Active Structure is essentially an analytic or planning tool, used to represent the objects and relations in some domain. To find applications that people will accept, we have continually "upped the ante" until we are now closing on high level cognitive activity, but in areas that people don't like thinking about.
Contracts and leases are written in a dense, highly clipped style, with many references to other parts of the document or to other documents. They are tedious to read, as the meaning does not leap off the page, but needs to be unravelled bit by bit. If one is unfamiliar with the particular contract, one can't jump to a relevant clause, because that clause will use terms defined in preceding or even succeeding clauses, and those definitions... - until you have to read the whole contract to be sure what it is saying.
What typically happens is that people smear contracts together in their head - they operate on a generalised contract because they don't want to spend the time going through an individual contract in detail. This leads to mistakes, and the mistakes can run into millions of dollars, but it is just not possible to force people to read these things. A lawyer may be willing to read it, but he/she will usually only have the most superficial idea of the business processes it describes, and there are enough mistakes in the typical contract to indicate that even lawyers don't like reading this stuff. The contract will usually have been cobbled together using clauses from other contracts using different defined terms, or amendments made over time - another large source of error.
By extracting the meaning structure of the document, and checking and linking all the references (a "legal compiler", in the computer language sense), the machine now has an excellent basis for answering questions about the contract. This is effectively the first time that the machine will know more about the subject at hand than the user, and the interface needs to reflect the change in "who knows what".
Why do this application first?
Because it is one that no-one likes to do and it is relatively easy - lawyers have reasonable spelling and grammar, and a contract will usually be written to minimise ambiguity. However, contracts involve intention, which is usually lacking in scientific or medical text.
Other applications in medicine or genetics or general legal may encroach on what the user feels is their speciality, so there is tension about shedding some knowledge-handling activities to a machine.
Tax law is very similar to property leases - terms, conditions, objects, relations, amounts, times, dates - so this is an obvious extension.
For general law, see SOX presentation.