What are the precise definitions of "segment" and "category" in this context?

Question

My questions comes from linguistics (syntax), but linguists can't explain to me things in rigorous terms, so I'm hoping to get some help here.

We have the following tree:

And my question is about this discussion of the tree:

.

Even though it says that the definitions are "familiar", they haven't been mentioned in this book before. My questions are: what exactly are "category" and "segment" in terms of the usual notions of nodes or sets of nodes? I couldn't make sense of them...

Answer 1

It is at least self-consistent to assume the following:

• A "segment" is a node in the tree. A "category" is a set of nodes, possibly with some restrictions on which sets can be categories but it's hard to tell. Maybe the only categories are the sets of all nodes with the same label, because those are the only kinds that show up in examples.
• When specifying categories, "GP" refers to the category containing only one segment (node), the one labeled GP. Something like "[XP, XP]" refers to the category containing the two segments (nodes) labeled XP.
• A segment "dominates" another segment if it's above the other segment in the tree. (That is, if there is a downward path in the tree from the dominating segment to the dominated segment.)