We consider the very weak paracomplete and paraconsistent logics that are obtained by a straightforward weakening of Classical Logic, as well as some of their maximal extensions that are a fragment of Classical Logic. We prove that these logics may be faithfully embedded in Classical Logic, and that the interpolation theorem obtains for them.

In this paper I present two new strategies for inconsistencyadaptive logics: the reliable sufficient information strategy of ACLuN3 andthe minimally abnormal sufficient information strategy of ACLuN4. I giveproof theory and semantics for both ACLuN3 and ACLuN4. I also compare them with the well-known inconsistency-adaptive logics ACLuN1 andACLuN2.