Abstract
In this paper we present a new hierarchy of analytical tableaux systems TNDC n, 1≤n, for da Costa's hierarchy of propositional paraconsistent logics Cn, 1≤n. In our tableaux formulation, we introduce da Costa's ?ball? operator ?o?, the generalized operators ?k? and ?(k)?, for 1≤k, and the negations ?~k?, for k≥1, as primitive operators, differently to what has been done in the literature, where these operators are usually defined operators. We prove a version of Cut Rule for the TNDC n, 1≤n, and also prove that these systems are logically equivalent to the corresponding systems Cn, 1≤n. The systems TNDC n constitute completely automated theorem proving systems for the systems of da Costa's hierarchy Cn, 1≤n