Given an arbitrary propositional formula PHI (linear constraints on some variables), what is the best way to determine the (approximate) upper and lower bound for each variable? Some variables may be unbounded. In this case, an algorithm should conclude that there's no upper/lower bound for those variables. e.g., PHI = (x=3 AND y>=1). The upper and lower bound for x are both 3. The lower bound for y is 1, and y does not have an upper bound. This is a very simple example, but is there a solution in general (perhaps using SMT solver)? This assumes the SAT/UNSAT domain of each variable is