Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain as much as possible from classical logic. In this paper we introduce a new, strong notion of maximal paraconsistency, which is based on possible extensions of the consequence relation of a logic. We investigate this notion in the framework of finite-valued paraconsistent logics, and show that for every $n>2$ there exists an extensive family of $n$-valued logics, each of which is maximally paraconsistent in our sense, is partial to classical logic, and is not equivalent to any $k$-valued logic with $k
['Arnon Avron', 'Ofer Arieli', 'Anna Zamansky']
On Strong Maximality of Paraconsistent Finite-Valued Logics