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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 — the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied ...
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
Before version 3.0, Python had two kinds of classes (both using the same syntax): old-style and new-style; [113] current Python versions only support the semantics of the new style. Python supports optional type annotations. [4] [114] These annotations are not enforced by the language, but may be used by external tools such as mypy to catch errors.
As examples, he mentions macro definitions, ordinary procedure definitions, grammatical extensions, data definitions, operator definitions, and control structure extensions. Orthophrase adds features to a language that could not be achieved using the base language, such as adding an input/output (I/O) system to a base language formerly with no ...
An explicit listing of the extension, which is only possible for finite sets and only practical for relatively small sets, is a type of enumerative definition. Extensional definitions are used when listing examples would give more applicable information than other types of definition, and where listing the members of a set tells the questioner ...
There are more extreme examples showing that second-order logic with standard semantics is more expressive than first-order logic. There is a finite second-order theory whose only model is the real numbers if the continuum hypothesis holds and that has no model if the continuum hypothesis does not hold. [ 5 ]
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 ...
RDF represents information using semantic triples, which comprise a subject, predicate, and object. Each item in the triple is expressed as a Web URI. Turtle provides a way to group three URIs to make a triple, and provides ways to abbreviate such information, for example by factoring out common portions of URIs.