ,
∼ ( x ∨ y ) =
∼ x ∧
∼ y {\displaystyle \sim (x\vee y)={}\sim x\wedge {}\sim y} ,
∼ 0 = 1 {\displaystyle \sim 0=1} ,
∼ 1 = 0 {\displaystyle \sim 1=0} . They were introduced by Berman, and were named after William of Ockham by Urquhart. Ockham algebras form a variety.
Examples Examples of Ockham algebras include Boolean algebras, De Morgan algebras, Kleene algebras, and Stone algebras.
References
Further reading Blyth, Thomas Scott (2001) [1994], "Ockham algebra", Encyclopedia of Mathematics, EMS Press Blyth, Thomas Scott; Varlet, J. C. (1994). Ockham algebras. Oxford University Press. ISBN 978-0-19-859938-8.