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- Conservative_extension abstract "In mathematical logic, a logical theory is a (proof theoretic) 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 (or assumed) 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.Recently, conservative extensions have been used for defining a notion of module for ontologies: if an ontology is formalized as a logical theory, a subtheory is a module if the whole ontology is a conservative extension of the subtheory.An extension which is not conservative may be called a proper extension.".
- Conservative_extension wikiPageExternalLink 002306.html.
- Conservative_extension wikiPageID "1840214".
- Conservative_extension wikiPageRevisionID "571246945".
- Conservative_extension hasPhotoCollection Conservative_extension.
- Conservative_extension subject Category:Model_theory.
- Conservative_extension subject Category:Proof_theory.
- Conservative_extension comment "In mathematical logic, a logical theory is a (proof theoretic) 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. ".
- Conservative_extension label "Conservative extension".
- Conservative_extension label "Estensione conservativa".
- Conservative_extension label "Extension conservatrice".
- Conservative_extension label "保守扩展".
- Conservative_extension sameAs Extension_conservatrice.
- Conservative_extension sameAs Estensione_conservativa.
- Conservative_extension sameAs m.0601dh.
- Conservative_extension sameAs Q864213.
- Conservative_extension sameAs Q864213.
- Conservative_extension wasDerivedFrom Conservative_extension?oldid=571246945.
- Conservative_extension isPrimaryTopicOf Conservative_extension.