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I'm reading Possession in Yucatec Maya by Christian Lehmann (March 2003) and I came across this passage:

The prototypical possessum is a concrete entity, normally an individual (as opposed to a mass), but not necessarily highly individuated. It may be empathic or anempathic. The relationship between possessor and possessum prototypically has zero intension.

This means that there is no relator which would link the two relata and could thus contribute a meaning of its own. Instead, the relation between the two elements is brought about by the relationality of one of them, which opens a place (an argument position) to be occupied by the other.

Chap. 1.2.2.1.2.1. Possessor and possessum, p. 5

What is meant by zero intension? And how does it apply to possession? I have read the definition of intension but I am not sure I still understand the concept completely.

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The "intension" is the meaning, excluding the reference. A demonstrative "this/that", e.g., might be said to refer to something, but otherwise have no information, and so it would have no intension. I guess what Lehmann is saying is that Yucatec possession is similar to "have" in English, which says there is some sort of relationship between the subject and object of "have" but says nothing about what that relationship is. Compare the relation of "I" and "hole" in the example sentence "I have a hole in the pocket." Or "the house" and "appearance" in "The house had a strange appearance to it."

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