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

Wei Li, Yuefei Sui

Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China.
State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing, China.

DOI: 10.4236/ijis.2013.32012                

Abstract

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 △|Γ, where Δ is a set of literals, and Γ is a finite set of formulas. We shall give two R-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 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 R-calculi are sound and complete with the pseudo-revision and the pre-revision, respectively.

Keywords

Belief Revision; R-Calculus; Maximal Consistent Set; Pseudo-Revision; Pre-Revision

Conflicts of Interest

The authors declare no conflicts of interest.

References

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