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 worldly success rests on a fallacy: the strange error that our perfection depends on the thoughts and opinions and applause of other men! A weird life it is, indeed, to be living always in somebody else’s imagination, as if that were the only place in which one could at last become real!”
—Thomas Merton (1915–1968)
“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)