Ockham algebra

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

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

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.

Further reading

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