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PhilLogic: Hitoshi Omori
November 20, 2012 @ 7:15 pm - 9:15 pm
Date: Tuesday 20 Nov.
Place: 7:15-9:15 p.m., 2nd floor seminar room, NYU Philosophy Dept (5, Washington Place).
Speaker: Hitoshi Omori, Kobe University, Visiting Fellow, Grad Center, CUNY
Title: Recent developments on systems with the consistency operator
Abstract: Non-classical logics that deny ex contradictione quodlibet
are said to be paraconsistent. Since the monumental work of Jaskowski
in 1948, a large number of paraconsistent systems have been developed.
In this talk, we focus on the consistency operator which is the
characteristic connective of da Costa’s systems. The main motivation
for adding the consistency operator is to make explicit, within the
system, the area in which you can infer classically. The aim of the
talk is threefold. First, we present some results within the framework
of Logics of Formal Inconsistency (LFIs) that generalizes da Costa’s
idea. Second, we show that the consistency operator may be employed,
in a sense to be specified, in developing other paraconsistent logics
such as modal logics, Nelson’s systems and the four-valued logic of
Belnap and Dunn. Finally, we consider two questions related to the
consistency operator. Those are (i) whether the consistency operator
forces us to accept classical negation, and (ii) whether naive set
theories based on LFIs can be developed.