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Intension

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 Intension is any property or quality connoted by a word, phrase, or another symbol. In the case of a word, the word's definition often implies an intension. For instance, the intensions of the word plant include properties such as "being composed of cellulose ", "alive", and "organism", among others. A comprehension is the collection of all such intensions.
wikipedia:: Intension
Intentionality is the power of minds to be about something: to represent or to stand for things, properties and states of affairs.[1] Intentionality is primarily ascribed to mental states, like perceptions, beliefs or desires, which is why it has been regarded as the characteristic mark of the mental by many philosophers. A central issue for theories of intentionality has been the problem of intentional inexistence: to determine the ontological status of the entities which are the objects of intentional states.

An early theory of intentionality is associated with Anselm of Canterbury's ontological argument for the existence of God, and with his tenets distinguishing between objects that exist in the understanding and objects that exist in reality.[2] The idea fell out of discussion with the end of the medieval scholastic period, but in recent times was resurrected by empirical psychologist Franz Brentano and later adopted by contemporary phenomenological philosopher Edmund Husserl. Today, intentionality is a live concern among philosophers of mind and language.[3] A common dispute is between naturalism, the view that intentional properties are reducible to natural properties as studied by the natural sciences, and the phenomenal intentionality theory, the view that intentionality is grounded in consciousness.
wikipedia:: Intentionality
wikipedia:: Intensional logic
Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe (extensions), by additional quantifiers that range over terms that may have such individuals as their value (intensions). The distinction between intensional and extensional entities is parallel to the distinction between sense and reference.
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Intension