Conservative extension

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In mathematical logic, a conservative extension is a supertheory of a theory which is often convenient for proving theorems, but proves no new theorems about the language of the original theory. Conservative extension_sentence_0

Similarly, a non-conservative extension is a supertheory which is not conservative, and can prove more theorems than the original. Conservative extension_sentence_1

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. Conservative extension_sentence_2

An extension which is not conservative may be called a proper extension. Conservative extension_sentence_3

Examples Conservative extension_section_0

Conservative extension_unordered_list_0

Model-theoretic conservative extension Conservative extension_section_1

Credits to the contents of this page go to the authors of the corresponding Wikipedia page: extension.