Volume 12 Number 2 (Mar. 2017)
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JCP 2017 Vol.12(2): 127-134 ISSN: 1796-203X
doi: 10.17706/jcp.12.2.127-134

The R-Calculus and the Finite Injury Priority Method

Li Wei1, Sui Yuefei2
1State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing, China.
2Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China.


Abstract—The R-calculus is a Gentzen-type deduction system to deduce a consistent theory Θ from a theory Γ to be revised and a theory Δ to revise. Because the semi-decidability of the deduction in the first-order logic, the R-calculus is semi-decidable. By using the limit lemma and finite injury priority method in recursion theory, we shall recursively construct a sequence {Θ_s: s∈ω} of formula sets such that the limit of {Θ_s: s∈ω} exists, say Θ;Δ|Γ⇒Θ is provable in the R-calculus, and each formula ϕ in Γ is enumerated in or extracted from Θ only finitely often, where Θ is a maximal consistent set of Γ by Δ. Moreover, a Gentzen-type deduction is constructed to deduce the sequence {Θ_s: s∈ω} by the deduction rules in which the deduction is recursive (decidable, computable).

Index Terms—Belief revision, R-calculus, finite injury priority method, simple set, recursively enumerable sets.

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Cite: Li Wei, Sui Yuefei, "The R-Calculus and the Finite Injury Priority Method," Journal of Computers vol. 12, no. 2, pp. 127-134, 2017.

General Information

ISSN: 1796-203X
Frequency: Monthly (2006-2014); Bimonthly (Since 2015)
Editor-in-Chief: Prof. Liansheng Tan
Executive Editor: Ms. Nina Lee
Abstracting/ Indexing: DBLP, EBSCO, DOAJ, ProQuest, INSPEC, ULRICH's Periodicals Directory, WorldCat, CNKI,etc
E-mail: jcp@iap.org
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