On the System CB1 and a Lattice of the Paraconsistent Calculi

Janusz Ciuciura

doi:10.12775/LLP.2019.035

Authors

Janusz Ciuciura Department of Logic and Methodology of Science, Institute of Philosophy, Faculty of Philosophy and History https://orcid.org/0000-0001-9965-9822

DOI:

https://doi.org/10.12775/LLP.2019.035

Keywords

paraconsistent logic, paraconsistency, hierarchy of the paraconsistent calculi

Abstract

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 CB¹, is an extension of systems PI, C min and B¹, and a proper subsystem of Sette’s calculus P¹. We also investigate the generalization of CB¹ to the hierarchy of related calculi.

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