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:
“...some sort of false logic has crept into our schools, for the people whom I have seen doing housework or cooking know nothing of botany or chemistry, and the people who know botany and chemistry do not cook or sweep. The conclusion seems to be, if one knows chemistry she must not cook or do housework.”
—Ellen Henrietta Swallow Richards (1842–1911)
“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)