Source: Notre Dame J. Formal Logic Volume 36, Number 1
(1995), 120-133.
Alchourrón, Gärdenfors and Makinson have developed and investigated a
set of rationality postulates which appear to capture much of what is
required of any rational system of theory revision. This set of postulates
describes a class of revision functions, however it does not provide a
constructive way of defining such a function. There are two principal
constructions of revision functions, namely an epistemic entrenchment and
a system of spheres. We refer to their approach as the AGM paradigm. We
provide a new constructive modeling for a revision function based on a
nice preorder on models, and furthermore we give explicit conditions
under which a nice preorder on models, an epistemic entrenchment, and a
system of spheres yield the same revision function. Moreover, we
provide an identity which captures the relationship between revision
functions and update operators (as defined by Katsuno and Mendelzon).
References
[1] Alchourron, C., P. Gärdenfors and D. Makinson, ``On the logic of theory change: Partial meet contraction and revision functions,'' The Journal of Symbolic Logic, vol. 50 (1985), pp. 510--530.
[2] Gärdenfors, P., Knowledge in Flux: Modeling the Dynamics of Epistemic States, MIT Press, Cambridge, 1988.
[3] Gärdenfors, P. and D. Makinson, ``Revisions of knowledge systems using epistemic entrenchment,'' pp. 83--95 in Proceedings of the Second Conference on Theoretical Aspects of Reasoning About Knowledge, edited by M. Y. Vardi, Morgan Kaufmann, Pacific Grove, 1988.
[4] Gärdenfors, P. and D. Makinson, ``Nonmonotonic inference based on expectations,'' Artificial Intelligence, vol. 65 (1994), pp. 197--245.
[5] Grove, A., ``Two modelings for theory change,'' Journal of Philosophical Logic, vol. 17 (1988), pp. 57--170.
[6] Katsuno, H. and A. Mendelzon, ``Propositional knowledge base revision and minimal change,'' Artificial Intelligence, vol. 52 (1991), pp. 263--294.
[7] Katsuno, H. and A. Mendelzon, ``On the difference between updating a knowledge base and revising it,'' pp. 183--203 in Belief Revision, edited by P. Gärdenfors, Cambridge University Press, Cambridge, 1992.
[8] Makinson, D., ``Five faces of minimality,'' Studia Logica, vol. 52 (1993), pp. 339 -- 379.
[9] Peppas, P., Belief Change and Reasoning about Action: An Axiomatic Approach to Modelling Inert Dynamic Worlds and the Connection to the Logic of Theory Change, PhD thesis, Department of Computer Science, University of Sydney, 1993.
[10] Rott, H., ``Two methods of constructing contractions and revisions of knowledge systems,'' Journal of Philosophical Logic, vol 20 (1991), pp. 149--173.
[11] Williams, M., Transmutations of Knowledge Systems, PhD thesis, Department of Computer Science, University of Sydney, 1993.
[12] Winslett, M., ``Reasoning about action using a possible models approach,'' pages 89--93 in Proceedings of the Seventh National (U.S.) Conference on Artificial Intelligence, Morgan Kaufmann, St. Paul, 1988.
Mathematical Reviews (MathSciNet):
MR947183
