Natural Deduction for Paraconsistent Logic
Abstract
In this paper, by using the method of natural deduction, via the method of subordinate proofs, we develop a hierarchy of natural deduction logical systems NDCn containing just deduction rules with no axiom schema. We prove that these systems NDCn , 1 n , are logically equivalent to the systems of Da Costa’s hierarchy of paraconsistent logics Cn , 1 n . Some of the deduction rules used to introduce these systems are new and do not correspond to Da Costa’s axioms rewritten, permitting the definition of a new paraconsistent semantics, such that soundness and completeness of the systems NDCn , 1 n< , may be directly obtained. Other natural deduction systems logically equivalent to Da Costa’s systems Cn, 1 n , are also introduced