A Sequent Calculus for a Paraconsistent Nonmonotonic Logic ?

In spite of sequent calculus being an appealing tool for describing logical systems, its use along with nonmonotonic logics has been largely neglected. Reasons may be the hardness in implementing a context sensitive mechanism able to detect changes in the theory. This seems to brake the locality of context of sequent rules. Nevertheless, a nonmo-notonic sequent calculus may be helpful if results obtained from other sequent calculus in formalising logical systems are here inherited. Furthermore , against the main trend, we make use of non-classical logics in formalising the deductive part of the reasoning. Here, this nonmonotonic basis is a paraconsistent logic of epistemic inconsistency, LEI, especially designed to deal with contradictions introduced by the reasoning under incomplete knowledge whereas the nonmonotonic part is performed by the inconsistent default logic, IDL. Thus, to provide an uniform description for the system IDL/LEI, in the sequent calculus style, is the aim of the present paper.