# Preference-based belief revision for rule-based agents

- 107 Downloads
- 4 Citations

## Abstract

Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a contraction operation for rule-based reasoners, which we call McAllester contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our contraction operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester contraction can be used to define a revision operation which is also polynomial time, and prove a representation theorem for the revision operation.

## Keywords

Belief revision Reason maintenance systems Preferences Rule-based agents## Preview

Unable to display preview. Download preview PDF.

## References

- Alchourrón C.E., Gärdenfors P., Makinson D. (1985) On the logic of theory change: Partial meet functions for contraction and revision. Journal of Symbolic Logic 50: 510–530CrossRefGoogle Scholar
- Alchourrón C.E., Makinson D. (1985) The logic of theory change: Safe contraction. Studia Logica 44: 405–422CrossRefGoogle Scholar
- Alechina, N., Bordini, R., Hübner, J., Jago, M., & Logan, B. (2006a). Automating belief revision for AgentSpeak. In M. Baldoni & U. Endriss (Eds.),
*Declarative Agent Languages and Technologies IV, 4th International Workshop, DALT 2006, Selected, Revised and Invited Papers*, Vol. 4327 of*Lecture Notes in Artificial Intelligence*, pp. 61–77.Google Scholar - Alechina, N., Jago, M., & Logan, B. (2006b). Resource-bounded belief revision and contraction. In M. Baldoni, U. Endriss, A. Omicini, & P. Torroni (Eds.),
*Declarative Agent Languages and Technologies III, Third International Workshop, DALT 2005, Utrecht, The Netherlands, July 25, 2005, Selected and Revised Papers*, Vol. 3904 of*Lecture Notes in Computer Science*, pp. 141–154.Google Scholar - Bezzazi, H., Janot, S., Konieczny, S., & Pérez, R. P. (1998). Analysing rational properties of change operators based on forward chaining. In B. Freitag, H. Decker, M. Kifer, & A. Voronkov (Eds.),
*Transactions and change in logic databases*, Vol. 1472 of*Lecture Notes in Computer Science*, pp. 317–339.Google Scholar - Chopra S., Parikh R., Wassermann R. (2001) Approximate belief revision. Logic Journal of the IGPL 9(6): 755–768CrossRefGoogle Scholar
- Dixon, S. (1993). A finite base belief revision system. In
*Proceedings of Sixteenth Australian Computer Science Conference (ACSC-16): Australian Computer Science Communications*(Vol. 15, pp. 445–451). Brisbane, Australia.Google Scholar - Dixon S., Foo N. (1993) Connections between the ATMS and AGM belief revision. In: Bajcsy R.(eds) Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence. San Mateo, California, pp 534–539Google Scholar
- Dixon, S., & Wobcke, W. (1993). The implementation of a first-order logic AGM belief revision system. In
*Proceedings of 5th IEEE International Conference on Tools with AI*(pp. 40–47). Boston, MA.Google Scholar - Doyle, J. (1977). Truth maintenance systems for problem solving. In
*Proceedings of the Fifth International Joint Conference on Artificial Intelligence*, IJCAI 77, p. 247.Google Scholar - Doyle, J. (1992). Reason maintenance and belief revision. Foundations vs. coherence theories. In P. Gärdenfors (Ed.),
*Belief revision*(pp. 29–51). Cambridge University Press.Google Scholar - Eiter T., Gottlob G. (1996) The complexity of nested counterfactuals and iterated knowledge base revisions. Journal of Computer and System Sciences 53(3): 497–512CrossRefGoogle Scholar
- Galliers, J. R. (1992) Autonomous belief revision and communication. In P. Gärdenfors (Ed.),
*Belief revision*(pp. 220–246). Cambridge University Press.Google Scholar - Gärdenfors P. (1988) Knowledge in flux: Modelling the dynamics of epistemic states. The MIT Press, Cambridge, MAGoogle Scholar
