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Published in:
A Logical Framework for Graded Predicates Read chapter Read first chapter

2017 | OriginalPaper | Chapter

On Subtler Belief Revision Policies

Author : Fernando R. Velázquez-Quesada

Published in: Logic, Rationality, and Interaction

Publisher: Springer Berlin Heidelberg

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Abstract

This paper proposes three subtle revision policies that are not propositionally successful (after a single application the agent might not believe the given propositional formula), but nevertheless are not propositionally idempotent (further applications might affect the agent’s epistemic state). It also compares them with two well-known revision policies, arguing that the subtle ones might provide a more faithful representation of humans’ real-life revision processes.

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previous chapter Conditional Doxastic Logic with Oughts and Concurrent Upgrades
next chapter Topo-Logic as a Dynamic-Epistemic Logic
Footnotes
1
Still, there are proposals rejecting the postulate. In Sect. 3 the reader can find some of them and their relationship with this manuscript’s contents.
 
2
In [14] the plausibility relation is also conversely well-founded, forbidding infinite strictly ascending \(\le \)-chains. Here the domain is finite, so this requirement is satisfied automatically.
 
3
Formally, \(\mathopen {\varvec{\langle \!\!\!\,\,\langle }}\pi \mathclose {\varvec{\rangle \!\!\!\,\,\rangle }}^{M}_{w} := \mathopen {\{} {u \in W \mid (w,u) \in \mathopen {\varvec{\langle \!\!\!\,\,\langle }}\pi \mathclose {\varvec{\rangle \!\!\!\,\,\rangle }}^{M}} \mathclose {\}}\).
 
4
With \({\text {Mx}}^{k}(W) := \bigcup _{i=0}^{k} {\text {L}}_{i}(W)\). This is the plausibility-order-is-total version of the standard definition.
 
5
In particular, it can characterise all layers of any https://static-content.springer.com/image/chp%3A10.1007%2F978-3-662-55665-8_22/438306_1_En_22_IEq109_HTML.gif .
 
6
For success, Moorean phenomena [29] might appear. For idempotence, the \(\mathcal {L}\)-formula \(\mathop {[{\scriptstyle \varvec{>}}]} \bot \) characterises the bottommost elements of the ordering; thus, if the initial ordering is not flat (not all worlds equally plausible), each \(\mathop {[{\scriptstyle \varvec{>}}]} \bot \)-revision will move to the top different worlds.
 
7
Thus, https://static-content.springer.com/image/chp%3A10.1007%2F978-3-662-55665-8_22/438306_1_En_22_IEq221_HTML.gif is such that https://static-content.springer.com/image/chp%3A10.1007%2F978-3-662-55665-8_22/438306_1_En_22_IEq222_HTML.gif .
 
8
This relies on the fact that \(\chi \) is propositional: the set of \(\chi \)-worlds does not change.
 
9
If \({\text {lay}}^{\chi }_{\curlyvee } - {\text {lay}}^{\lnot \chi }_{\curlywedge } < 0\), then there is already a strong belief on \(\chi \) at M, and any \(m \ge 0\) works.
 
10
Thus, https://static-content.springer.com/image/chp%3A10.1007%2F978-3-662-55665-8_22/438306_1_En_22_IEq280_HTML.gif is such that https://static-content.springer.com/image/chp%3A10.1007%2F978-3-662-55665-8_22/438306_1_En_22_IEq281_HTML.gif .
 
11
Thus, https://static-content.springer.com/image/chp%3A10.1007%2F978-3-662-55665-8_22/438306_1_En_22_IEq320_HTML.gif is such that https://static-content.springer.com/image/chp%3A10.1007%2F978-3-662-55665-8_22/438306_1_En_22_IEq321_HTML.gif .
 
12
If \({\text {lay}}^{\chi }_{\curlywedge } - {\text {lay}}^{\lnot \chi }_{\curlywedge } < 0\), then there is already a belief on \(\chi \) at M, and any \(m \ge 0\) works.
 
13
Some forms of propaganda are based on this.
 
14
Still, the axiom system for the general layered upgrade already provides a syntactic (albeit indirect) characterisation of the presented policies.
 
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Metadata
Title
On Subtler Belief Revision Policies
Author
Fernando R. Velázquez-Quesada
Copyright Year
2017
Publisher
Springer Berlin Heidelberg
Book
Logic, Rationality, and Interaction

Print ISBN: 978-3-662-55664-1

Electronic ISBN: 978-3-662-55665-8

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-662-55665-8_22

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