A reconstruction of multipreference closure

The paper describes a preferential approach for dealing with exceptions in KLM logics, based on the rational closure. It is well known that closure does not allow an independent handling of inheritance different defeasible properties concepts. In this work, we consider alternative construction, called Multi Preference (MP-closure), which has been first considered reasoning DLs. We reconstruct notion MP-closure propositional case and show it natural (weaker) variant Lehmann's lexicographic closure, appears to be too bold some cases. defines consequence relation that, although weaker than stronger Relevant Closure.