Some articles on axiom systems, axioms, axiom, system:
... Different modal logics can be derived from taking different subsets of these axioms, and these logics are normally named after the important axioms being employed ... In this case though, the knowledge axiom no longer seems right—agents only sometimes believe the truth—so it is usually replaced with the Consistency Axiom ... When D replaces T in S5, the resulting system is known as KD45 ...
... the "game" of Euclidean geometry (which is seen as consisting of some strings called "axioms", and some "rules of inference" to generate new strings from given ones ... true statements are assigned to the axioms and the rules of inference are truth-preserving), then you have to accept the theorem, or, rather, the interpretation you have ... Many formalists would say that in practice, the axiom systems to be studied will be suggested by the demands of science or other areas of mathematics ...
Famous quotes containing the words systems and/or axiom:
“We have done scant justice to the reasonableness of cannibalism. There are in fact so many and such excellent motives possible to it that mankind has never been able to fit all of them into one universal scheme, and has accordingly contrived various diverse and contradictory systems the better to display its virtues.”
—Ruth Benedict (18871948)
“You are bothered, I suppose, by the idea that you cant possibly believe in miracles and mysteries, and therefore cant make a good wife for Hazard. You might just as well make yourself unhappy by doubting whether you would make a good wife to me because you cant believe the first axiom in Euclid. There is no science which does not begin by requiring you to believe the incredible.”
—Henry Brooks Adams (18381918)