Axiomatization of Credulous Reasoning in Default Logics using Sequent Calculus

The family of default logics formalize the default reasoning using nonmonotonic inference rules called defaults. In this paper we propose a uniform abstract characterization of credulous default inference associated to all versions (classical, justified, constrained, rational) of propositional default logic using the credulous default sequent calculi. These axiomatic systems combine sequent and anti-sequent calculus rules for propositional logic with reduction rules specific to the application of the defaults.