In mathematics, an Ockham algebra is a
bounded
Boundedness or bounded may refer to:
Economics
* Bounded rationality, the idea that human rationality in decision-making is bounded by the available information, the cognitive limitations, and the time available to make the decision
* Bounded e ...
distributive lattice
In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such structures are collections of sets for which the lattice operations can be given by set uni ...
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 , and were named after
William of Ockham
William of Ockham, OFM (; also Occam, from la, Gulielmus Occamus; 1287 – 10 April 1347) was an English Franciscan friar, scholastic philosopher, apologist, and Catholic theologian, who is believed to have been born in Ockham, a small vill ...
by . Ockham algebras form a
variety
Variety may refer to:
Arts and entertainment Entertainment formats
* Variety (radio)
* Variety show, in theater and television
Films
* ''Variety'' (1925 film), a German silent film directed by Ewald Andre Dupont
* ''Variety'' (1935 film), ...
.
Examples of Ockham algebras include
Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in e ...
s,
De Morgan algebra
__NOTOC__
In mathematics, a De Morgan algebra (named after Augustus De Morgan, a British mathematician and logician) is a structure ''A'' = (A, ∨, ∧, 0, 1, ¬) such that:
* (''A'', ∨, ∧, 0,&nbs ...
s,
Kleene algebra
In mathematics, a Kleene algebra ( ; named after Stephen Cole Kleene) is an idempotent (and thus partially ordered) semiring endowed with a closure operator. It generalizes the operations known from regular expressions.
Definition
Various ineq ...
s, and
Stone algebra In mathematics, a Stone algebra, or Stone lattice, is a pseudo-complemented distributive lattice such that ''a''* ∨ ''a''** = 1. They were introduced by and named after Marshall Harvey Stone.
Boolean algebras are Stone algebras, and ...
s.
References
* (pd
availablefrom
GDZ)
*
*
*
{{algebra-stub
Algebraic logic
*