Ockham algebra

{{format footnotes |date=May 2024}}

In mathematics, an Ockham algebra is a bounded distributive lattice L with a dual endomorphism, that is, an operation \sim\colon 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 {{harvtxt|Berman|1977}}, and were named after William of Ockham by {{harvtxt|Urquhart|1979}}. Ockham algebras form a variety.

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

References

  • {{Citation | last1=Berman | first1=Joel | title=Distributive lattices with an additional unary operation | doi=10.1007/BF01837887 | mr=0480238 | year=1977 | journal=Aequationes Mathematicae | issn=0001-9054 | volume=16 | issue=1 | pages=165–171|url=http://gdz.sub.uni-goettingen.de/en/dms/loader/img/?PID=GDZPPN002030497}} (pdf [http://gdz.sub.uni-goettingen.de/en/dms/load/toc/?PID=GDZPPN002030497 available] from GDZ)
  • {{eom|id=o/o110030|first=Thomas Scott |last=Blyth|title=Ockham algebra}}
  • {{cite book|first=Thomas Scott| last=Blyth|first2=J. C. |last2=Varlet|title=Ockham algebras|year=1994|publisher=Oxford University Press|isbn=978-0-19-859938-8}}
  • {{Citation | last1=Urquhart | first1=Alasdair |authorlink= Alasdair Urquhart | title=Distributive lattices with a dual homomorphic operation | doi=10.1007/BF00370442 | mr=544616 | year=1979 | journal=Polska Akademia Nauk. Institut Filozofii i Socijologii. Studia Logica | issn=0039-3215 | volume=38 | issue=2 | pages=201–209| hdl=10338.dmlcz/102014 | hdl-access=free }}

Category:Algebraic logic

*

{{algebra-stub}}