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.
Highlights
The AGM postulates ([1],[4,5,6]) are for the revision K of a theory K by a formula ; and the DP postulates ([2]) are for the iterated revision K 1 n.The R -calculus has the following features: is a finite set of literals;, the R -calculus is based on pseudo-revision, i.e., to contract from ∪ ∪ if ∪ ∪ is inconsistent, which makes the R -calculus not preserve the minimal change principle.We shall give two R -calculi such that in one R -calculus, say R1, for any consistent formula set and finite formula set, there is a IJIS W
The R -calculus is based on pseudo-revision, i.e., to contract from ∪ ∪ if ∪ ∪ is inconsistent, which makes the R -calculus not preserve the minimal change principle
We prove by induction on i n that there is a formula set i such that i | i, i 1 i 1 | i 1 is provable, where 0, and i 1 i 1, n
Summary
The AGM postulates ([1],[4,5,6]) are for the revision K of a theory K by a formula ; and the DP postulates ([2]) are for the iterated revision. The R -calculus has the following features: is a finite set of literals (propositional variables or the negation of propositional variables);. The paper is organized as follows: the section gives the R -calculus in [3] and basic definitions; the third section defines an R -calculus R1 for the pseudorevision and proves that R1 is sound and complete with respect to the pseudo-revision; the fourth section defines another R -calculus R2 for the pre-revision and prove that R2 is sound and complete with respect to the pseudo-revision, and the last section concludes the whole paper
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