Several forms of iterable belief change exist, differing in the kind of change and its strength: some operators introduce formulae, others remove them; some add formulae unconditionally, others only as additions to the previous beliefs; some only relative to the current situation, others in all possible cases. A sequence of changes may involve several of them: for example, the first step is a revision, the second a contraction and the third a refinement of the previous beliefs. The ten operators considered in this article are shown to be all reducible to three: lexicographic revision, refinement and severe withdrawal. In turn, these three can be expressed in terms of lexicographic revision at the cost of restructuring the sequence. This restructuring needs not to be done explicitly: an algorithm that works on the original sequence is shown. The complexity of mixed sequences of belief change operators is also analyzed. Most of them require only a polynomial number of calls to a satisfiability checker, some are even easier.

Mixed Iterated Revisions: Rationale, Algorithms, and Complexity / Liberatore, Paolo. - In: ACM TRANSACTIONS ON COMPUTATIONAL LOGIC. - ISSN 1529-3785. - 24:3(2023), pp. 1-49. [10.1145/3583071]

Mixed Iterated Revisions: Rationale, Algorithms, and Complexity

Paolo Liberatore
Primo
Formal Analysis
2023

Abstract

Several forms of iterable belief change exist, differing in the kind of change and its strength: some operators introduce formulae, others remove them; some add formulae unconditionally, others only as additions to the previous beliefs; some only relative to the current situation, others in all possible cases. A sequence of changes may involve several of them: for example, the first step is a revision, the second a contraction and the third a refinement of the previous beliefs. The ten operators considered in this article are shown to be all reducible to three: lexicographic revision, refinement and severe withdrawal. In turn, these three can be expressed in terms of lexicographic revision at the cost of restructuring the sequence. This restructuring needs not to be done explicitly: an algorithm that works on the original sequence is shown. The complexity of mixed sequences of belief change operators is also analyzed. Most of them require only a polynomial number of calls to a satisfiability checker, some are even easier.
2023
iterated belief revision, translation algorithm, computational complexity
01 Pubblicazione su rivista::01a Articolo in rivista
Mixed Iterated Revisions: Rationale, Algorithms, and Complexity / Liberatore, Paolo. - In: ACM TRANSACTIONS ON COMPUTATIONAL LOGIC. - ISSN 1529-3785. - 24:3(2023), pp. 1-49. [10.1145/3583071]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1683514
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