Belief Change without Compactness
DOI:
https://doi.org/10.19153/cleiej.24.1.4Keywords:
Belief Revision, Belief Update, Comapctness, Non-Monotonic ReasoningAbstract
Dealing with dynamics is a vital problem in Artificial Intelligence (AI). An intelligent system should be able to perceive and interact with its environment to perform its tasks satisfactorily. To do so, it must sense external actions that might interfere with its tasks, demanding the agent to self-adapt to the environment dynamics. In AI, the field that studies how a rational agent should change its knowledge in order to respond to a new piece of information is known as Belief Change. It assumes that an agent’s knowledge is specified in an underlying logic that satisfies some properties including compactness: if an information is entailed by a set X of formulae, then this information should also be entailed by a finite subset of X. Several logics with applications in AI, however, do not respect this property. This is the case of many temporal logics such as LTL and CTL. Extending Belief Change to these logics would provide ways to devise self-adaptive intelligent systems that could respond to change in real time. This is a big challenge in AI areas such as planning, and reasoning with sensing actions. Extending belief change beyond the classical spectrum has been shown to be a tough challenge, and existing approaches usually put some constraints upon the system, which are either too restrictive or dispense some of the so desired rational behaviour an intelligent system should present. This is a summary of the thesis “Belief Change without Compactness” by Jandson S Ribeiro. The thesis extends Belief Change to accommodate non-compact logics, keeping the rationality criteria and without imposing extra constraints. We provide complete new semantic perspectives for Belief Change by extending to non-compact logics its three main pillars: the AGM paradigm, the KM paradigm and Non-monotonic Reasoning.
References
E. M. Clarke, O. Grumberg, and D. A. Peled, Model checking. MIT Press, 2001.
P. G ?ardenfors, Knowledge in flux: Modeling the dynamics of epistemic states. The MIT press, 1988.
C.E.Alchourr ?on,P.G ?ardenfors,andD.Makinson,“Onthelogicoftheorychange:Partialmeet contraction and revision functions,” The Journal of Symbolic Logic, vol. 50, no. 2, pp. 510–530, 1985.
H. Rott, “Preferential belief change using generalized epistemic entrenchment,” Journal of Logic, Lan- guage and Information, vol. 1, no. 1, pp. 45–78, 1992.
S. O. Hansson, A Textbook of Belief Dynamics: Theory Change and Database Updating. Kluwer Aca- demic, 1999, vol. 11.
H. Katsuno and A. O. Mendelzon, “On the difference between updating a knowledge base and revising it,” in Belief revision, P. G ?ardenfors, Ed., Cambridge University Press, 2003, pp. 183–203.
F. Baader, D. Calvanese, D. McGuinness, P. Patel-Schneider, and D. Nardi, The description logic handbook: Theory, implementation and applications. Cambridge university press, 2003.
A. Horn, “On sentences which are true of direct unions of algebras,” The Journal of Symbolic Logic, vol. 16, no. 1, pp. 14–21, 1951.
D. M. Gabbay, I. Hodkinson, and M. Reynolds, Temporal Logic (Vol. 1): Mathematical Foundations and Computational Aspects. New York, NY, USA: Oxford University Press, Inc., 1994, isbn: 0-19-853769-7.
C.Baral,T.Eiter,M.Bj ?areland,andM.Nakamura,“Maintenancegoalsofagentsinadynamic environment: Formulation and policy construction,” Artif. Intell., vol. 172, no. 12-13, pp. 1429–1469, 2008.
Y. Zhang and Y. Ding, “CTL model update for system modifications,” Journal of Artificial Intelligence Research, vol. 31, pp. 113–155, 2008.
M. J. Fischer and R. E. Ladner, “Propositional dynamic logic of regular programs,” Journal of computer and system sciences, vol. 18, no. 2, pp. 194–211, 1979.
M. M. Ribeiro, R. Wassermann, G. Flouris, and G. Antoniou, “Minimal change: Relevance and recovery revisited,” Artificial Intelligence, vol. 201, pp. 59–80, 2013.
P. T. Guerra and R. Wassermann, “On the uncomputability of partial meet contraction for linear-time temporal logic,” South American Journal of Logic, vol. 4, pp. 385–406, 2018.
J. S. Ribeiro, A. Nayak, and R. Wassermann, “Towards belief contraction without compactness,” in Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, KR 2018, 2018, pp. 287–296.
J. S. Ribeiro, A. Nayak, and R. Wassermann, “Belief change and non-monotonic reasoning sans compactness,” in The Thirty-Third AAAI Conference on Artificial Intelligence, AAAI 2019, 2019, pp. 3019–3026.
J. S. Ribeiro, A. Nayak, and R. Wassermann, “Belief update without compactness in non-finitary languages,” in Proceedings of the Twenty- Eighth International Joint Conference on Artificial Intelligence, IJCAI 2019, 2019, pp. 1858–1864.
G. Flouris, “On belief change and ontology evolution,” Ph.D. dissertation, University of Crete, 2006.
M. M. Ribeiro, Belief revision in non-classical logics. Springer Science & Business Media, 2013.
D. Lewis, Counterfactuals. Oxford, 1976.
P. G ?ardenfors and D. Makinson, “Nonmonotonic inference based on expectations,” Artificial Intelli- gence, vol. 65, no. 2, pp. 197–245, 1994.
T. A. Meyer, W. A. Labuschagne, and J. Heidema, “Refined epistemic entrenchment,” Journal of Logic, Language and Information, vol. 9, no. 2, pp. 237–259, 2000.
M. L. Ginsberg, “Counterfactuals,” Artif. Intell., vol. 30, no. 1, pp. 35–79, 1986.
D. J. Lehmann and M. Magidor, “What does a conditional knowledge base entail?” Artif. Intell.,
vol. 55, no. 1, pp. 1–60, 1992.
A. Grove, “Two modellings for theory change,” Journal of philosophical logic, vol. 17, no. 2, pp. 157– 170, 1988.
S. Lindstr ?om and W. Rabinowicz, “Epistemic entrenchment with incomparabilities and relational belief revision,” in The logic of theory change, Springer, 1991, pp. 93–126.
D. Makinson and P. G ?ardenfors, “Relations between the logic of theory change and nonmonotonic logic,” in The logic of theory change, Springer, 1991, pp. 183–205.
P. Peppas, “Belief revision,” in Handbook of Knowledge Representation, 2008, pp. 317–359.
D. Zhang and N. Y. Foo, “Infinitary belief revision,” J. Philosophical Logic, vol. 30, no. 6, pp. 525–570, 2001.
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Jandson S Ribeiro
This work is licensed under a Creative Commons Attribution 4.0 International License.
CLEIej is supported by its home institution, CLEI, and by the contribution of the Latin American and international researchers community, and it does not apply any author charges whatsoever for submitting and publishing. Since its creation in 1998, all contents are made publicly accesibly. The current license being applied is a (CC)-BY license (effective October 2015; between 2011 and 2015 a (CC)-BY-NC license was used).
