In the past, I implemented coordination models using SAT and regular constraint satisfaction as the core workhorse in their engines. Continuing in this line of work, I would like to make the models more interactive, and the best way I see of doing this is to open up the constraint solver so that it is no longer a black box.
Thus, I'm interested in learning more about constraint satisfaction where the constraints have what I will call external variables, predicates and functions, that is, the constraint language may have predicates such as $\mathbf{P}(x)$ which can only be satisfied by consulting some agent external to the solver, and then only when $x$ is ground. A scenario where this is useful is whenever $\mathbf{P}$ corresponds to some external decision process that cannot be incorporated into the constraint solver. Such constraint solvers could be called open (as constraints are not entirely known) or interactive (as interaction is required to proceed with constraint satisfaction).
I would like to know both:
- theoretical research done in this direction
- tools or libraries that implement constraint solvers that allow interaction with the external world during the constraint solving process.
