An Experiment with Satisfiability Modulo SAT

In recent years, the approach of satisfiability modulo theories (SMT) has been very successful in solving many constraint satisfaction problems. In a typical SMT solver, the base constraints are expressed as a set of propositional clauses, where each Boolean variable is an abstraction of an atomic formula of first-order logic and the interpretation of the formula is constrained by a background theory. A widely studied theory is the linear pseudo-Boolean logic. Following this approach, we present an experiment of a SMT solver where the background theory can be specified in propositional logic and implemented by a procedure. We chose such a procedural background theory because we found no better ways to attack a previously open problem in combinatorial design, i.e., the existence of diagonally ordered magic squares of all orders.

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