Journal of Symbolic Logic

Parallel interpolation, splitting, and relevance in belief change

George Kourousias and David Makinson

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Abstract

The splitting theorem says that any set of formulae has a finest representation as a family of letter-disjoint sets. Parikh formulated this for classical propositional logic, proved it in the finite case, used it to formulate a criterion for relevance in belief change, and showed that AGM partial meet revision can fail the criterion. In this paper we make three further contributions. We begin by establishing a new version of the well-known interpolation theorem, which we call parallel interpolation, use it to prove the splitting theorem in the infinite case, and show how AGM belief change operations may be modified, if desired, so as to ensure satisfaction of Parikh’s relevance criterion.

Article information

Source
J. Symbolic Logic, Volume 72, Issue 3 (2007), 994-1002.

Dates
First available in Project Euclid: 2 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1191333851

Digital Object Identifier
doi:10.2178/jsl/1191333851

Mathematical Reviews number (MathSciNet)
MR2354910

Zentralblatt MATH identifier
1124.03004

Citation

Kourousias, George; Makinson, David. Parallel interpolation, splitting, and relevance in belief change. J. Symbolic Logic 72 (2007), no. 3, 994--1002. doi:10.2178/jsl/1191333851. https://projecteuclid.org/euclid.jsl/1191333851


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