Boolean algebra
A Boolean algebra is a system consisting of a set S and two operations, n and ? (cap and cup), subject to the following axioms. For all sets a,b,c, that are members of S:
1 a n (b n c) = (a n b) n c.
Also a ? (b ? c) = (a ? b) ? c (associativity)
2 a n b = b n a.
Also a ? b = b ? a (commutativity)
3 a n (b ? c) = (a n b) ? (a n c).
Also a ? (b n c) = (a ? b) n (a ? c) (distributivity)
4 There belong to S two elements, 0 and 1, with the properties a ? 0 = a; a n 1 = a (identity)
5 For each set a in S there exists a set a' with the properties that a ? a' = 1, a n a' = 0 (complementation).
The propositional calculus can be represented as a Boolean algebra, with n representing &, ? representing ∨, and 1 = T, 0 = F. The Boolean operators are then the truth functors, such as &, ∨, and ¬. A Boolean search is a search for things meeting a condition defined with these operators.

Philosophy dictionary. . 2011.

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