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.
{(Monday, Sunday), (Tuesday, Monday), (Wednesday, Tuesday), (Thursday, Wednesday), (Friday, Thursday), (Saturday, Friday), (Sunday, Saturday)}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 can be written as
Read more about Extension (predicate Logic): Relationship With Characteristic Function
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—Abraham Lincoln (1809–1865)