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axiomatic$6314$ - ترجمة إلى الهولندية
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, dat niet bewezen hoeft te worden
set theory
![[[Georg Cantor]]](https://commons.wikimedia.org/wiki/Special:FilePath/Georg Cantor 1894.jpg?width=200 "[[Georg Cantor]]")
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
wet van groepen (richting in de wiskunde die zich bezighoudt met zinsomschrijvingen betreffende groepen en hun bewijs)
تعريف
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)
ويكيبيديا
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.
