Relevance in belief revision

Peppas, Pavlos; Williams, Mary-Anne; Chopra, Samir; Foo, Norman Y.

doi:10.1016/j.artint.2015.08.007

Cited by 36 publications

(34 citation statements)

References 7 publications

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“…Accordingly, Parikh proposed a new axiom, named (P), to supplement the AGM postulates for revision. Axiom (P) was further analysed in [Peppas et al, 2015], where two different interpretations of it were identified, called the weak and the strong version of (P). 3 The weak version of (P), denoted by (wP), is sufficient for the promised results.…”

Section: Parikh's Notion Of Relevancementioning

confidence: 99%

“…Condition (wP) says that the revision of S by ϕ will not affect any belief content outside L x . In order to present the possible-world characterization of (wP), as introduced in [Peppas et al, 2015], we need some additional terminology. 4 Definition 2 (Diff).…”

Section: Parikh's Notion Of Relevancementioning

confidence: 99%

“…For every theory K of L, there is a unique finest Ksplitting, denoted by F ; i.e., one which refines every other K-splitting [Parikh, 1999]. 5 Definition 4 (Extended Diff, [Peppas et al, 2015]). Let K be a theory of L, and let F be the finest K-splitting.…”

Section: Parikh's Notion Of Relevancementioning

confidence: 99%

See 2 more Smart Citations

Observations on Darwiche and Pearl's Approach for Iterated Belief Revision

Aravanis

Peppas

Williams

2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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Notwithstanding the extensive work on iterated belief revision, there is, still, no fully satisfactory solution within the classical AGM paradigm. The seminal work of Darwiche and Pearl (DP approach, for short) remains the most dominant, despite its well-documented shortcomings. In this article, we make further observations on the DP approach. Firstly, we prove that the DP postulates are, in a strong sense, inconsistent with Parikh's relevance-sensitive axiom (P), extending previous initial conflicts. Immediate consequences of this result are that an entire class of intuitive revision operators, which includes Dalal's operator, violates the DP postulates, as well as that the Independence postulate and Spohn's conditionalization are inconsistent with (P). Lastly, we show that the DP postulates allow for more revision polices than the ones that can be captured by identifying belief states with total preorders over possible worlds, a fact implying that a preference ordering (over possible worlds) is an insufficient representation for a belief state.

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Section: Parikh's Notion Of Relevancementioning

confidence: 99%

Section: Parikh's Notion Of Relevancementioning

confidence: 99%

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Observations on Darwiche and Pearl's Approach for Iterated Belief Revision

Aravanis

Peppas

Williams

2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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“…Splittability is, in turn, a function of the contingent beliefs of an agent. Parikh's approach is often referred to as the language-splitting model, and, since its proposal, has been extensively studied; see, indicatively, the works by Chopra and Parikh (2000), Makinson and Kourousias (2006), Kourousias and Makinson (2007), Makinson (2009), Peppas, Williams, Chopra, and Foo (2015), and Aravanis, Peppas, and Williams (2019). Peppas et al (2015) identified two different interpretations of Parikh's axiom (P), called the weak and the strong version of (P), both of which are plausible depending on the application.…”

Section: Introductionmentioning

confidence: 99%

Relevance in Belief Update

AravanisTheofanis

2021

jair

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It has been pointed out by Katsuno and Mendelzon that the so-called AGM revision operators, defined by Alchourrón, Gärdenfors and Makinson, do not behave well in dynamically-changing applications. On that premise, Katsuno and Mendelzon formally characterized a different type of belief-change operators, typically referred to as KM update operators, which, to this date, constitute a benchmark in belief update. In this article, we show that there exist KM update operators that yield the same counter-intuitive results as any AGM revision operator. Against this non-satisfactory background, we prove that a translation of Parikh’s relevance-sensitive axiom (P), in the realm of belief update, suffices to block this liberal behaviour of KM update operators. It is shown, both axiomatically and semantically, that axiom (P) for belief update, essentially, encodes a type of relevance that acts at the possible-worlds level, in the context of which each possible world is locally modified, in the light of new information. Interestingly, relevance at the possible-worlds level is shown to be equivalent to a form of relevance that acts at the sentential level, by considering the building blocks of relevance to be the sentences of the language. Furthermore, we concretely demonstrate that Parikh’s notion of relevance in belief update can be regarded as (at least a partial) solution to the frame, ramification and qualification problems, encountered in dynamically-changing worlds. Last but not least, a whole new class of well-behaved, relevance-sensitive KM update operators is introduced, which generalize Forbus’ update operator and are perfectly-suited for real-world implementations.

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“…Other approaches in modularity appeared in Belief Change [CP00, HW02, Par09], often with the concept of logical relevance [KM07, Mak09,PWCF15] which essentially states that one formula is relevant to another if either aids or hinders its proof. Among these, the most pertinent of these proposals to this thesis is the theory Local Change theory [HW02], discussed in subsection.…”

Section: 4mentioning

confidence: 99%

Modularity in belief change of description logic bases

Guimarães¹

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Ontologies written in OWL and OWL 2 are one of the most prominent tools in Knowledge Representation nowadays. They allow the sharing of knowledge of a domain unambiguously and operate with implicit knowledge using reasoning algorithms. However, ontologies can become large and very complex, difficulting their maintenance and evolution. One complicating factor is that a small change can trigger unexpected and unwanted consequences.Solutions to sound maintenance have emerged separately in Belief Change and Ontology Repair.Despite having distinct views, proposals in both fields often rely on the Description Logics, which underpin OWL and OWL 2. Hence, the approaches from both fields for repairing ontologies are very similar at the algorithmic level. Consequently, both areas need to address the high complexity of the debugging problem and cope with the exponential number of correct outcomes.There are studies in Ontology Repair which use modularity techniques to extract smaller subsets of the ontology which are sufficient to fix a particular consequence. Still, the effect of modules on the Belief Change framework is poorly understood: either the postulates or the mechanisms which select the final result might change when a module replaces the input. Also, the impact on computational performance was only assessed in small corpora and with few variations in parameters. Further, the number of outcomes is still exponential, and existing solutions rarely provide means to mitigate this issue.In this direction, this thesis provides a clearer understanding of the effects of modularity in the theoretical framework that guarantees rational (sound) changes. Also, it evaluates the performance impact of modularity empirically using locality-based modules in a broader setting. Additionally, it also investigates how modules can aid users to filter and select the best results efficiently. A category of modules is identified for which the postulates from Belief Change remain the same, and under mild conditions, the result is unchanged. The analysis of experimental data shows that modules are beneficial for performance, often displaying gains of orders of magnitude. Further, the methods proposed to aid in the selection of repairs are shown to be competitive with existing methods.

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Relevance in belief revision

Cited by 36 publications

References 7 publications

Observations on Darwiche and Pearl's Approach for Iterated Belief Revision

Observations on Darwiche and Pearl's Approach for Iterated Belief Revision

Relevance in Belief Update

Modularity in belief change of description logic bases

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