intensionally

Intensionally defined classes usually have necessary conditions associated with membership in each class.

One often has the choice of specifying a set intensionally or extensionally.

In most upper ontologies, the classes are defined intensionally.

Class may be defined either extensionally or intensionally.

If, however, a set is defined intensionally, then it is a set of things that meet some requirement to be a member.

An alloying element intensionally added to modify the characteristics of iron hydride is titanium.

The set is defined extensionally using power domain semantics rather than intensionally using causal axioms.

Similarly, in natural language there are many predicates (relations) that are intensionally different but are extensionally identical.

Then, the two argument predicates "has one person named", "is the oldest person in" are intensionally distinct, but extensionally equal for "Joe" in that "town" now.

"Gandy actually wrote "Church's thesis" not "Turing's thesis" as written here, but surely Gandy meant the latter, at least intensionally, because Turing did not prove anything in 1936 or anywhere else about general recursive functions."

Thus, the "seven deadly sins" can be defined intensionally as those singled out by Pope Gregory I as particularly destructive of the life of grace and charity within a person, thus creating the threat of eternal damnation.

This would be parallel to the fact that the object in an adverbal construction tends to separate the adjective from the verb to which it is most closely bound intensionally, by occupying the place immediately after the verb, as objects normally do (see Section 5.3).