Characterizing Relevant Belief Revision Operators

Perrussel, Laurent; Marchi, Jerusa; Zhang, Dongmo

doi:10.1007/978-3-642-17432-2_5

Cited by 5 publications

(4 citation statements)

References 13 publications

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“…Hansson and Wassermann (2002) classify work that addresses the concepts of relevance and dependence of formulas into two groups. First, some authors capture relevance/dependence of formulas through syntactic means such as variable sharing and language splitting (including Chopra & Parikh, 2000;Falappa, García, Kern-Isberner, & Simari, 2011;Ismail & Kasrin, 2010;Kourousias & Makinson, 2007;Makinson & Kourousias, 2006;Makinson, 2007;Parikh, 1999;Perrussel, Marchi, & Zhang, 2011;Suntisrivaraporn, Qi, Ji, & Haase, 2008;Wu, Zhang, & Zhang, 2011). Second, some authors focus on inferential dependency of formulas or, in other words, how some formulas deductively contribute to the inference of other formulas.…”

Section: Related Workmentioning

confidence: 99%

Kernel Contraction and Base Dependence

Oveisi¹,

Delgrande²,

Pelletier³

et al. 2017

jair

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The AGM paradigm of belief change studies the dynamics of belief states in light of new information. Finding, or even approximating, those beliefs that are dependent on or relevant to a change is valuable because, for example, it can narrow the set of beliefs considered during belief change operations. A strong intuition in this area is captured by Gärdenforss preservation criterion (GPC), which suggests that formulas independent of a belief change should remain intact. GPC thus allows one to build dependence relations that are linked with belief change. Such dependence relations can in turn be used as a theoretical benchmark against which to evaluate other approximate dependence or relevance relations. Fariñas and Herzig axiomatize a dependence relation with respect to a belief set, and, based on GPC, they characterize the correspondence between AGM contraction functions and dependence relations. In this paper, we introduce base dependence as a relation between formulas with respect to a belief base, and prove a more general characterization that shows the correspondence between kernel contraction and base dependence. At this level of generalization, different types of base dependence emerge, which we show to be a result of possible redundancy in the belief base. We further show that one of these relations that emerge, strong base dependence, is parallel to saturated kernel contraction. We then prove that our latter characterization is a reversible generalization of Fariñas and Herzigs characterization. That is, in the special case when the underlying belief base is deductively closed (i.e., it is a belief set), strong base dependence reduces to dependence, and so do their respective characterizations. Finally, an intriguing feature of Fariñas and Herzigs formalism is that it meets other criteria for dependence, namely, Keyness conjunction criterion for dependence (CCD) and Gärdenforss conjunction criterion for independence (CCI). We prove that our base dependence formalism also meets these criteria. Even more interestingly, we offer a more specific criterion that implies both CCD and CCI, and show our base dependence formalism also meets this new criterion.

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Section: Related Workmentioning

confidence: 99%

Kernel Contraction and Base Dependence

Oveisi¹,

Delgrande²,

Pelletier³

et al. 2017

jair

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“…The set K M as defined above is used for a specific kind of model-based revision in [10]the authors link their paper to Parikh's and Makinson's work on the notion of relevant belief change, but do not explicitly discuss the relation between K M and K N . In [12], the same authors propose a solution to the problem of relevance in belief revision in terms of preferences over prime implicants, minimal conjunctions of literals that entail K. The idea of defining revision of K in view of its prime implicate set was put forward in [3], where it is conjectured that this revision obeys relevance. However, so far no one seems to have made the distinction between K M and other sets in K N .…”

Section: Theoremmentioning

confidence: 99%

Prime implicates and relevant belief revision

Putte¹

2011

Journal of Logic and Computation

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This article discusses Parikh's axiom of relevance in belief revision, and recalls some results from Kourousias and Makinson (2007, J. Symbolic Logic, 72, 994-1002) in this context. The crucial distinction is emphasized between the uniqueness of the finest splitting of K and the fact that K has several normal forms associated with that finest splitting. The main new result of this article is a new proof for the theorem that the set of prime implicates of K is a normal form for the finest splitting of K. It is explained how this proof avoids a mistake in an earlier proof from Wu and Zhang (2010, Knowledge-Based Syst., 23, 70-76). As a corollary, relevance can be redefined without reference to the finest splitting, using the notion of path-relevance from Makinson (2009, J. Appl. Logic, 7, 377-387). Finally, a weak yet sufficient condition for irrelevance is presented.

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“…It is worth pausing at this point and noting that the problem of relevance is a crucial topic in many areas of Artificial Intelligence, and, as a consequence, has received considerable attention (Subramanian, Greiner, & Judea Pearl, 1997). Confined to relevance-sensitive belief change, reference is indicatively made to the work of Gärdenfors (1990), Nebel (1999), Chopra and Parikh (2000), Chopra, Georgatos, and Parikh (2001), Kourousias and Makinson (2007), Makinson (2009), Wu and Zhang (2008), Perrussel, Marchi, and Zhang (2010), Parikh (2011), Delgrande and Peppas (2018). An interesting application of local change for diagnosis (i.e., the process of finding the faulty compartment of a malfunctioning system) has been proposed by Wassermann (2001a), while Hansson and Wassermann (2002) used local change for handling local inconsistencies that actual agents in the real world hold.…”

Section: Introductionmentioning

confidence: 99%

Full Characterization of Parikh's Relevance-Sensitive Axiom for Belief Revision

Aravanis

Peppas

Williams

2019

jair

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In this article, the epistemic-entrenchment and partial-meet characterizations of Parikh's relevance-sensitive axiom for belief revision, known as axiom (P), are provided. In short, axiom (P) states that, if a belief set $K$ can be divided into two disjoint compartments, and the new information $\varphi$ relates only to the first compartment, then the revision of $K$ by $\varphi$ should not affect the second compartment. Accordingly, we identify the subclass of epistemic-entrenchment and that of selection-function preorders, inducing AGM revision functions that satisfy axiom (P). Hence, together with the faithful-preorders characterization of (P) that has already been provided, Parikh's axiom is fully characterized in terms of all popular constructive models of Belief Revision. Since the notions of relevance and local change are inherent in almost all intellectual activity, the completion of the constructive view of (P) has a significant impact on many theoretical, as well as applied, domains of Artificial Intelligence.

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Characterizing Relevant Belief Revision Operators

Cited by 5 publications

References 13 publications

Kernel Contraction and Base Dependence

Kernel Contraction and Base Dependence

Prime implicates and relevant belief revision

Full Characterization of Parikh's Relevance-Sensitive Axiom for Belief Revision

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