On identification of inconsistencies in formal theories. I

Logical calculi are described which identify inconsistencies in formal theories. This first article describes the characteristic features of the logic of inconsistent systems (“paraconsistent logic”) within the framework of which inconsistency can be proved. PCont (“contradiction”) propositional calculus and some its extenstions are constructed. A criterion for derivability of a formula in PCont is established and some assertions are made on the relation of PCont and the classical logic.