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conservative extension

Meaning of "conservative extension" in the English dictionary

DICTIONARY

PRONUNCIATION OF CONSERVATIVE EXTENSION

conservative extension


WHAT DOES CONSERVATIVE EXTENSION MEAN IN ENGLISH?

Conservative extension

In mathematical logic, a logical theory is a conservative extension of a theory if the language of extends the language of; every theorem of is a theorem of; and any theorem of that is in the language of is already a theorem of. More generally, if Γ is a set of formulas in the common language of and, then is Γ-conservative over if every formula from Γ provable in is also provable in. To put it informally, the new theory may possibly be more convenient for proving theorems, but it proves no new theorems about the language of the old theory. Note that a conservative extension of a consistent theory is consistent. Hence, conservative extensions do not bear the risk of introducing new inconsistencies. This can also be seen as a methodology for writing and structuring large theories: start with a theory,, that is known to be consistent, and successively build conservative extensions, , ... of it. The theorem provers Isabelle and ACL2 adopt this methodology by providing a language for conservative extensions by definition.

WORDS THAT BEGIN LIKE CONSERVATIVE EXTENSION

conservation · conservation area · conservation grade · conservation of charge · conservation of energy · conservation of mass · conservation of momentum · conservation of parity · conservational · conservationist · conservatism · conservative · Conservative and Unionist Party · Conservative Judaism · Conservative Party · conservatively · conservativeness · conservatize · conservatoire · conservator

WORDS THAT END LIKE CONSERVATIVE EXTENSION

air suspension · apprehension · ascension · coefficient of expansion · commission · comprehension · declension · dimension · en pension · expansion · extension · file extension · hair extension · hypertension · mansion · pension · pretension · recension · surface tension · suspension · tension

Synonyms and antonyms of conservative extension in the English dictionary of synonyms

SYNONYMS

Translation of «conservative extension» into 25 languages

TRANSLATOR

TRANSLATION OF CONSERVATIVE EXTENSION

Find out the translation of conservative extension to 25 languages with our English multilingual translator.

The translations of conservative extension from English to other languages presented in this section have been obtained through automatic statistical translation; where the essential translation unit is the word «conservative extension» in English.
zh

Translator English - Chinese

保守的延伸
1,325 millions of speakers
es

Translator English - Spanish

extensión conservadora
570 millions of speakers
en

English

conservative extension
510 millions of speakers
hi

Translator English - Hindi

रूढ़िवादी विस्तार
380 millions of speakers
ar

Translator English - Arabic

تمديد المحافظ
280 millions of speakers
ru

Translator English - Russian

консервативное расширение
278 millions of speakers
pt

Translator English - Portuguese

extensão conservadora
270 millions of speakers
bn

Translator English - Bengali

রক্ষণশীল এক্সটেনশন
260 millions of speakers
fr

Translator English - French

extension conservative
220 millions of speakers
ms

Translator English - Malay

Lanjutan konservatif
190 millions of speakers
de

Translator English - German

konservative Erweiterung
180 millions of speakers
ja

Translator English - Japanese

保守的な延長
130 millions of speakers
ko

Translator English - Korean

보수적 확장
85 millions of speakers
jv

Translator English - Javanese

Ekstensi konservatif
85 millions of speakers
vi

Translator English - Vietnamese

mở rộng bảo thủ
80 millions of speakers
ta

Translator English - Tamil

பழமைவாத நீட்டிப்பு
75 millions of speakers
mr

Translator English - Marathi

पुराणमतवादी विस्तार
75 millions of speakers
tr

Translator English - Turkish

Muhafazakar uzantı
70 millions of speakers
it

Translator English - Italian

estensione conservativa
65 millions of speakers
pl

Translator English - Polish

konserwatywny rozszerzenie
50 millions of speakers
uk

Translator English - Ukrainian

консервативне розширення
40 millions of speakers
ro

Translator English - Romanian

extensie conservator
30 millions of speakers
el

Translator English - Greek

συντηρητική επέκταση
15 millions of speakers
af

Translator English - Afrikaans

konserwatiewe uitbreiding
14 millions of speakers
sv

Translator English - Swedish

konservativ förlängning
10 millions of speakers
no

Translator English - Norwegian

konservativ forlengelse
5 millions of speakers

Trends of use of conservative extension

TRENDS

TENDENCIES OF USE OF THE TERM «CONSERVATIVE EXTENSION»

Principal search tendencies and common uses of conservative extension
List of principal searches undertaken by users to access our English online dictionary and most widely used expressions with the word «conservative extension».

