Implementation of SQL's three-valued logic

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Is there a module in any SQL implementation that checks satisfiability/validity of a formula in 3-valued logic? If so, is there an open-source one? My purpose is to evaluate the performance of such a module (if exists) on the specific task of checking satisfiability/validity of formulas in 3-valued logic, and not for general query computations.

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You could represent the problem using bit-vector logic. For instance, the QF_BV bit-vector logic of the z3 SMT solver.

As an example: http://listedfor11o.blogspot.com/2013/03/multi-valued-logic-in-z3.html