One Sound and Complete R-Calculus with Pseudo-Subtheory Minimal Change Property


The AGM axiom system is for the belief revision (revision by a single belief), and the DP axiom system is for the iterated revision (revision by a finite sequence of beliefs). Li [1] gave an R-calculus for R-configurations Δ|Γ, where Δ is a set of atomic formulas or the negations of atomic formulas, and Γ is a finite set of formulas. In propositional logic programs, one R-calculus N will be given in this paper, such that N is sound and complete with respect to operator s(Δ,t), where s(Δ,t)is a pseudo-theory minimal change of t by Δ.

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Li, W. and Sui, Y. (2013) One Sound and Complete R-Calculus with Pseudo-Subtheory Minimal Change Property. Journal of Computer and Communications, 1, 20-25. doi: 10.4236/jcc.2013.15004.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] W. Li, “R-Calculus: An Inference System for Belief Revision,” The Computer Journal, Vol. 50, 2007, pp. 378-390.
[2] C. E. Alchourrón, P. Gärdenfors and D. Makinson, “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions,” Journal of Symbolic Logic, Vol. 50, 1985, pp. 510-530.
[3] A. Bochman, “A Foundational Theory of Belief and Belief Change,” Artificial Intelligence, Vol. 108, 1999, pp. 309-352.
[4] M. Dalal, “Investigations into a Theory of Knowledge Base Revision: Preliminary Report,” Proceedings of AAAI-88, St. Paul, 1988, pp. 475-479.
[5] P. Gärdenfors 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., 1995, pp. 35-132.
[6] A. Darwiche and J. Pearl, “On the Logic of Iterated Belief Revision,” Artificial Intelligence, Vol. 89, 1997, pp. 1-29.
[7] E. Fermé and S. O. Hansson, “AGM 25 Years, Twenty- Five Years of Research in Belief Change,” Journal of Philosophical Logic, Vol. 40, 2011, pp. 295-331.
[8] N. Friedman and J. Y. Halpern, “Belief Revision: A Critique,” In: L. C. Aiello, J. Doyle and S. C. Shapiro, Eds., Journal of of Logic, Language and Information, Principles of Knowledge Representation and Reasoning, Proceedings of the 5th Conference, 1996, pp. 421-431.
[9] S. O. Hansson, “Theory Contraction and Base Contraction Unified,” Journal of Symbolic Logic, Vol. 58, 1993, pp. 602-626.
[10] A. Herzig and O. Rifi, “Propositional Belief Base Update and Minimal Change,” Artificial Intelligence, Vol. 115, 1999, pp. 107-138.
[11] K. Satoh, “Nonmonotonic Reasoning by Minimal Belief Revision,” Proceedings of the International Conference on Fifth Generation Computer Systems, Tokyo, 1988, pp. 455-462.

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