Structured belief bases

Reinhard Kahle

DOI: http://dx.doi.org/10.12775/LLP.2002.003

Abstract


In this paper we discuss a formal approach to belief representation which stores proof-theoretic information together with formulae. It is illustrated how this additional information can be used in the context of belief revision. The general aims of this paper are the following three: First, we would like to give a descriptive approach to belief revision, in contrast to a normative one. Secondly, the given theory should avoid (the consequences of) logical omniscience of beliefs. Finally, from a broader point of view, the presented approach can be considered as a case study within the programme of proof-theoretic semantics. In this programme, the question is raised whether and how proof-theoretic information can be used as a basis for semantics.

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References


Carlos Alchourrón, Peter Gärdenfors, and David Makinson. On the logic of theory change: Partial meet functions for contraction and revision. Journal of Symbolic Logic, 50(2):510–530, 1985.

Carlos Alchourrón and David Makinson. On the logic of theory change: Contraction functions and their associated revision functions. Theoria, 48:14–37, 1982.

Carlos Alchourrón and David Makinson. On the logic of theory change: Safe contraction. Studia Logica, 44:405–422, 1985.

Carlos Alchourrón and David Makinson. Maps between some different kinds of contraction function: the finite case. Studia Logica, 45:187–198, 1986.

J. de Kleer. An assumption-based TMS. Artificial Intelligence, 28:127–162, 1986.

J. Doyle. A truth maintenance system. Artificial Intelligence, 12:231–272, 1979.

Ronald Fagin, Joseph Halpern, Yoram Moses, and Moshe Vardi. Reasoning about Knowledge. MIT Press, 1995.

André Fuhrmann. Theory contraction through base contraction. Journal of Philosophical Logic, 20:175–203, 1991.

André Fuhrmann. An Essay on Contraction. Studies in Logic, Language and Information. CSLI Publications, 1997.

Dov Gabbay. Labelled Deductive Systems, Volume 1, volume 33 of Oxford Logic Guides. Oxford University Press, 1996.

Sven Ove Hansson. Belief Base Dynamics. PhD thesis, Uppsala University, 1991.

Sven Ove Hansson. Revision of belief sets and belief bases. In Didier Dubois and Henri Prade, editors, Handbook of Defeasible Reasoning and Uncertainty Management Systems, Volume 3: Belief Change, pages 16–75. Kluwer Academic Publishers, Dordrecht, 1998.

Sven Ove Hansson. A Textbook of Belief Dynamics. Theory Change and Database Updating. Kluwer, 1999.

Reinhard Kahle. A proof-theoretic view of intensionality. In Paul Dekker, editor, Proceedings of the 12th Amsterdam Colloquium, pages 163–168. Amsterdam University, 1999.

Reinhard Kahle and Peter Schroeder-Heister, editors. Proof-theoretic semantics. In preparation, 200x.

David McAllester. Truth maintenance. In Thomas Dietterich and William Swartout, editors, Proceedings of the Eight National Conference on Artificial Intelligence, pages 1109–1116. AAAI Press, 1990.

Abhaya Nayak. Foundational belief change. Journal of Philosophical Logic, 23:495–533, 1994.

Bernhard Nebel. How hard is it to revise a belief base? In Didier Dubois and Henri Prade, editors, Handbook of Defeasible Reasoning and Uncertainty Management Systems, Volume 3: Belief Change, pages 77–145. Kluwer Academic Publishers, Dordrecht, 1998.

Stuart Russell and Peter Norvig. Artificial Intelligence — A Modern Approach. Prentice Hall, 1995.








ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

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