Concept B is a specialization of concept A if and only if:
every instance of concept B is also an instance of concept A; and
there are instances of concept A which are not instances of concept B.
For instance, 'Bird' is a specialization of 'Animal' because every bird is an animal, and there are animals which are not birds (dogs, for instance).
In logic, specialization occurs when you take a statement such as:
"All cars are red"
And use it to derive statements such as:
"My car is red"
"Fred's car is red"
Specialization is an important way to generate propositional knowledge, by applying general knowledge, such as the theory of gravity, to specific instances, such as "when I release this apple, it will fall to the floor".
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