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In this paper, we present a calculus of paraconsistent logic. We propose an axiomatisation and a semantics for the calculus, and prove several important meta-theorems. The calculus, denoted as CB 1 , is an extension of systems PI, C min and B 1 , and a proper subsystem of Sette’s calculus P 1 . We also investigate the generalization of CB 1 to the hierarchy of related calculi.

On the system CB1 and a lattice of the paraconsistent calculi