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ετυμολογία

axiomatic$6314$ - translation to γερμανικά

SET OF AXIOMS FROM WHICH SOME OR ALL AXIOMS CAN BE USED IN CONJUNCTION TO LOGICALLY DERIVE THEOREMS

Axiomatization; Axiomatisation; Axiomatic method; Axiomatic framework; Axiom system; Axiomatic reasoning; Hilbert-style calculi; Axiomatic theory; Axiomatic definition; Axiomatic approach; Axiomatic logic; Axiomatic proof; Axiomatic System

axiomatic

adj. axiomatisch, auf Axiomen beruhend, unanzweifelbar

set theory

BRANCH OF MATHEMATICS THAT STUDIES SETS, WHICH ARE COLLECTIONS OF OBJECTS

Axiomatic Set Theory; SetTheory; Set Theory; Formal set theory; Axiomatic set theory; Theory of sets; Ordinary set theory; Set theorist; Classical set theory; Set-theoretic; Axioms of set theory; Axiom of set theory; Axiomatic set theories; Transfinite set theory; Abstract set theory; Mathematical set theory; Set theory (mathematics); Applications of set theory; History of set theory

Gruppentheorie (Mathematik)

Ορισμός

axiomatic semantics

<theory> A set of assertions about properties of a system and how they are effected by program execution. The axiomatic semantics of a program could include pre- and post-conditions for operations. In particular if you view the program as a state transformer (or collection of state transformers), the axiomatic semantics is a set of invariants on the state which the state transformer satisfies. E.g. for a function with the type: sort_list :: [T] -> [T] we might give the precondition that the argument of the function is a list, and a postcondition that the return value is a list that is sorted. One interesting use of axiomatic semantics is to have a language that has a finitely computable sublanguage that is used for specifying pre and post conditions, and then have the compiler prove that the program will satisfy those conditions. See also operational semantics, denotational semantics. (1995-11-09)

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Βικιπαίδεια

Axiomatic system

In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system. A formal theory is an axiomatic system (usually formulated within model theory) that describes a set of sentences that is closed under logical implication. A formal proof is a complete rendition of a mathematical proof within a formal system.

https://en.wikipedia.org/wiki/Axiomatic system