A possessive relation is an asymmetric relation R between two entities (referents) X and Y which is constituted as follows:

1. X is typically highly empathic and, consequently, non-relational.
2. Y is typically lower in empathy than X.
3. In the unmarked case, Y is relational.
4. Beyond condition #3, the intension of R is typically empty; i.e., it typically reduces to Y's relationality.

If #1 and #2 are fulfilled, then X typically controls Y.

X is the possessor, Y is the possessum (or possessed or possessee).

A possessive construction is a construction constituted by a possessive relation.

is a focal instance by this definition:

does not fulfill condition #2. does not fulfill condition #1.

In all of – , the possessive relation is used in reference.

If there are, in a language, two constructions of possessive reference which differ in the fulfillment of #3, then

• an inalienable possessive relation is one based on the relationality of the possessum
• an alienable possessive relation is one whose possessum is not relational.

Constructions that do not fulfill one or more of the definitory conditions may be less prototypically possessive. They are typically more complex structurally. Most important among these are constructions in which a possessive relation is predicated, as in – (possessor: I; possessum: house):

The term ‘possession’ applies

• to the relation thus defined
• to a functional domain of language that is centered around possessive relations of various kinds.

Reference:

Lehmann, Christian 2002, Possession in Yucatec Maya. Second, revised edition. Erfurt: Seminar für Sprachwissenschaft der Universität (ASSidUE, 10) [download]