How do you use Axiomatization in a sentence? See 10+ example sentences showing how this word appears in different contexts, plus the exact meaning.
Axiomatization meaning
- The reduction of some system or concept to a set of axioms.
- The result of establishing a concept within a system of axioms; axiomatic system.
Using Axiomatization
- The main meaning on this page is: The reduction of some system or concept to a set of axioms. | The result of establishing a concept within a system of axioms; axiomatic system.
- In the example corpus, axiomatization often appears in combinations such as: axiomatization of, the axiomatization, effective axiomatization.
Context around Axiomatization
- Average sentence length in these examples: 21.2 words
- Position in the sentence: 6 start, 5 middle, 2 end
- Sentence types: 13 statements, 0 questions, 0 exclamations
Corpus analysis for Axiomatization
- In this selection, "axiomatization" usually appears near the start of the sentence. The average example has 21.2 words, and this corpus slice is mostly made up of statements.
- Around the word, effective, complete, mathematical and begins stand out and add context to how "axiomatization" is used.
- Recognizable usage signals include a complete axiomatization of full and a complete axiomatization of newtonian. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "axiomatization" sits close to words such as aami, abada and abbottabad, which helps place it inside the broader word index.
Example types with axiomatization
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
Therefore, no formal system is a complete axiomatization of full number theory. (12 words)
One such axiomatization begins with the following axioms that describe a discrete ordered semiring. (14 words)
We fix some axiomatization of the predicate calculus: logical axioms and rules of inference. (14 words)
Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory. (37 words)
As an interpretation, it is not in conflict with the mathematical axiomatization of probability theory; rather, it provides guidance for how to apply mathematical probability theory to real-world situations. (30 words)
Effective axiomatization A formal system is said to be effectively axiomatized (also called effectively generated) if its set of theorems is a recursively enumerable set (Franzén 2004, p. 112). (29 words)
Example sentences (13)
After having completed the axiomatization of set theory, he began to confront the axiomatization of quantum mechanics.
As an interpretation, it is not in conflict with the mathematical axiomatization of probability theory; rather, it provides guidance for how to apply mathematical probability theory to real-world situations.
Effective axiomatization A formal system is said to be effectively axiomatized (also called effectively generated) if its set of theorems is a recursively enumerable set (Franzén 2004, p. 112).
Every set has an ordinal rank This was actually the original form of von Neumann's axiomatization.
For axiomatization of algebraically closed fields, this is the best possible, as there are counterexamples if a single prime is excluded.
He did this by giving a complete axiomatization of Newtonian mechanics with no reference to numbers or functions at all.
It is based on an axiomatization of the properties of ordinal numbers : each natural number has a successor and every non-zero natural number has a unique predecessor.
Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.
Nowadays alternative approaches for axiomatization of probability theory exist; see “ Algebra of random variables ”, for example.
One such axiomatization begins with the following axioms that describe a discrete ordered semiring.
There are several properties that a formal system may have, including completeness, consistency, and the existence of an effective axiomatization.
Therefore, no formal system is a complete axiomatization of full number theory.
We fix some axiomatization of the predicate calculus: logical axioms and rules of inference.
Common combinations with axiomatization
These word pairs occur most frequently in English texts: