The Pragmatic Approach to Paraconsistency
Several schools of paraconsistency have been developed over the years. Each of these schools is based on certain philosophical ideas concerning the nature of truth, knowledge, and reasoning; and each of them has led to a huge family of paraconsistent logics. The pragmatic approach to paraconsistency studies all those logics from the point of view of their potential usefulness in concrete applications in which paraconsistent reasoning may be needed for practical reasons (e.g. in the case of knowledge bases which are based on information coming from different and not necessarily compatible sources). Accordingly, each logic is examined according to objective mathematical criteria, like effectivity (including decidability, the availability of concrete, useful semantics, and the existence of a corresponding analytic proof system), and maximality (or minimality) with respect to some desirable properties.
In this talk we shall describe the main results of the investigation of the various schools of paraconsistent logic from the pragmatic point of view, with particular emphasis on the two most famous ones: the Brazilian school of da Costa, and the relevance school of Anderson and Belnap.