In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — an extensional context (or transparent context) is a syntactic environment in which a sub-sentential expression e can be replaced by an expression with the same extension and without affecting the truth-value of the sentence as a whole. Extensional contexts are contrasted with opaque contexts where truth-preserving substitutions are not possible.
Take the case of Clark Kent, who is secretly Superman. Suppose that Lois Lane fell out of a window and Superman caught her. Thus the sentence "Superman caught Lois Lane" is true. Because this sentence is an extensional context, the sentence "Clark Kent caught Lois Lane" is also true. Anybody that Superman caught, Clark Kent caught.
In opposition to extensional contexts are intensional contexts (which can involve modal operators and modal logic), where terms cannot be substituted without potentially compromising the truth-value. Suppose that Lois Lane believes that Clark Kent will investigate a news story with her. Thus, the sentence "Lois Lane believes that Clark Kent will investigate a news story with her" is true. However, the statement, "Lois Lane believes that Superman will investigate a news story with her," is false. This is because 'believes' typically induces an intensional context. Lois Lane doesn't believe that Superman is Clark Kent and the propositional attitude "believe" induces an intensional context, so the substitution alters the meaning of the original sentence.
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sentence. De dicto and de re Extension (semantics) Extensional definition Extensionalism Intensional logic Opaque context Propositional attitude W.V. Quine...
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extensional) context", where the term "x" does not have to refer to anything at all (as in, e.g., "Jason worships Zeus"). In an "intensional context"...
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designated, extensions. Contexts in which extension is all that matters are, naturally, called extensional, while contexts in which extension is not enough...
profile. Compatibility contexts include the previously removed fixed-function APIs, equivalent to the ARB_compatibility extension released alongside OpenGL...
extended doubleword, and doubleword to quadword, respectively (in the x86 context a byte has 8 bits, a word 16 bits, a doubleword and extended doubleword...
and it becomes this axiom that is referred to as the axiom of extensionality in this context. An ur-element is a member of a set that is not itself a set...
isomorphic to the group Q {\displaystyle Q} . Group extensions arise in the context of the extension problem, where the groups Q {\displaystyle Q} and N...
as their value (intensions). The distinction between intensional and extensional entities is parallel to the distinction between sense and reference....
as constituted by hyperintensional contexts, and generalized from there to intensional and extensionalcontexts. The underlying logic is a Frege-style...
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Greek borrowings that are regularly used only in IPA contexts. The characters of the IPA extensions subheading were part of the original Unicode 1.0. The...
some modifications and extensions to the diff formats that are used and understood by certain programs and in certain contexts. For example, some revision...
cycles per memory access). On an address-space switch, as occurs when context switching between processes (but not between threads), some TLB entries...
variables and, by extension, to forming linear combinations of random variables. The operation here is a special case of convolution in the context of probability...
serious deterrence, and that the law should be looked at upon in the wider context of "saving lives", particularly citizens. In 2004, Amnesty International...
connotation in Wiktionary, the free dictionary. Context as Other Minds Double entendre ExtensionExtensional definition Intension Intensional definition Loaded...
it would be better if PPAPI Flash were available in a more "official" context. "NPAPI deprecation: developer guide". www.chromium.org. Archived from...
An extension agency is an organisation that practises extension, in the context of community development. An example is the Cooperative Extension Service...
informal standard in many contexts of configuration, but many applications on other operating systems use different file name extensions, such as conf and cfg...
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