Deductive belief change. (English) Zbl 07730286
Summary: In a 2003-article, Sven Ove Hansson discusses the justificatory structure of a belief base, by highlighting that some beliefs of the belief base are held only because they are (deductively) justified by some other beliefs. He concludes that the relation between the justificatory structure of a belief base and the vulnerability of its beliefs (which in turn reflects their resistance to change) remains an open issue, both on a conceptual and on a technical level. Motivated by Hanssons’ remarks, we introduce in this article a new interesting type of change-operation, called deductive belief change (contraction and revision), and abbreviated as DBC. DBC associates in a natural manner the deductive justification that the logical sentences of the language have, in the context of a belief base \(B\), with their vulnerability relative to \(B\). According to DBC, the more explicit \(B\)-beliefs imply a sentence \(\varphi\), the more resistant to change \(\varphi\) is, with respect to \(B\). We characterize DBC both axiomatically, in terms of natural postulates, and constructively, in terms of kernel belief change, illustrating its simple and intuitive structure. Interestingly enough, as we prove, kernel belief change (and its central specialization partial-meet belief change) already encodes a strong coupling between justificatory structure and vulnerability, as it implements DBC. Furthermore, we show that deductive belief revision, properly adapted to the belief-sets realm, is indistinguishable from Parikh’s relevance-sensitive revision, a fundamental type of revision which, due to its favourable properties, constitutes a promising candidate for a variety of real-world applications. As a last contribution, we study relevance in the context of belief bases, and prove that kernel belief change respects Parikh’s notion of relevance.
MSC:
| 03B42 | Logics of knowledge and belief (including belief change) |
| 68T27 | Logic in artificial intelligence |
| 68T30 | Knowledge representation |
Keywords:
deductive justification; vulnerability; kernel belief change; relevance; knowledge representationReferences:
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