A first order, four-valued, weakly paraconsistent logic and its relation with rough sets semantics

A first order four-valued logic, called DDT, is presented in the paper as an extension of Belnap’s logic using a weak negation and establishing an appropriate semantic for the predicate calculus. The logic uses a simple algebraic structure, that is the smallest non trivial interlaced bilattice on the four truth values, thus resulting in a boolean algebra on the set of truth values. The logic is a language for reasoning under uncertainty, enabling to capture hesitation due either to inconsistent or incomplete information, while keeping a clear distinction between these epistemic states. The logic was originally developed for preference modelling purposes (for which a brief account is given in the paper). The paper demonstrates and discusses the equivalence between the semantics of this logic and of rough sets semantics. On this basis, this papers presents the possibility of inducing rules from examples, that can be integrated in systems whose inference is expressed in the above logic. Such an approach enhances the potentialities of the use of rough sets in classification, reasoning and decision support.