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2019 | OriginalPaper | Chapter

Belief Change Properties of Forgetting Operations over Ranking Functions

Authors : Gabriele Kern-Isberner, Tanja Bock, Kai Sauerwald, Christoph Beierle

Published in: PRICAI 2019: Trends in Artificial Intelligence

Publisher: Springer International Publishing

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Abstract

Intentional forgetting means to deliberately give up information and is a crucial part of change or consolidation processes, or to make knowledge more compact. Two well-known forgetting operations are contraction in the AGM theory of belief change, and various types of variable elimination in logic programming. While previous work dealt with postulates being inspired from logic programming, in this paper we focus on evaluating forgetting in epistemic states according to postulates coming from AGM belief change theory. We consider different forms of contraction, marginalization, and conditionalization as major representatives of forgetting operators to be evaluated. We use Spohn’s ranking functions as a common semantic base to show that all operations can be realized in one logical framework, thereby exploring the richness of forgetting operations in a comparable way.

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Literature
1.
go back to reference Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symb. Logic 50(2), 510–530 (1985)MathSciNetCrossRef Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symb. Logic 50(2), 510–530 (1985)MathSciNetCrossRef
2.
go back to reference Beierle, C., Kern-Isberner, G., Sauerwald, K., Bock, T., Ragni, M.: Towards a general framework for kinds of forgetting in common-sense belief management. KI - Künstliche Intelligenz 33(1), 57–68 (2019)CrossRef Beierle, C., Kern-Isberner, G., Sauerwald, K., Bock, T., Ragni, M.: Towards a general framework for kinds of forgetting in common-sense belief management. KI - Künstliche Intelligenz 33(1), 57–68 (2019)CrossRef
3.
go back to reference Caridroit, T., Konieczny, S., Marquis, P.: Contraction in propositional logic. Int. J. Approx. Reason. 80, 428–442 (2017)MathSciNetCrossRef Caridroit, T., Konieczny, S., Marquis, P.: Contraction in propositional logic. Int. J. Approx. Reason. 80, 428–442 (2017)MathSciNetCrossRef
4.
go back to reference Chopra, S., Ghose, A., Meyer, T.A., Wong, K.-S.: Iterated belief change and the recovery axiom. J. Philos. Logic 37(5), 501–520 (2008)MathSciNetCrossRef Chopra, S., Ghose, A., Meyer, T.A., Wong, K.-S.: Iterated belief change and the recovery axiom. J. Philos. Logic 37(5), 501–520 (2008)MathSciNetCrossRef
5.
go back to reference de Finetti, B.: La prévision, ses lois logiques et ses sources subjectives. Ann. Inst. H. Poincaré 7(1), 1–68 (1937). Engl. transl. Theory Probab. J. (1974). Wiley de Finetti, B.: La prévision, ses lois logiques et ses sources subjectives. Ann. Inst. H. Poincaré 7(1), 1–68 (1937). Engl. transl. Theory Probab. J. (1974). Wiley
6.
go back to reference Eiter, T., Fink, M., Sabbatini, G., Tompits, H.: On updates of logic programs: semantics and properties. Technical report, TU Vienna (2001) Eiter, T., Fink, M., Sabbatini, G., Tompits, H.: On updates of logic programs: semantics and properties. Technical report, TU Vienna (2001)
7.
go back to reference Eiter, T., Kern-Isberner, G.: A brief survey on forgetting from a knowledge representation and reasoning perspective. KI 33(1), 9–33 (2019) Eiter, T., Kern-Isberner, G.: A brief survey on forgetting from a knowledge representation and reasoning perspective. KI 33(1), 9–33 (2019)
9.
go back to reference Goldszmidt, M., Pearl, J.: Qualitative probabilities for default reasoning, belief revision, and causal modeling. Artif. Intell. 84, 57–112 (1996)MathSciNetCrossRef Goldszmidt, M., Pearl, J.: Qualitative probabilities for default reasoning, belief revision, and causal modeling. Artif. Intell. 84, 57–112 (1996)MathSciNetCrossRef
10.
go back to reference Gonçalves, R., Knorr, M., Leite, J.: The ultimate guide to forgetting in answer set programming. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference, KR 2016, pp. 135–144. AAAI Press (2016) Gonçalves, R., Knorr, M., Leite, J.: The ultimate guide to forgetting in answer set programming. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference, KR 2016, pp. 135–144. AAAI Press (2016)
11.
go back to reference Katsuno, H., Mendelzon, A.: Propositional knowledge base revision and minimal change. Artif. Intell. 52, 263–294 (1991)MathSciNetCrossRef Katsuno, H., Mendelzon, A.: Propositional knowledge base revision and minimal change. Artif. Intell. 52, 263–294 (1991)MathSciNetCrossRef
12.
go back to reference Kern-Isberner, G., Bock, T., Beierle, C., Sauerwald, K.: Axiomatic evaluation of epistemic forgetting operators. In: Proceedings of the 32nd International FLAIRS Conference, FLAIRS-32, pp. 470–475. AAAI Press (2019) Kern-Isberner, G., Bock, T., Beierle, C., Sauerwald, K.: Axiomatic evaluation of epistemic forgetting operators. In: Proceedings of the 32nd International FLAIRS Conference, FLAIRS-32, pp. 470–475. AAAI Press (2019)
13.
go back to reference Kern-Isberner, G., Bock, T., Sauerwald, K., Beierle, C.: Iterated contraction of propositions and conditionals under the principle of conditional preservation. In: 3rd Global Conference on Artificial Intelligence, GCAI 2017. EPiC Series in Computing, vol. 50, pp. 78–92. EasyChair (2017) Kern-Isberner, G., Bock, T., Sauerwald, K., Beierle, C.: Iterated contraction of propositions and conditionals under the principle of conditional preservation. In: 3rd Global Conference on Artificial Intelligence, GCAI 2017. EPiC Series in Computing, vol. 50, pp. 78–92. EasyChair (2017)
14.
15.
go back to reference Saribatur, Z.G., Eiter, T.: Omission-based abstraction for answer set programs. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, KR 2018, pp. 42–51. AAAI Press (2018) Saribatur, Z.G., Eiter, T.: Omission-based abstraction for answer set programs. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, KR 2018, pp. 42–51. AAAI Press (2018)
16.
go back to reference Spohn, W.: Ordinal conditional functions: a dynamic theory of epistemic states. In: Harper, W.L., Skyrms, B. (eds.) Causation in Decision, Belief Change, and Statistics, II, pp. 105–134. Kluwer Academic Publishers (1988) Spohn, W.: Ordinal conditional functions: a dynamic theory of epistemic states. In: Harper, W.L., Skyrms, B. (eds.) Causation in Decision, Belief Change, and Statistics, II, pp. 105–134. Kluwer Academic Publishers (1988)
17.
go back to reference Spohn, W.: The Laws of Belief: Ranking Theory and Its Philosophical Applications. Oxford University Press, Oxford (2012)CrossRef Spohn, W.: The Laws of Belief: Ranking Theory and Its Philosophical Applications. Oxford University Press, Oxford (2012)CrossRef
Metadata
Title
Belief Change Properties of Forgetting Operations over Ranking Functions
Authors
Gabriele Kern-Isberner
Tanja Bock
Kai Sauerwald
Christoph Beierle
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-030-29908-8_37

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