Ranking Functions for Belief Change - A Uniform Approach to Belief Revision and Belief Progression

Aaron Hunter

Abstract

In this paper, we explore the use of ranking functions in reasoning about belief change. It is well-known that the semantics of belief revision can be defined either through total pre-orders or through ranking functions over states. While both approaches have similar expressive power with respect to single-shot belief revision, we argue that ranking functions provide distinct advantages at both the theoretical level and the practical level, particularly when actions are introduced. We demonstrate that belief revision induces a natural algebra over ranking functions, which treats belief states and observations in the same manner. When we introduce belief progression due to actions, we show that many natural domains can be easily represented with suitable ranking functions. Our formal framework uses ranking functions to represent belief revision and belief progression in a uniform manner; we demonstrate the power of our approach through formal results, as well as a series of natural problems in commonsense reasoning.

References

  1. Alchourrón, C., Gärdenfors, P., and Makinson, D. (1985). On the logic of theory change: Partial meet functions for contraction and revision. Journal of Symbolic Logic, 50(2):510-530.
  2. Baltag, A., Moss, L., and Solecki, S. (1998). The logic of public announcements, common knowledge and private suspicions. In Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge (TARK-98), pages 43-56.
  3. Boutilier, C. (1995). Generalized update: Belief change in dynamic settings. In Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI 1995), pages 1550-1556.
  4. Delgrande, J., Dubois, D., and Lang, J. (2006). Iterated revision as prioritized merging. In Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning (KR2006).
  5. Delgrande, J. and Levesque, H. (2012). Belief revision with sensing and fallible actions. In Proceedings of the International Conference on Knowledge Representation and Reasoning (KR2012).
  6. Dubois, D. and Prade, H. (2004). Possibilistic logic: a retrospective and prospective view. Fuzzy Sets and Systems, 144(1):3-23.
  7. Hunter, A. and Delgrande, J. (2006). Belief change in the context of fallible actions and observations. In Proceedings of the National Conference on Artificial Intelligence(AAAI06).
  8. Hunter, A. and Delgrande, J. (2011). Iterated belief change due to actions and observations. Journal of Artificial Intelligence Research, 40:269-304.
  9. Katsuno, H. and Mendelzon, A. (1991). On the difference between updating a knowledge base and revising it. In Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning (KR 1991), pages 387-394.
  10. Katsuno, H. and Mendelzon, A. (1992). Propositional knowledge base revision and minimal change. Artificial Intelligence, 52(2):263-294.
  11. Lang, J. (2007). Belief update revisited. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI07), pages 2517-2522.
  12. Levesque, H., Pirri, F., and Reiter, R. (1998). Foundations for the situation calculus. Linköping Electronic Articles in Computer and Information Science, 3(18):1- 18.
  13. Lorini, E. (2011). A dynamic logic of knowledge, graded beliefs and graded goals and its application to emotion modelling. In LORI, pages 165-178.
  14. Shapiro, S., Pagnucco, M., Lesperance, Y., and Levesque, H. (2011). Iterated belief change in the situation calculus. Artificial Intelligence, 175(1):165-192.
  15. Spohn, W. (1988). Ordinal conditional functions. A dynamic theory of epistemic states. In Harper, W. and Skyrms, B., editors, Causation in Decision, Belief Change, and Statistics, vol. II, pages 105-134. Kluwer Academic Publishers.
  16. Stalnaker, R. (2009). Iterated belief revision. Erkenntnis, 70(1-2):189-209.
  17. van Ditmarsch, H., van der Hoek, W., and Kooi, B. (2007). Dynamic Epistemic Logic. Springer.
Download


Paper Citation


in Harvard Style

Hunter A. (2014). Ranking Functions for Belief Change - A Uniform Approach to Belief Revision and Belief Progression . In Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-758-015-4, pages 412-419. DOI: 10.5220/0004812704120419


in Bibtex Style

@conference{icaart14,
author={Aaron Hunter},
title={Ranking Functions for Belief Change - A Uniform Approach to Belief Revision and Belief Progression},
booktitle={Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2014},
pages={412-419},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004812704120419},
isbn={978-989-758-015-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - Ranking Functions for Belief Change - A Uniform Approach to Belief Revision and Belief Progression
SN - 978-989-758-015-4
AU - Hunter A.
PY - 2014
SP - 412
EP - 419
DO - 10.5220/0004812704120419