# Expanding the realm of the idea of da Costa

## Hitoshi Omori

### Kobe University, Visiting Fellow, Grad Center, CUNY

Non-classical logics that deny ex falso quod libet are said to be paraconsistent. Since the monumental work of Stanislaw Jaskowski in 1948, a large number of paraconsistent systems have been developed. Those include systems of da Costa, Nelson, Belnap-Dunn, Priest, Batens and Scotch-Jennings. In this talk, we focus on the consistency operator which is the characteristic connective of da Costa’s systems. We understand that the main idea of da Costa is to make explicit, within the system, the area in which you can infer classically. The aim of the talk is twofold. First, we review some of the results within the framework of Logics of Formal Inconsistency. Then, we introduce and present some results on normality operator which generalizes consistency operator so that one can deal not only with inconsistency, but also with incompleteness. Second, we show that the normality operator may be employed, in a sense to be specified, in developing other paraconsistent logics such as modal logics, Nelson’s systems and expansions of the four-valued logic of Belnap and Dunn.

Hitoshi Omori is a visting fellow in the CUNY Graduate Center program in Philosophy, visiting from Kobe University. His main research interests are Logic, Logic And Foundations Of Mathematics, Philosophy of Logic, Philosophical Logic, Modal Logic and Non-Classical Logic.