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A sound and complete R-calculi with respect to contraction and minimal change

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Abstract

AGM postulates are for belief revision (revision by a single belief), and DP postulates are for iterated revision (revision by a finite sequence of beliefs). R-calculus is given 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. We shall give two R-calculi C and M (sets of deduction rules) such that for any finite consistent sets Γ, Δ of formulas in the propositional logic, there is a consistent set Θ ⊆ Γ of formulas such that Δ|Γ ⟹ Δ, Θ is provable and Θ is a contraction of Γ by Δ or a minimal change of Γ by Δ; and prove that C and M are sound and complete with respect to the contraction and the minimal change, respectively.

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References

  1. Hansson S O. Theory contraction and base contraction unified. Journal of Symbolic Logic, 1993, 602–625

    Google Scholar 

  2. Li W. R-calculus: an inference system for belief revision. The Computer Journal, 2007, 50(4): 378–390

    Article  Google Scholar 

  3. Alchourrón C E, Gärdenfors P, Makinson D. On the logic of theory change: partial meet contraction and revision functions. Journal of Symbolic Logic, 1985, 510–530

    Google Scholar 

  4. Herzig A, Rifi O. Propositional belief base update and minimal change. Artificial Intelligence, 1999, 115(1): 107–138

    Article  MATH  MathSciNet  Google Scholar 

  5. Satoh K. Nonmonotonic reasoning by minimal belief revision. In: Proceedings of the 5th the International Conference on Generation Computer Systems. 1988, 455–462

    Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Software Development Environment, Beihang University, Beijing, 100191, China

    Wei Li

  2. Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100190, China

    Yuefei Sui

Authors
  1. Wei Li
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  2. Yuefei Sui
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Correspondence to Wei Li.

Additional information

Wei Li is a professor in the School of Computer Science and Engineering, Beihang University, China and is a member of the Chinese Academy of Sciences. Li is mostly engaged in the applied research of computer software and theory, and the Internet, including programming languages, software development, artificial intelligence, and integrated circuit design.

Yuefei Sui is a professor in the Institute of Computing Technology, Chinese Academy of Sciences. His main interests include knowledge representation, applied logic, and the theory of computability.

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Li, W., Sui, Y. A sound and complete R-calculi with respect to contraction and minimal change. Front. Comput. Sci. 8, 184–191 (2014). https://doi.org/10.1007/s11704-014-3102-1

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  • DOI: https://doi.org/10.1007/s11704-014-3102-1

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