NATURAL DEDUCTION FOR PARACONSISTENT LOGIC

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 NDC n containing just deduction rules (or deduction schemata) withno axiom schema. We prove that these systems NDC n , 1≤n≤ω, are logically equivalent to the systems of Da Costa's hierarchy of paraconsistent logics C n , 1≤n≤ω. 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 NDC n , 1≤n≤ω, may be directly obtained. Other natural deduction systems logically equivalent to Da Costa's systems C n , 1≤n≤ω, are also introduced.