On identification of inconsistencies in formal theories. II

As a follow up of Ref. [1] logical calculi are considered in which proofs of conflict are possible. A classical first order language LPCont is designed whose object language is LPCont and the formalized metalanguage is classical logic. Some extensions of LPCont are discussed and its relation with Bochvar's logic $B_3$ [2] is established. In conclusion some woder aspects of the logic of inconsistent systems (such as logical paradoxes) are taken up.