Notre Dame Journal of Formal Logic

Constructive Modelings for Theory Change

Pavlos Peppas and Mary-Anne Williams

Abstract

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).

Article information

Source
Notre Dame J. Formal Logic, Volume 36, Number 1 (1995), 120-133.

Dates
First available in Project Euclid: 19 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1040308831

Digital Object Identifier
doi:10.1305/ndjfl/1040308831

Mathematical Reviews number (MathSciNet)
MR1359110

Zentralblatt MATH identifier
0844.03017

Subjects
Primary: 03B60: Other nonclassical logic
Secondary: 03C90: Nonclassical models (Boolean-valued, sheaf, etc.) 68T27: Logic in artificial intelligence

Citation

Peppas, Pavlos; Williams, Mary-Anne. Constructive Modelings for Theory Change. Notre Dame J. Formal Logic 36 (1995), no. 1, 120--133. doi:10.1305/ndjfl/1040308831. https://projecteuclid.org/euclid.ndjfl/1040308831


Export citation

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.