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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

REFERENCES

[1]Alchourrón, Carlos A., Gärdenfors, Peter, and Makinson, David, On the logic of theory change: partial meet contraction and revision functions, this Journal, vol. 50 (1985), pp. 510–530.Google Scholar
[2]Chopra, Samir, Georgatos, Konstantinos, and Parikh, Rohit, Relevance sensitive non-monotonic inference on belief sequences, Journal of Applied Non-Classical Logics, vol. 11 (2001), no. 1-2, pp. 131–150.CrossRefGoogle Scholar
[3]Chopra, Samir and Parikh, Rohit, Relevance sensitive belief structures, Annals of Mathematics and Artificial Intelligence, vol. 28 (2000), no. 1–4, pp. 259–285.CrossRefGoogle Scholar
[4]Craig, William, Linear reasoning. A new form of the Herbrand-Gentzen theorem, this Journal, vol. 22 (1957), no. 3, pp. 250–268.Google Scholar
[5]Craig, William, Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory, this Journal, vol. 22 (1957), no. 3, pp. 269–285.Google Scholar
[6]Hansson, Sven O., A textbook of belief dynamics: Theory change and database updating, Applied Logic Series, Kluwer Academic Publishers, 1999.CrossRefGoogle Scholar
[7]Hodges, Wilfrid, A shorter model theory, Cambridge University Press, 1997.Google Scholar
[8]Makinson, David, Friendliness for logicians, We will show them! Essays in honour of Dov Gabbay (Artemov, Sergei N., Barringer, Howard, Garcez, Artur S. d'Avila, Lamb, Luis C., and Woods, John, editors), vol. two, College Publications, 2005, pp. 259–292. Also appearing in Logica Universalis, (J.–Y. Béziau, editor), second edition, Birkhäuser Verlag, Basel, 2007.Google Scholar
[9]Parikh, Rohit, Beliefs, belief revision, and splitting languages, Logic, language, and computation (Moss, Lawrence, Ginzburg, Jonathan, and de Rijke, Maarten, editors), vol. 2, CSLI Publications, Stanford, California, 1999, pp. 266–278.Google Scholar
[10]Peppas, Pavlos, Chopra, Samir, and Foo, Norman, Distance semantics for relevance-sensitive belief revision, KR2004: Principles of knowledge representation and reasoning (Dubois, Didier, Welty, Christopher A., and Williams, Mary-Anne, editors), AAAI Press, Menlo Park, California, 2004, pp. 319–328.Google Scholar
[11]Rott, Hans, Change, choice and inference: A study of belief revision and nonmonotonic reasoning, Oxford University Press, Oxford, 2001.CrossRefGoogle Scholar