- One thing I’m interested in is functorially relating purely qualitative models to quantitative ones, or mixed quantitative-qualitative models where you have some numerical information of the sort you describe, but not all of it. That’s a situation we often find ourselves in: having a mixture of quantitative and qualitative information about what’s going on in a complicated system.
- When I say “functorially”, I mean for starters: there should be a functor from “quantitative models” of system dynamics to “qualitative models”.
This is something I’ve been working on. In a turn of phrase I once concocted, it’s like passing from the qualitative theory of differential equations to the differential theory of qualitative equations. See the Chategory topic on Differential Logic.