Abstract
Similarity among worlds plays a pivotal role in providing the semantics for different kinds of belief change. Although similarity is, intuitively, a context-sensitive concept, the accounts of similarity presently proposed are, by and large, context blind. We propose an account of similarity that is context sensitive, and when belief change is concerned, we take it that the epistemic input provides the required context. We accordingly develop and examine two accounts of probabilistic belief change that are based on such evidence-sensitive similarity. The first switches between two extreme behaviors depending on whether or not the evidence in question is consistent with the current knowledge. The second gracefully changes its behavior depending on the degree to which the evidence is consistent with current knowledge. Finally, we analyze these two belief change operators with respect to a select set of plausible postulates.
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Notes
- 1.
In general, we write \(B^*_\alpha \) to mean the (the result of) revision of B with \(\alpha \) by application of operator \(*\).
- 2.
Similar axioms of distance have been adopted in mathematics and psychology for a long time.
- 3.
The term separability has been defined differently by different authors.
- 4.
Other interpretations of expansion in the probabilistic setting may be considered in the future.
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Acknowledgements
Gavin Rens was supported by a Clause Leon Foundation postdoctoral fellowship while conducting this research. This research has been partially supported by the Australian Research Council (ARC), Discovery Project: DP150104133. This work is based on research supported in part by the National Research Foundation of South Africa (Grant number UID 98019). Thomas Meyer has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agr. No. 690974.
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Rens, G., Meyer, T., Kern-Isberner, G., Nayak, A. (2018). Probabilistic Belief Revision via Similarity of Worlds Modulo Evidence. In: Trollmann, F., Turhan, AY. (eds) KI 2018: Advances in Artificial Intelligence. KI 2018. Lecture Notes in Computer Science(), vol 11117. Springer, Cham. https://doi.org/10.1007/978-3-030-00111-7_29
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