Typed Feature Structures, for Rehana

Many years ago I wanted to think about the (algebraic) structures that linguists use to describe their bits of syntax and semantics. Sometimes these are called AVMs (for attribute-value matrices), some times they are called "(typed) feature structures". They're directed acyclic graphs, rooted, and with a transition and a labelling structure. Here's the very old paper I wrote about trying to see them as purely labelled graphs.

I wanted to ask some combinatorists/graph theorists friends what they could tell me about operations on these graphs...I still want to. I hope they will say something interesting about unification in computing...