Science Fair Project Encyclopedia
Lindenbaum-Tarski algebra
In mathematical logic, the Lindenbaum-Tarski algebra A of a logical theory T consists of the equivalence classes of sentences p of the theory, under the equivalence relation ~ defined by
- p ~ q when p and q are logically equivalent in T.
That is, in T q can be deduced from p, and p from q.
Operations in A are inherited from those available in T, typically conjunction and disjunction, where they are well-defined on the classes. When negation is present in T, then A is a Boolean algebra, under some mild conditions.
Sometimes called simply Lindenbaum algebra, this construction is named for Adolf Lindenbaum (1904-1941 or 1942) and Alfred Tarski.
12-03-2008 10:22:39
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details