Abstract
In probabilistic accounts of belief change, traditionally Bayesian conditioning is employed when the received information is consistent with the current knowledge, and imaging is used otherwise. It is well recognised that imaging can be used even if the received information is consistent with the current knowledge. Imaging assumes, inter alia, a relational measure of similarity among worlds. In a recent work, Rens and Meyer have argued that when, in light of new evidence, we no longer consider a world \(\omega \) to be a serious possibility, worlds more similar to it should be considered relatively less plausible, and hence more dissimilar (distant) a world is from \(\omega \), the larger should be its share in the original probability mass of \(\omega \). In this paper we argue that this approach leads to results that revolt against our causal intuition, and propose a converse account where a larger share of \(\omega \)’s mass move to worlds that are more similar (closer) to it instead.
This research has been partially supported by the Australian Research Council (ARC), Discovery Project: DP150104133.
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Notes
- 1.
Assuming such a unique closest world exists. Short of it, an appropriate distribution mechanism should be employed.
- 2.
Recall the standard refrain of the politicians, I don’t answer hypothetical questions.
- 3.
The distance between different A-worlds, or between different \(\overline{A}\)-worlds is not shown since they will not be used in the calculation.
- 4.
The more distant/different a world is from a target world, the higher is its relative weight.
- 5.
We need not worry about adding the new probabilities of relevant \(\overline{A}\)-worlds since they are all zero.
- 6.
Arguably the use of similarity in common parlance is non-symmetric. For instance, if John is non-violent, we would say John is like Gandhi. But saying Gandhi is like John would mean a very different thing. Capturing such asymmetry in our simple framework may not be quite feasible.
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Mishra, S., Nayak, A. (2016). Causal Basis for Probabilistic Belief Change: Distance vs. Closeness. In: Sombattheera, C., Stolzenburg, F., Lin, F., Nayak, A. (eds) Multi-disciplinary Trends in Artificial Intelligence. MIWAI 2016. Lecture Notes in Computer Science(), vol 10053. Springer, Cham. https://doi.org/10.1007/978-3-319-49397-8_10
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