A Rewriting Decision Procedure for Dijkstra-Scholten's Syllogistic Logic with Complements

We present an equational decision procedure a la Dijkstra & Scholten for the `Syllogistic Logic with Complements'. First, we give an equational axiomatization of Dijkstra & Scholten's propositional logic and show how it gives a decision procedure for propositional logic by equational term rewriting. We also show how one can efficiently obtain certain propositional models (i.e., truth assignments over propositional variables) from the canonical forms given by the system. We then present the Syllogistic Logic with Complements and show how the decision procedure for propositional logic can be easily extended to obtain a decision procedure for this subset of First-Order Logic. Moreover, an executable specification of both decision procedures is presented in the Maude system, and examples illustrating the use of both canonical equational systems are given