Maksymalne logiki tolerujące sprzeczność

Abstrakt

Maximal paraconsistent logics

As we know there is an infinite number of various paraconsistent logics i.e. logics that, unlike classical logic, allow reasoning within inconsistent but non-trivial theories. It seems that certain natural assumptions about them could reduce the number of systems to those that are especially important. One of the main assumptions about paraconsistent logics is that they should be as rich as possible. In formal terms this may mean that paraconsistent logics should be maximal. In this paper we provide an overview of the main maximality results obtained: first by D. Batens, then by T. Skura, and R. Tuziak, and finally by O. Arieli, A. Avron, and A. Zamansky. We compare the approaches to the problem and examine the very notion of maximality. We argue that maximal calculi are worth examining and especially interesting as formal systems that can be successfully applied to inconsistent databases.