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Parallel interpolation, splitting, and relevance in belief change

Published online by Cambridge University Press:  12 March 2014

George Kourousias  and
David Makinson
George Kourousias
Affiliation:
Department of Computer Science, Group of Logic & Computation, King's College London, Strand London WC2R 2LS, UK, E-mail: [email protected]
David Makinson
Affiliation:
Department of Philosophy, Logic & Scientific Method, London School of Economics, Houghton Street, London WC2A 2AE, UK, E-mail: [email protected]
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 3 , September 2007 , pp. 994 - 1002
Copyright
Copyright © Association for Symbolic Logic 2007

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References

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