- Essentially what we are talking about is a real democratization of contractual agreements. Whereas today contracts are restricted to deals with enough value to justify a lawyer's time (mortgages, business deals, land transfer etc…), in the future there is no limit to what could be codified into simple contracts. You could imagine forming a self-enforcing contract around something as simple as sharing a lawnmower with your neighbor, hiring a babysitter, or forming a gourmet coffee club at work. Where this could really revolutionize things is in developing nations, where the ability to exchange small-scale microloans with self-enforcing contractual agreements that come at little or no cost would be a quantum leap forward.
I'm not that familiar with those efforts. What I've seen was along the lines of translating legal texts (regulations, particularly regulations for multiple countries, and contracts) into deontic logic, so that checking compliance or whether something is permissible (in the case of regulations), or whether some party has fulfilled their obligations (in the case of contracts) could be automated. For the use case described in the linked article, the straightforward approach would require a trusted third party service to decide when/if to release the funds. Maybe it would be possible to do away with the third party, I don't know off the top of my head.
If you see any of that stuff mentioned today, it's probably in a textbook chapter about how overly optimistic people were in the early days of AI. The law isn't that precise. Also, for why you don't want judged replaced by theorem provers for deontic logic, see Forrester's paradox.
But I think Thought Infection's point is that the 'trusted third party' is a preordained bitcoin deposit that only triggers when bits and pieces of contracts are filled. Right? I don't know. Long day and I didn't reread the article before I typed this.