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Extension (predicate logic)

The extension of a predicate – a truth-valued function – is the set of tuples of values that, used as arguments, satisfy the predicate. Such a set of tuples is a relation.

For example the statement "d2 is the weekday following d1" can be seen as a truth function associating to each tuple (d2, d1) the value true or false. The extension of this truth function is, by convention, the set of all such tuples associated with the value true, i.e.

By examining this extension we can conclude that "Tuesday is the weekday following Saturday" (for example) is false.

Using set-builder notation, the extension of the n-ary predicate $\Phi$ can be written as

Relationship with characteristic function

If the values 0 and 1 in the range of a characteristic function are identified with the values false and true, respectively – making the characteristic function a predicate – , then for all relations R and predicates $\Phi$ the following two statements are equivalent:

\Phi

is the characteristic function of R;

Add-on (Mozilla)

Mozilla add-ons are installable enhancements to the Mozilla Foundation's projects, including Firefox, Thunderbird, SeaMonkey, and Sunbird. Add-ons allow the user to add or augment application features, use themes to their liking, and handle new types of content.

There are three major categories of add-ons: "Extensions", "Themes", and "Plug-ins". The main repository for distributing the first two type is the eponymous Mozilla Add-ons website.

Types

There are several types of add-ons:

Extensions: Modify the behavior of existing features or add new features. The feature could be something in the user interface or a functional feature that manifests itself when a certain action is performed. Themes are examples of extensions that primarily concern themselves with the user interface. Search engine definitions are examples of functional extensions. A list of extensions can be found in the List of Firefox extensions article, although there are others for Thunderbird, SeaMonkey and Sunbird.

Anonymous View

Extension (predicate logic)

Relationship with characteristic function

Add-on (Mozilla)

Types

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