A fundamental theorem that serves as a basis for deduction of other theorems. E.g., "A point has no mass; a line has no width. A plane is a flat surface with no mass and contains an infinity of points and lines"
A self-evident and necessary truth, or a proposition whose truth is so evident as first sight that no reasoning or demonstration can make it plainer; a proposition which it is necessary to take for granted; as, "The whole is greater than a part;"
A self-evident and necessary truth; a proposition which it is necessary to take for granted; a proposition whose truth is so evident that no reasoning or demonstration can make it plainer. For example, "The whole is greater than a part
A self-evident proposition; a statement that needs no proof because its truth is considered obvious
An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy
A symbolic algebra system, featuring a high level graphical user interface in front of a knowledge based core A complete hypertext users' guide is included; from Numerical Algorithms Group
n A self-evident or universally recognized truth maxim An established rule, principle or law
Strictly speaking, an axiom is one of a set of fundamental formulas that one starts with to prove theorems by deduction In CYC®, the axioms are those formulas that have been locally asserted into the CYC® KB CYC® axioms are well-formed CYC® formulas, since the system won't let you add formulas to CYC® that are not well-formed However, not all well-formed CYC® formulas are axioms, since not all of them are actually in the KB And some of the formulas in the KB are not, strictly speaking, axioms, since they were added to the KB via inference, instead of being locally asserted In informal usage, though, Cyclists don't always adhere to the strict meaning of axiom, and may refer to a formula they are considering adding to the KB or have recently removed from the KB as an axiom Axiom is also the name of one of the internal KB data structure types
A statement which is accepted as a basis for further logical argument Generally axioms are self-evident truths or principles which are basic enough that there are no principles more basic from which to prove them
(postulate) In a mathematical or logical system, an initial proposition or statement that is accepted as true without proof and from which further statements, or theorems, can be derived In a mathematical proof, the axioms are often well-known formulae for which the proof has already been established
(logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident
Logical condition constraining the behaviour of an object May be expressed as an invariant, or as a precondition or postcondition on one of the object's methods
An assumption that cannot be rigorously proved to be true, but seems to be true from experience or observation