Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T17:57:30.151Z Has data issue: false hasContentIssue false
  • English
  • Français

Belief contraction in the context of the general theory of rational choice

Published online by Cambridge University Press:  12 March 2014

Hans Rott
Hans Rott*
Affiliation:
Fachgruppe Philosophie, Universität Konstanz, Postfach 5560, D-78434 Konstanz, Germany, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper reorganizes and further develops the theory of partial meet contraction which was introduced in a classic paper by Alchourrón, Gärdenfors, and Makinson. Our purpose is threefold. First, we put the theory in a broader perspective by decomposing it into two layers which can respectively be treated by the general theory of choice and preference and elementary model theory. Second, we reprove the two main representation theorems of AGM and present two more representation results for the finite case that “lie between” the former, thereby partially answering an open question of AGM. Our method of proof is uniform insofar as it uses only one form of “revealed preference”, and it explains where and why the finiteness assumption is needed. Third, as an application, we explore the logic characterizing theory contractions in the finite case which are governed by the structure of simple and prioritized belief bases.

Keywords

Theory changebelief revisionrational choicepreferencepartial meet contractionbase contraction
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 4 , December 1993 , pp. 1426 - 1450
Copyright
Copyright © Association for Symbolic Logic 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Alchourrón, Carlos, Gärdenfors, Peter, and Makinson, David, On the logic of theory change: Partial meet contraction functions and their associated revision functions, this Journal, vol. 50 (1985), pp. 510–530.Google Scholar
[2]Alchourrón, Carlos and Makinson, David, Maps between some different kinds of contraction function: The finite case, Studia Logica, vol. 45 (1986), pp. 187–198.CrossRefGoogle Scholar
[3]Chernoff, Herman, Rational selection of decision functions, Econometrica, vol. 22 (1954), pp. 422–443.CrossRefGoogle Scholar
[4]Fuhrmann, André and Morreau, Michael (editors), The logic of theory change, Lecture Notes in Computer Science, vol. 465, Springer-Verlag, Berlin, 1991.CrossRefGoogle Scholar
[5]Gärdenfors, Peter, Knowledge in flux: Modeling the dynamics of epistemic states, Bradford Books, MIT Press, Cambridge, Massachusetts, 1988.Google Scholar
[6]Gärdenfors, Peter (editor), Belief revision, Cambridge University Press, Cambridge, 1992.CrossRefGoogle Scholar
[7]Gärdenfors, Peter and Makinson, David, Revisions of knowledge systems using epistemic entrenchment, Theoretical Aspects of Reasoning About Knowledge (Vardi, M., editor), Morgan Kaufmann, Los Altos, 1988, pp. 83–95.Google Scholar
[8]Grove, Adam, Two modellings for theory change, Journal of Philosophical Logic, vol. 17 (1988), pp. 157–170.CrossRefGoogle Scholar
[9]Hansson, Sven Ove, Similarity semantics and minimal changes of belief, Erkenntnis, vol. 37 (1992), pp. 401–429.CrossRefGoogle Scholar
[10]Herzberger, Hans G., Ordinal preference and rational choice, Econometrica, vol. 41 (1973), pp. 187–237.CrossRefGoogle Scholar
[11]Katsuno, Hirofumi and Mendelzon, Alberto O., Propositional knowledge base revision and minimal change, Artificial Intelligence, vol. 52 (1991), pp. 263–294.CrossRefGoogle Scholar
[12]Kraus, Sarit, Lehmann, Daniel, and Magidor, Menachem, Nonmonotonic reasoning, preferential models and cumulative logics, Artificial intelligence, vol. 44 (1990), pp. 167–207.CrossRefGoogle Scholar
[13]Lehmann, Daniel and Magidor, Menachem, What does a conditional knowledge base entail?, Artificial Intelligence, vol. 55 (1992), pp. 1–60.CrossRefGoogle Scholar
[14]Lewis, David, Counterfactuals, Blackwell, Oxford, 1973 (second edition 1986).Google Scholar
[15]Lewis, David, Ordering semantics and premise semantics for counterfactuals, Journal of Philosophical Logic, vol. 10(1981), pp. 217–234.CrossRefGoogle Scholar
[16]Lindström, Sten, A semantic approach to nonmonotonic reasoning: Inference and choice, University of Uppsala, 04 1991, manuscript.Google Scholar
[17]Makinson, David and Gärdenfors, Peter, Relations between the logic of theory change and nonmonotonic logic, The logic of theory change (Fuhrmann, A. and Morreau, M., editors), Lecture Notes in Computer Science, vol. 465, Springer-Verlag, Berlin and New York, 1991, pp. 185–205.CrossRefGoogle Scholar
[18]Nebel, Bernhard, A knowledge level analysis of belief revision, Proceedings of the 1st international conference on principles of knowledge representation and reasoning (Brachman, R., Levesque, H., and Reiter, R., editors), Morgan Kaufmann, San Mateo, California, 1989, pp. 301–311.Google Scholar
[19]Nebel, Bernhard, Syntax-based approaches to belief revision, Belief revision (Gärdenfors, P., editor), Cambridge University Press, Cambridge, 1992, pp. 52–88.CrossRefGoogle Scholar
[20]Rott, Hans, Two methods of constructing contractions and revisions of knowledge systems, Journal of Philosophical Logic, vol. 20(1991), pp. 149–173.CrossRefGoogle Scholar
[21]Rott, Hans, On the logic of theory change: More maps between different kinds of contraction function, Belief revision (Gärdenfors, P., editor), Cambridge University Press, Cambridge, 1992, pp. 122–141.CrossRefGoogle Scholar
[22]Rott, Hans, Preferential belief change using generalized epistemic entrenchment, Journal of Logic, Language and Information, vol. 1 (1992), pp. 45–78.CrossRefGoogle Scholar
[23]Sen, Amartya K., Choice, welfare, and measurement, Blackwell, Oxford, 1982.Google Scholar
[24]Suzumura, Kotaro, Rational choice, collective decisions, and social welfare, Cambridge University Press, Cambridge, 1983.CrossRefGoogle Scholar