Properties of Iterated Multiple Belief Revision

Zhang, Dongmo

doi:10.1007/978-3-540-24609-1_27

Cited by 7 publications

(7 citation statements)

References 12 publications

(15 reference statements)

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“…The four semantics for iterated belief revisions are not the only ones defined in the literature (Williams, 1994;Darwiche & Pearl, 1997;Areces & Becher, 2001;Benferhat et al, 2004;Konieczny & Pino Pérez, 2000;Zhang, 2004); a recent survey counted at least twenty seven revision-related operators (Rott, 2009). Natural and lexicographic semantics are regarded as extreme forms of revision satisfying the Darwiche-Pearl postulates (Darwiche & Pearl, 1997), where minimal and maximal hearing is respectively given to the new information.…”

Section: Discussionmentioning

confidence: 99%

“…Some require additional information (like the strength of every revision, Spohn, 1988;Williams, 1994;Benferhat et al, 2004), others are families of revisions rather than single ones (Darwiche & Pearl, 1997;Zhang, 2004). These, in particular, open an interesting line of research: whether a revision sequence can be generated by some ordering and some revision semantics satisfying a given set of conditions, like the Darwiche and Pearl (1997) postulates.…”

Section: Discussionmentioning

confidence: 99%

“…Many belief revision operators are based on some sort of plausibility order (Spohn, 1988;Boutilier, 1996;Nayak, 1994;Williams, 1994;Areces & Becher, 2001;Zhang, 2004;Benferhat, Kaci, Le Berre, & Williams, 2004;Hild & Spohn, 2008;Fermé & Hansson, 2011). Whenever revising can be done in two or more different ways, the result is the disjunction of either all of them (Alchourròn & Makinson, 1982;Fagin, Ullman, & Vardi, 1983;Winslett, 1988) or the most plausible ones only according to the order (Gärdenfors, 1988;Katsuno & Mendelzon, 1991;Peppas, 2008;Nebel, 1992;Fermé & Hansson, 2011).…”

Section: Introductionmentioning

confidence: 99%

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Revision by History

Liberatore¹

2015

jair

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This article proposes a solution to the problem of obtaining plausibility information, which is necessary to perform belief revision: given a sequence of revisions, together with their results, derive a possible initial order that has generated them; this is different from the usual assumption of starting from an all-equal initial order and modifying it by a sequence of revisions. Four semantics for iterated revision are considered: natural, restrained, lexicographic and reinforcement. For each, a necessary and sufficient condition to the existence of an order generating a given history of revisions and results is proved. Complexity is proved coNP complete in all cases but one (reinforcement revision with unbounded sequence length).

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Revision by History

Liberatore¹

2015

jair

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“…We start with the following generalization of the DP postulates to sets of formulas, as suggested by [ Zhang, 2004 ] .…”

Section: Parallel Revision and Iterated Revisionmentioning

confidence: 99%

Parallel belief revision: Revising by sets of formulas

Delgrande

Jin

2012

Artificial Intelligence

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The area of belief revision studies how a rational agent may incorporate new information about a domain into its belief corpus. An agent is characterized by a belief state K, and receives a new item of information α which is to be included among its set of beliefs. Revision then is a function from a belief state and a formula to a new belief state. We propose here a more general framework for belief revision, in which revision is a function from a belief state and a finite set of formulas to a new belief state. In particular, we distinguish revision by the set {α, β} from the set {α ∧ β}. This seemingly innocuous change has significant ramifications with respect to iterated belief revision. A problem in approaches to iterated belief revision is that, after first revising by a formula and then by a formula that is inconsistent with the first formula, all information in the original formula is lost. This problem is avoided here in that, in revising by a set of formulas S, the resulting belief state contains not just the information that members of S are believed to be true, but also the counterfactual supposition that if some members of S were later believed to be false, then the remaining members would nonetheless still be believed to be true. Thus if some members of S were in fact later believed to be false, then the other elements of S would still be believed to be true. Hence, we provide a more nuanced approach to belief revision. The general approach, which we call parallel belief revision, is independent of extant approaches to iterated revision. We present first a basic approach to parallel belief revision. Following this we combine the basic approach with an approach due to Jin and Thielscher for iterated revision. Postulates and semantic conditions characterizing these approaches are given, and representation results provided. We conclude with a discussion of the possible ramifications of this approach in belief revision in general.

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“…[61,36,54,28,29,18,46,33,34,35,56,41,44,57,64,62,32,38,16]. The relation of this problem to reasoning about actions has been identified earlier [60,55,51], since the effects of executing an action in a given situation can be modeled as the change of a theory representing the current state by a formula representing the action effects.…”

Section: Related Workmentioning

confidence: 99%

Comparing action descriptions based on semantic preferences

Eiter

Erdem

Fink

et al. 2007

Ann Math Artif Intell

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Abstract.Incorporating new information into a knowledge base is an important problem which has been widely considered. In this paper, we study the problem in a formal framework for reasoning about action and change, in which action domains are described in an action language that has a transition-based semantics. Going beyond previous works, we consider (i) a richer action language that allows for non-deterministic, and concurrent actions, as well as the representation of indirect effects and dependencies between fluents, (ii) more general updates than elementary statements, and, most importantly, (iii) meta-level knowledge, such as observations, assertions, or general domain properties that remain invariant under change, expressed in an action query language. For this setting, we formalize a notion of update of an action domain description, relative to a generic preference relation on action domain descriptions that selects most preferred solutions. We study semantic and computational aspects of this notion, where we establish basic properties of updates and a decomposition result that gives rise to a divide and conquer approach to computing solutions under certain conditions. Furthermore, we study the computational complexity of decision problems around computing solutions, both for the generic setting and for two particular preference relations, viz. set-inclusion and weight-based preference. While deciding the existence of solutions and recognizing solutions are PSPACE-complete problems in general, the problems fall back into the polynomial hierarchy under restrictions on the meta-level conditions. We finally discuss methods to compute solutions and approximate solutions (which disregard preference). Our results provide a semantic and computational basis for developing systems that incorporate new information into action descriptions in an action language, in the presence of additional conditions at the meta-level.

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Properties of Iterated Multiple Belief Revision

Cited by 7 publications

References 12 publications

Revision by History

Revision by History

Parallel belief revision: Revising by sets of formulas

Comparing action descriptions based on semantic preferences

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