Modellings for belief change: Prioritization and entrenchment*

<span title="2008-06-28">2008</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="" style="color: black;">Theoria</a> </i> &nbsp;
I should like to thank Ulf Friedrichsdorf, Sven Ove Hansson, David Pearce, and an anonymous referee for clarifying discussions and comments. A preliminary version of this paper reporting on the very special case of belief bases without prioritization appeared under the title 'Modellings for belief change: Base contraction, multiple contraction, and epistemic entrenchment (Preliminary report)' in the Proceedings J ELI A '92, 3rd European Workshop on Logics in A I, Berlin, September 7-10, 1992,
more &raquo; ... ringer LNAI series 633, pp. 139-153. 2 Specializing -< to C, we get a method which is applied by Veltman [29] and Kratzer [13] for the analysis of counterfactuals, and by Poole [22] for nonmonotonic reasoning. For more connections with the latter area of research, see Ncbel [21]. 4 Andre Fuhrmann [5] was probably the first to study pick and bunch contractions. He called them choice and meet contractions. For danger of confusion with maxichoice and (full, partial) meet contraction, we introduce new names. 5 We note some special cases for -< = C. For theories K and sentences 0 and i/f such that at least one of 0 and y/ is in K, K 1 (0 V y/) C K l[0,y/]. For the proof of this and related things, the following fact is relevant: For every theory K, every K' e KL0 e K\ by y/->0 e K [theory!] and maximality) and (ii) 0->y/ 6 K' (Proof: since K' \r 0, we get A" ^(0-1//)-0, so K U {-+yf} tf 0, so 0--y/€ K\ by 0->y eK [theory!] and maximality). However, in general A±[0,y/| (ZAT1 (0 V y/) even if A" is a theory; consider K -Cn({p,q}), for which K ±-[p,q] = {Cn(p V q), Cn(p~q)} t but K 1 (p V q) = {Cn(p~q)}. And HL (0 V y/) C HI [0,y] breaks down for non-theories //; just consider H = {p,q,p V q}, for which HI (p V q) -{0 J and HI \p,q\ = {{pvq}}. * This example disproves a claim of Nebel [21, p. 56]. A similar counterexample has independently been provided by Wcydert [30, p. 131]. 9 The importance of the maximizing property has been stressed repeatedly in the work of Sven Ovc Hansson.-If base contractions arc supplemented by a recovery-guaranteeing appendage (sec Section 6.2.2 below) and if everything is Unite, prioritization is formally superfluous. It is shown in [28, Theorem 7] that then every prioritized base contraction can be simulated by a suitably chosen unprioritized belief base. But the simple bases to be used are grossly unintuitive.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1111/j.1755-2567.1992.tb01154.x</a> <a target="_blank" rel="external noopener" href="">fatcat:gn47gjdpd5dhrcne5lxhwviywe</a> </span>
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