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 American Constitution, one of the few modern political documents drawn up by men who were forced by the sternest circumstances to think out what they really had to face instead of chopping logic in a university classroom.”
—George Bernard Shaw (1856–1950)
“I know all those people. I have friendly, social, and criminal relations with the whole lot of them.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)