Abstract
All formal models of belief change involve choices between different ways to accommodate new information. However, the models differ in their loci of choice, i.e. in what formal entities the choice mechanism is applied to. Four models of belief change with different loci of choice are investigated in terms of how they satisfy a set of important properties of belief contraction and revision. It is concluded that the locus of epistemic choice has a large impact on the properties of the resulting belief change operation.
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Notes
- 1.
See [12] for a proof that Finite-based contraction does not hold. The proof that Finite-based revision does not hold has not been published, and is therefore given here: Let S be an infinite set of logical atoms in the language, let p be another such atom, and let K = Cn({¬p}). Then {¬p ∨ s∣s ∈ S} is a subset of K that does not imply ¬p. It follows from compactness and the axiom of choice that there is some X such that {¬p ∨ s∣s ∈ S} ⊆ X ∈ K⊥¬p [1]. Let γ be a selection function such that γ(K⊥¬p) = {X} and let ∗ be the revision based on γ. Then {¬p ∨ s∣s ∈ S}∪{p} ⊆ K ∗ p, and since K ∗ p is logically closed we have S ⊆ K ∗ p and consequently K ∗ p is not finite-based.
- 2.
- 3.
Provided that the language has an infinite number of non-equivalent sentences. For a proof, see [12].
- 4.
More precisely: if there is more than one top candidate and the top candidates are all p-remainders for some sentence p, then their intersection is not itself a top candidate.
- 5.
In the limiting case when the outcome set contains no element that satisfies the descriptor, nothing is changed, i.e. the original belief set is the outcome of the operation.
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Hansson, S.O. (2018). Belief Change. In: Hansson, S., Hendricks, V. (eds) Introduction to Formal Philosophy. Springer Undergraduate Texts in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-77434-3_20
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