The Sound and Complete R-Calculi with Respect to Pseudo-Revision and Pre-Revision

The AGM postulates ([1]) are for the belief revision (revision by a single belief), and the DP postulates ([2]) are for the iterated revision (revision by a finite sequence of beliefs). Li [3] gave an R-calculus for R-configurations ,   where Δ is a set of literals, and Γ is a finite set of formulas. We shall give two -calculi such that for any consistent set Γ and finite consistent set of formulas in the propositional logic, in one calculus, there is a pseudo-revision Θ of Γ by Δ such that R    is provable and and in another calculus, there is a pre-revision Ξ of Γ by Δ such that ;    ∪   is provable, and for some pseudo-revision Θ; and prove that the deduction systems for both the -calculi are sound and complete with the pseudo-revision and the pre-revision, respectively.    ,     R