2018
DOI: 10.1007/s11225-018-9812-x
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Truth-Tracking by Belief Revision

Abstract: Abstract.We study the learning power of iterated belief revision methods. Successful learning is understood as convergence to correct, i.e., true, beliefs. We focus on the issue of universality: whether or not a particular belief revision method is able to learn everything that in principle is learnable. We provide a general framework for interpreting belief revision policies as learning methods. We focus on three popular cases: conditioning, lexicographic revision, and minimal revision. Our main result is tha… Show more

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Cited by 9 publications
(11 citation statements)
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References 28 publications
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“…This special case is a topological translation of one of our previous results[3,4]. However, the result about problemsolving universality is not only new and much more general, but also much harder to prove, involving new topological notions and results 2.…”
mentioning
confidence: 57%
See 1 more Smart Citation
“…This special case is a topological translation of one of our previous results[3,4]. However, the result about problemsolving universality is not only new and much more general, but also much harder to prove, involving new topological notions and results 2.…”
mentioning
confidence: 57%
“…However, there does exist a line of research that combines belief revision with learning-theoretic notions, line pursued by Kelly [21,26], Kelly, Schulte and Hendricks [19], Martin and Osherson [28] and ourselves [13,3,4,14]. In this paper we continue this research program, using topological characterizations and methods.…”
Section: Introductionmentioning
confidence: 99%
“…Instead, it may eventually allow her to come to believe the true probability (at least, with a high degree of accuracy). This belief may even stabilize, to such a degree that it approaches the 'softer', defeasible notion of 'knowledge', which is the main focus in Epistemology (Lehrer 1990;Stalnaker 1996;Rott 2004) and (inductive) Learning Theory (Gold 1967;Baltag et al 2019a). This convergence in belief and the resulting acquisition of statistical knowledge is what we aim to capture in this paper.…”
Section: Introductionmentioning
confidence: 87%
“…Connections to belief revision theory Grove sphere models (in non-probabilistic form, consisting of possible worlds instead of distributions) form the standard semantic framework in Belief Revision Theory (Grove 1988). Plausibility models (again, in their non-probabilistic version) are well-known equivalent relational descriptions of sphere models, that are preferred in Dynamic Epistemic Logic (Baltag and Smets 2008a, b;Baltag et al 2019a;van Benthem 2007van Benthem , 2011, as well as in the "dynamic interactive epistemology" approach developed by game-theorists (Board 2004). These are in fact adaptations to doxastic modeling of the older setting of Lewis spheres, with its equivalent description in terms of a comparative similarity relation (Lewis 2000).…”
Section: Probabilistic Plausibility Modelsmentioning
confidence: 99%
“…This is not the first application of learning theoretic tools to dynamic epistemic logic (see [13][14][15][16]) or to the logical theories of belief revision (see, e.g. [4,5,19]). The present work is however pioneering in studying the learning of the internal structure of actions in dynamic epistemic logic.…”
Section: Learning Action Modelsmentioning
confidence: 99%