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Notes
- 1.
The following review is mainly based on Arora and Barak [14], which is also recommended for further reference.
- 2.
Katsuno and Mendelzon [75] have argued for distinguishing between belief updates and belief revisions. Their argument, however, depends on not explicitly expressing the time for which a statement is held true. We assume, therefore, that belief revisions subsume updates.
- 3.
Winslett [118] introduces this phrase to characterise various kinds of intersection operations among potentially conflicting sentences and sets of sentences.
- 4.
- 5.
For simplicity, we work with propositional formulas and leave corresponding theory-elements implicit. Note that the propositional logical form of these formulas can be obtained by aptly chosen substantial laws. For example, the substantial law ∀x(P(x) ∨ Q(x)) yields a formula of the form p ∨ q when applied to whatever intended applications. To be more precise: any application of this law is given by a structure 〈D, P, Q〉. If the sets P and Q of such a structure are empty, applying the law ∀x(P(x) ∨ Q(x)) to this structure yields the claim that P(a) ∨ Q(a), where D = {a}.
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Andreas, H. (2020). Truth Maintenance. In: Dynamic Tractable Reasoning. Synthese Library, vol 420. Springer, Cham. https://doi.org/10.1007/978-3-030-36233-1_7
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