- Gärdenfors, P., & Makinson, D. (1988). Revisions of knowledge systems using epistemic entrenchment. In M. Y. Vardi (Ed.),
*Proceedings of the Second Conference on Theretical Aspects of Reasoning About Knowledge*(pp. 83–95).Google Scholar - Hansson S.O. (1991) Belief contraction without recovery. Studia Logica 50(2): 251–260CrossRefGoogle Scholar
- Hansson S.O. (1993) Theory contraction and base contraction unified. Journal of Symbolic Logic 58(2): 602–625CrossRefGoogle Scholar
- Hansson S.O. (1994) Kernel contraction. Journal of Symbolic Logic 59: 845–859CrossRefGoogle Scholar
- Hansson S.O. (1997) Semi-revision. Journal of Applied Non-Classical Logic 7(1–2): 151–175Google Scholar
- Katsuno H., Mendelzon A. (1991) Propositional knowledge base revision and minimal change. Artificial Intelligence 52: 263–294CrossRefGoogle Scholar
- Kowalski, R. (1979).
*Logic for problem solving*. North Holland.Google Scholar - Makinson D. (1985) How to give it up: A survey of some formal aspects of the logic of theory change. Synthese 62: 347–363CrossRefGoogle Scholar
- Makinson D. (1987) On the status of the postulate of recovery in the logic of theory change. Journal of Philosophical Logic 16: 383–394CrossRefGoogle Scholar
- McAllester, D. A. (1980). An outlook on truth maintenance. AI Memo 551, Massachusetts Institute of Technology Artificial Intelligence Laboratory.Google Scholar
- McAllester, D. A. (1990). Truth maintenance. In
*Proceedings of the Eighth National Conference on Artificial Intelligence (AAAI’90)*(pp. 1109–1116).Google Scholar - McGuinness, D. L., Abrahams, M. K., Resnick, L. A., Patel-Schneider, P. F., Thomason, R. H., Cavalli-Sforza, V., & Conati, C. (1994). Classic knowledge representation system tutorial. http://www.bell-labs.com/project/classic/papers/ClassTut/ClassTut.html.
- Nebel, B. (1989). A knowledge level analysis of belief revision. In R. Brachman, H. J. Levesque, & R. Reiter (Eds.),
*Principles of Knowledge Representation and Reasoning: Proceedings of the First International Conference*(pp. 301–311). San Mateo.Google Scholar - Nebel B. (1992). Syntax-based approaches to belief revision. In P. Gärdenfors (Ed.),
*Belief revision*(pp. 52–88). Cambridge University Press.Google Scholar - Nebel, B. (1994). Base revision operations and schemes: Representation, semantics and complexity. In A. G. Cohn (Ed.),
*Proceedings of the Eleventh European Conference on Artificial Intelligence (ECAI’94)*(pp. 341–345). Amsterdam, The Netherlands.Google Scholar - Rott, H. (1998). Just because: Taking belief bases seriously. In S. R. Buss, P. Hájaek, & P. Pudlák (Eds.),
*Logic Colloquium ’98—Proceedings of the 1998 ASL European Summer Meeting*, Vol. 13 of*Lecture Notes in Logic*, pp. 387–408.Google Scholar - Tennant N. (2003) Theory-contraction is NP-complete. Logic Journal of the IGPL 11(6): 675–693CrossRefGoogle Scholar
- Tennant N. (2006) New foundations for a relational theory of theory-revision. Journal of Philosophical Logic 35(5): 489–528CrossRefGoogle Scholar
- Wasserman, R. (2001). Resource-bounded belief revision. Ph.D. thesis, ILLC, University of Amsterdam.Google Scholar
- Williams, M.-A. (1992). Two operators for theory base change. In
*Proceedings of the Fifth Australian Joint Conference on Artificial Intelligence*(pp. 259–265).Google Scholar - Williams, M.-A. (1995). Iterated theory base change: A computational model. In
*Proceedings of Fourteenth International Joint Conference on Artificial Intelligence (IJCAI-95)*(pp. 1541–1549). San Mateo.Google Scholar - Williams, M.-A. (1997). Anytime belief revision. In
*Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence, IJCAI 97*(Vol. 1, pp. 74–81).Google Scholar