Logic Without Arithmetical Relations
Let the successor relation, succ, be a binary relation such that is true if and only if .
Over first order logic, succ is strictly less expressive than <, which is less expressive than +, which is less expressive than bit. + and are as expressive as bit.
Read more about this topic: FO (complexity)
Famous quotes containing the words logic and/or relations:
“The logic of the world is prior to all truth and falsehood.”
—Ludwig Wittgenstein (1889–1951)
“When any one of our relations was found to be a person of a very bad character, a troublesome guest, or one we desired to get rid of, upon his leaving my house I ever took care to lend him a riding-coat, or a pair of boots, or sometimes a horse of small value, and I always had the satisfaction of finding he never came back to return them.”
—Oliver Goldsmith (1728–1774)