Nick Smith Seems like we're thinking about similar things — would love to hear/read more about your project.
I went down the linguistics route (I'm two years in now), and as much as I'm happy to find people interested in it, from the previous discussion I can only sense that it would be more of a distraction for you than it would actually help. What you seem to be looking for is what linguists and cognitive scientists call "categorization". When I found out about it, I was shocked how much linguists ask the same questions we ask when we try to design a good data model.
If you stay on the "classic" generative linguistics path (Chomsky et al.), you'd better get extremely comfortable around hierarchies and taxonomies. It seems most of the work here in the last few decades is basically trying to fit into the classic models what we learn about how the brain works, which more and more diverts from what can be meaningfully expressed with those models that are primarily based on set theory, perhaps with some fuzzy logic applied to it. It looks a lot like the frustration you voiced earlier — we can make it work by stretching the current models and making them much more complex, but it's everything but satisfying.
There are linguists who realized that and who went looking for new approaches. I've been looking deeply into cognitive linguistics and think that's a great field to look at for inspiration. There's Rosch's prototype theory, which is still pretty close to classic categorization with a little bit of fuzzy logic sprinkled in, but that's just the gateway drug into metaphorical structuring and image schemas, and then all your set-theory based logic goes out the window, and you're left with embodied cognition and stuff that is way too ambiguous for what we'd like for static modeling. It seems you have extremely specific use cases in mind, and so I don't feel good about recommending you look into this.
When you say you're looking for more powerful models, "something more powerful than graphs", I wonder what that means to you?
If you want more flexibility in modeling, you need to take into account that this always comes in the form of trade-offs. Mathematics has this pretty much figured out though. If you look at algebraic structures you can pick one with few rules, which gives you a lot of flexibility of what you can model with them, but then you can't do much with these models — if you can't make any assumptions about structure, you can't run algorithms against it. And you will see that graphs are already pretty high up there in terms of flexibility, but to do anything useful with them, you'd have to look at slightly more restrictive (semi-)lattices or… tada… trees again. There's a reason why almost anything can be represented as a graph. Look at Category Theory as an extreme (not to be confused with the "categories" from above). I guess that's the only branch left that qualifies as "more powerful than graphs", but then all its useful applications are only useful once you pull them back down into the land of graphs, sets, and trees.
I'm currently working under the assumption that "a better model" doesn't exist, or at least that I'm certainly not clever enough to invent it, and that the models we have are more than what's needed for progress — the problem is just that we need different models at different times. That's why I'm betting on homomorphic representations and (bi-directional) transformations between them to solve some of the problems of static models that lack the flexibility we need to model dynamic systems.