[en] Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we investigate the integration of the two formalisms by studying belief change for a (preferential) non-monotonic framework. We show that the standard AGM approach to be- lief change can be transferred to a preferential non-monotonic framework in the sense that change operations can be defined on conditional knowledge bases. We take as a point of depar- ture the results presented by Casini and Meyer (2017), and we develop and extend such results with characterisations based on semantics and entrenchment relations, showing how some of the constructions defined for propositional logic can be lifted to our preferential non-monotonic framework.
Disciplines :
Computer science
Author, co-author :
Casini, Giovanni ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
Ferme, Eduardo; Universidade da Madeira > NOVA-LINCS > Associate Professor
Meyer, Thomas; University of Cape Town > Computer Science > Full Professor
Alchourrón, C.; Gärdenfors, P.; and Makinson, D. 1985. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50:510–530.
Booth, R., and Paris, J. 1998. A note on the rational closure of knowledge bases with both positive and negative knowledge. Journal of Logic, Lang. and Inform. 7(2):165–190.
Britz, K.; Heidema, J.; and Meyer, T. 2008. Semantic preferential subsumption. In Lang, J., and Brewka, G., eds., Proceedings of the 11th International Conference on Principles of Knowledge Representation and Reasoning, KR 2008, 476–484. AAAI Press/MIT Press.
Britz, K.; Meyer, T.; and Varzinczak, I. 2011. Semantic foundation for preferential Description Logics. In Wang, D., and Reynolds, M., eds., Proceedings of the 24th Australasian Joint Conference on Artificial Intelligence, number 7106 in LNAI, 491–500. Springer.
Casini, G., and Meyer, T. 2016. Using defeasible information to obtain coherence. In Proceedings of the 15th International Conference on Principles of Knowledge Representation and Reasoning, KR 2016, 537–540.
Casini, G., and Meyer, T. 2017. Belief change in a preferential non-monotonic framework. In Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI-17, 929–935.
Casini, G., and Straccia, U. 2010. Rational closure for defeasible Description Logics. In Janhunen, T., and Niemelä, I., eds., Proceedings of the 12th European Conference on Logics in Artificial Intelligence (JELIA), number 6341 in LNCS, 77–90. Springer-Verlag.
Casini, G., and Straccia, U. 2013. Defeasible inheritance-based Description Logics. J. Artif. Intell. Res. (JAIR) 48:415–473.
Casini, G.; Meyer, T.; Moodley, K.; and Nortjé, R. 2014. Relevant closure: A new form of defeasible reasoning for description logics. In Fermé, E., and Leite, J., eds., Logics in Artificial Intelligence, 92–106. Springer International Publishing.
Delgrande, J.; Schaub, T.; Tompits, H.; and Woltran, S. 2013. A model-theoretic approach to belief change in answer set programming. ACM Trans. Comput. Logic 14(2):1–46.
Fermé, E. 1999. Revising the AGM postulates. Ph.D. Dissertation, University of Buenos Aires.
Gärdenfors, P., and Makinson, D. 1988. Revisions of knowledge systems using epistemic entrenchment. In Proceedings of the 2nd Conference on Theoretical Aspects of Reasoning About Knowledge, TARK’88, 83–95. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc.
Gärdenfors, P. 1988. Knowledge in Flux: Modeling the Dynamics of Epistemic States. MIT Press.
Giordano, L.; Gliozzi, V.; Olivetti, N.; and Pozzato, G. L. 2013. A non-monotonic Description Logic for reasoning about typicality. Artif. Intell. 195:165–202.
Giordano, L.; Gliozzi, V.; Olivetti, N.; and Pozzato, G. L. 2015. Semantic characterization of rational closure: From propositional logic to Description Logics. Artif. Intell. J. 226:1–33.
Grove, A. 1988. Two modellings for theory change. Journal of Philosophical Logic 17:157–170.
Hansson, S. 1999. A Textbook of Belief Dynamics: Theory Change and Database Updating. Kluwer Academic Publishers.
Hunter, A. 2016. Nearly counterfactual revision. In Khoury, R., and Drummond, C., eds., Advances in Artificial Intelligence: 29th Canadian Conference on Artificial Intelligence, Canadian AI 2016, Victoria, BC, Canada, May 31 - June 3, 2016. Proceedings. Cham: Springer International Publishing. 263–269.
Katsuno, H., and Mendelzon, A. 1991. Propositional knowledge base revision and minimal change. Artificial Intelligence 3(52):263–294.
Kern-Isberner, G. 1999. Postulates for conditional belief revision. In Proceedings of the 16th International Joint Conference on Artifical Intelligence - Volume 1, IJCAI’99, 186–191. San Francisco, CA, USA: Morgan Kaufmann Publ.
Kraus, S.; Lehmann, D.; and Magidor, M. 1990. Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44:167–207.
Lehmann, D., and Magidor, M. 1992. What does a conditional knowledge base entail? Artif. Intell. 55:1–60.
Lehmann, D. 1995. Another perspective on default reasoning. Annals of Mathematics and Artificial Intelligence 15(1):61–82.
Levi, I. 1977. Subjunctives, dispositions and chances. Syn-these 34:423–455.
Lukasiewicz, T. 2008. Expressive probabilistic Description Logics. Artif. Intell. 172(6-7):852–883.
Makinson, D. 1993. Five faces of minimality. Studia Logica 52:339–379.
Qi, G., and Hunter, A. 2007. Measuring incoherence in Description Logic-based ontologies. In The Semantic Web, volume 4825 of LNCS. Springer. 381–394.
Rott, H. 1991. Two methods of constructing contractions and revisions of knowledge systems. J. of Phil. Logic 20:149–173.
Wobcke, W. 1995. Belief revision, conditional logic and nonmonotonic reasoning. Notre Dame J. Formal Logic 36(1):55–102.
