🤖 AI Summary
This work addresses a key limitation of traditional credibility-limited belief revision, which treats cognitive inputs as indivisible wholes and thus struggles to handle composite inputs where only parts are realizable. To overcome this, the paper proposes a selective credibility-limited belief revision framework that introduces a source-world-dependent mechanism for selectively accepting input components, transforming them into weaker proxies before performing revision. The framework defines two well-behaved classes of update operators—consistency-preserving and maximally consistency-preserving—and provides both semantic characterizations and axiomatic foundations by integrating proxy transformation functions with credibility-based accessibility relations to model belief dynamics. Theoretical analysis demonstrates that this approach strictly generalizes and unifies the Katsuno-Mendelzon update semantics and existing credibility-limited methods, offering enhanced expressivity and broader applicability.
📝 Abstract
Belief update concerns changes in an agent's beliefs induced by changes in the underlying world. Standard Katsuno-Mendelzon update assumes that an epistemic input can be incorporated from every initially possible world, whereas credibility-limited belief update restricts, for each source world, the successor worlds regarded as credible or reachable. Nevertheless, existing credibility-limited approaches treat the epistemic input as an indivisible whole, and therefore cannot represent cases in which only part of a compound epistemic input can be realized. We introduce selective credibility-limited belief update, in which the epistemic input is transformed, relative to each source world, into a weaker proxy before the credibility-limited transition is performed. We provide semantic and axiomatic characterizations of the resulting class of update operators. We then identify two well-behaved sub-classes; namely, consistency-preserving update operators, which require every transformed epistemic input to be credible from its source world whenever the original epistemic input is consistent, and maximal consistency-preserving update operators, which additionally require the selected proxy to be maximally informative among the credible consequences of the original epistemic input. Finally, we establish the generality of the proposed framework by showing that credibility-limited belief update is recovered as a special case, while Katsuno--Mendelzon belief update emerges when credibility restrictions are removed and the transformation functions are taken to be identities. These results demonstrate that the framework provides a unified and strictly more expressive account of belief update, encompassing established approaches while supporting source-dependent selective acceptance.