Josh Tennenbaum has been promoting this general approach for a while, -- see e.g. his keynote from the DARPA AI Next Colloquium in 2019: https://youtu.be/usRf7fYDgmw
The piece of the 2023 paper that's most relevant to contract checking is Section 3.3, "Language for reasoning about agents and plans" -- though like the rest of the approach, there's more probabilistic inference in it than would (I think) generally be motivated in legal argumentation, or for that matter in applications like those discussed in a paper Andre suggested