Ockham algebra

In mathematics, an Ockham algebra is a bounded distributive lattice ${\displaystyle L}$ with a dual endomorphism, that is, an operation ${\displaystyle \sim \colon L\to L}$ satisfying

• ${\displaystyle \sim (x\wedge y)={}\sim x\vee {}\sim y}$,
• ${\displaystyle \sim (x\vee y)={}\sim x\wedge {}\sim y}$,
• ${\displaystyle \sim 0=1}$,
• ${\displaystyle \sim 1=0}$.

They were introduced by Berman,¹ and were named after William of Ockham by Urquhart.² Ockham algebras form a variety.

Examples of Ockham algebras include Boolean algebras, De Morgan algebras, Kleene algebras, and Stone algebras.