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

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|┌, where Δ is a set of atomic formulas or the negations of atomic formulas, and ┌ 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 ┌, Δ of formulas in the propositional logic, there is a consistent set Θ\subseteq┌ of formulas such that Δ|┌\RightarrowΔ, Θ is provable and Θ is a contraction of ┌ by Δ or a minimal change of ┌ by Δ; and prove that C and M are sound and complete with respect tothe contraction and the minimal change, respectively.

Keywords

belief revision / R-calculus / minimal change / contraction

References

[1] HanssonS O. Theory contraction and base contraction unified. Journal of Symbolic Logic, 1993, 602-625

[2] LiW. R-calculus: an inference system for belief revision. The Computer Journal, 2007, 50(4): 378-390

[3] AlchourrónC E, GärdenforsP, MakinsonD. On the logic of theory change: partial meet contraction and revision functions. Journal of Symbolic Logic, 1985, 510-530

[4] HerzigA, RifiO. Propositional belief base update and minimal change. Artificial Intelligence, 1999, 115(1): 107-138

[5] SatohK. Nonmonotonic reasoning by minimal belief revision. In: Proceedings of the 5th the International Conference on Generation Computer Systems. 1988, 455-462

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