IJIS  Vol.3 No.2 , April 2013
The Sound and Complete R-Calculi with Respect to Pseudo-Revision and Pre-Revision
Author(s) Wei Li*, Yuefei Sui*
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.

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.
References
[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.

 
 
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