Examples of use in the English literature, quotes and news about conservative extension

EXAMPLES

10 ENGLISH BOOKS RELATING TO «CONSERVATIVE EXTENSION»

Discover the use of conservative extension in the following bibliographical selection. Books relating to conservative extension and brief extracts from same to provide context of its use in English literature.
1
Modular Ontologies: Concepts, Theories and Techniques for ...
We say that Q is a deductive S-conservative extension of Q1 w.r.t. L, if for every axiom α over L with Sig(α) ⊆ S, we have Q |= α iff Q1 |= α. We say that Q is a model S-conservative extension of Q1 if, for every model I1 of Q1, there exists a model ...
Heiner Stuckenschmidt, Christine Parent, Stefano Spaccapietra, 2009
2
Set Theory
We say that E' is a conservative extension of E if for every $ e Wff(L), if E' I- (j>, then also E h </>. We say that E' is an effective conservative extension if the derivation of (j> in E can be calculated from the derivation of </> in E'. Informally, an ...
Andras Hajnal, Peter Hamburger, 1999
3
Logic, Language, Information and Computation: 16th ...
Every model-theoretic conservative extension is an FO-conservative extension, but the converse is well-known to fail. Both notions can, in principle, be used without modification to analyse the effect of adding axioms T to a given ontology T. It ...
Hiroakira Ono, Makoto Kanazawa, Ruy de Queiroz, 2009
4
Handbook of Process Algebra
Conservative extension Over and over again. process calculi such as CCS [I57], CSP [I86]. and ACP [28] have been extended with new features, and the original TSSs, which provide the semantics for these process algebras. were extended ...
J.A. Bergstra, A. Ponse, S.A. Smolka, 2001
5
The Connectives
Another example of arguably untoward disruptiveness is what we shall be calling failures of the condition of 'conservation of synonymy' in 8.23; again, such failures do not amount to non-conservative extension in the technical sense. End of ...
Lloyd Humberstone, 2011
6
Proceedings of the 10Th Asian Logic Conference
Suppose that TQ D RCA0 and that T D T0 is a n^+2 axiomatizable conservative extension of Tq. Then 7\ D is the maximal fig^ axiomatizable II* + 1 conservative extension of To if for every n^+a axiomatizable conservative extension T% D To of ...
Toshiyasu Arai, 2010
7
Ontology Representation: Design Patterns and Ontologies that ...
(2006) introduce a notion of safe reuse, direct formal reuse of a signature in an ontology, based on the definition of conservative extension in description logics: Definition 5.4.6 (Conservative Extension) An ontology O is an S-conservative ...
Rinke Hoekstra, 2009
8
ZUM '98: The Z Formal Specification Notation: 11th ...
In particular, consistency will be ensured if the theory of each initial sequence is a conservative extension of that formed by the sequence obtained by deleting its last paragraph. A sufficient condition for consistency is that every paragraph ...
Jonathan P. Bowen, Andreas Fett, Michael G. Hinchey, 1998
9
An Introduction to Mathematical Logic and Type Theory
F2 is a conservative extension of T1 iff for every wff C of C (F1) , \-y\ C iff h^a C. Clearly a conservative extension is an extension. Logistic systems Tl and T2 are equivalent iff each is an extension of the other. In this case, they have the same ...
Peter B. Andrews, 2002
10
Theoretical Aspects of Computer Software: International ...
This paper uses mostly syntactic arguments, like those sketched in [2,4], to establish conservative extension: the proofs involve rewriting a distinguishing context in the extended language to a distinguishing context in the original language.
Masami Hagiya, John C. Mitchell, 1994

4 NEWS ITEMS WHICH INCLUDE THE TERM «CONSERVATIVE EXTENSION»

Find out what the national and international press are talking about and how the term conservative extension is used in the context of the following news items.
1
Canada could stay in Afghanistan past 2014
“Canadians do not want another Conservative extension of the mission in Afghanistan and the NDP will not support one,” said Mulcair. «Toronto Sun, Apr 12»
2
Stephen Harper says Canadian troops could stay in Afghanistan …
“Canadians do not want yet another Conservative extension of the mission in Afghanistan and the NDP will not support one,” Mulcair said. «Toronto Star, Apr 12»
3
Scott Loeffler and Creeping Sabanization
Michigan fans did not like offensive coordinator Mike Debord, seeing him as a conservative extension of Carr who would run the ball or die ... «SB Nation Atlanta, Jan 12»
4
Alternative Axioms: NBG Set Theory
In any event, NBG is a conservative extension of ZFC — it proves exactly the same statements about sets as ZFC does. ZFC does not have ... «ScienceBlogs, Jun 07»
REFERENCE
« EDUCALINGO. Conservative extension [online]. Available <https://educalingo.com/en/dic-en/conservative-extension>. May 2024 ».
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