This paper presents the new adaptive logic APT. APT has the peculiar property that it enables one to interpret a (possibly inconsistent) theory Gamma 'as pragmatically as possible'. The aim is to capture the idea of a partial structure (in the sense of da Costa and associates) that adequately models a (possibly inconsistent) set of beliefs Gamma. What this comes to is that APT localizes the 'consistent core' of Gamma, and that it delivers all sentences that are compatible with this core. For the core itself, APT is just as rich as Classical Logic. APT is defined from a modal adaptive logic APV that is based itself on two other adaptive logics. I present the semantics of all three systems, as well as their dynamic proof theory. The dynamic proof theory for APV is unusual (even within the adaptive logic programme) in that it incorporates two different kinds of dynamics.

%B Paraconsistency. The Logical Way to the Inconsistent %I Marcel Dekker %C New York %P 167–185 %G eng