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

Affiliation(s)

State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing, China.

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.

Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China.

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.

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

Cite this paper

W. Li and Y. Sui, "The Sound and Complete*R*-Calculi with Respect to Pseudo-Revision and Pre-Revision," *International Journal of Intelligence Science*, Vol. 3 No. 2, 2013, pp. 110-117. doi: 10.4236/ijis.2013.32012.

W. Li and Y. Sui, "The Sound and Complete

References

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[2] A. Darwiche and J. Pearl, “On the Logic of Iterated Belief Revision,” Artificial Intelligence, Vol. 89, No. 1-2, 1997, pp. 1-29. doi:10.1016/S0004-3702(96)00038-0

[3] W. Li, “R-Calculus: An Inference System for Belief Revision,” The Computer Journal, Vol. 50, No. 4, 2007, pp. 378-390. doi:10.1093/comjnl/bxl069

[4] E. Fermé and S. O. Hansson, “AGM 25 Years, Twenty-Five Years of Research in Belief Change,” Journal of Philosophical Logic, Vol. 40, No. 2, 2011, pp. 295-331. doi:10.1007/s10992-011-9171-9

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[1] C. E. Alchourron, P. Gardenfors and D. Makinson, “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions,” The Journal of Symbolic Logic, Vol. 50, No. 2, 1985, pp. 510-530. doi:10.2307/2274239

[2] A. Darwiche and J. Pearl, “On the Logic of Iterated Belief Revision,” Artificial Intelligence, Vol. 89, No. 1-2, 1997, pp. 1-29. doi:10.1016/S0004-3702(96)00038-0

[3] W. Li, “R-Calculus: An Inference System for Belief Revision,” The Computer Journal, Vol. 50, No. 4, 2007, pp. 378-390. doi:10.1093/comjnl/bxl069

[4] E. Fermé and S. O. Hansson, “AGM 25 Years, Twenty-Five Years of Research in Belief Change,” Journal of Philosophical Logic, Vol. 40, No. 2, 2011, pp. 295-331. doi:10.1007/s10992-011-9171-9

[5] N. Friedman and J. Y. Halpern, “Belief Revision: A Critique, to Appear in J. of Logic, Language and Information,” In: L. C. Aiello, J. Doyle and S. C. Shapiro, Eds., Proceedings of the 5th Conference of Principles of Knowledge Representation and Reasoning, 1996, pp. 421-431.

[6] P. Gardenfors and H. Rott, “Belief Revision,” In: D. M. Gabbay, C. J. Hogger and J. A. Robinson, Eds., Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 4, Epistemic and Temporal Reasoning, Oxford Science Pub., Oxford, 1995, pp. 35-132.