Ockham algebra

In mathematics, an Ockham algebra is a bounded distributive lattice with a dual endomorphism, that is, an operation ~ satisfying ~(x ∧ y) = ~x ∨ ~y, ~(x ∨ y) = ~x ∧ ~y, ~0 = 1, ~1 = 0. They were introduced by (Berman 1977), and were named after William of Ockham by (Urquhart 1979). Ockham algebras form a variety. Examples of Ockham algebras include Boolean algebras, De Morgan algebras, Kleene algebras, and Stone algebras.

References

• Berman, Joel (1977), "Distributive lattices with an additional unary operation", Aequationes Mathematicae 16 (1): 165–171, doi:10.1007/BF01837887, ISSN 0001-9054, http://gdz.sub.uni-goettingen.de/en/dms/loader/img/?PID=GDZPPN002030497  (pdf available from GDZ)
• Hazewinkel, Michiel, ed. (2001), "Ockham algebra", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=o/o110030 
• Blyth, Thomas Scott; Varlet, J. C. (1994). Ockham algebras. Oxford University Press. ISBN 978-0-19-859938-8. 
• Urquhart, Alasdair (1979), "Distributive lattices with a dual homomorphic operation", Polska Akademia Nauk. Institut Filozofii i Socijologii. Studia Logica 38 (2): 201–209, doi:10.1007/BF00370442, ISSN 0039-3215