Measuring inconsistency in probabilistic logic: rationality postulates and Dutch book interpretation

Bona, Glauber De; Finger, Marcelo

doi:10.1016/j.artint.2015.06.006

Cited by 27 publications

(24 citation statements)

References 40 publications

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“…Other kinds of measures of inconsistency have been developed for probabilistic knowledge [33,28,5] and fuzzy knowledge [27]. These augment logical information with quantitative information, and the measures consider distance with respect to numerical assignments.…”

Section: Definition 28mentioning

confidence: 99%

Analysing inconsistent information using distance-based measures

Grant¹,

Hunter²

2017

International Journal of Approximate Reasoning

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There have been a number of proposals for measuring inconsistency in a knowledgebase (i.e. a set of logical formulae). These include measures that consider the minimally inconsistent subsets of the knowledgebase, and measures that consider the paraconsistent models (3 or 4 valued models) of the knowledgebase. In this paper, we present a new approach that considers the amount by which each formula has to be weakened in order for the knowledgebase to be consistent. This approach is based on ideas of knowledge merging by Konienczny and Pino-Perez. We show that this approach gives us measures that are different from existing measures, that have desirable properties, and that can take the significance of inconsistencies into account. The latter is useful when we want to differentiate between inconsistencies that have minor significance from inconsistencies that have major significance. We also show how our measures are potentially useful in applications such as evaluating violations of integrity constraints in databases and for deciding how to act on inconsistency.

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Section: Definition 28mentioning

confidence: 99%

Analysing inconsistent information using distance-based measures

Grant¹,

Hunter²

2017

International Journal of Approximate Reasoning

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“…Hájek 2008). However, incoherence comes in degrees, and the bad consequences of being incoherent equally come in degrees (Schervish et al 2000, 2002, 2003, De Bona & Finger 2015, De Bona & Staffel 2017, 2018. We can intuitively think of the degree of incoherence of a credence function as the distance between it and some closest coherent credence function.…”

Section: The Descriptive and Normative Consequences Of Rejecting Pcmentioning

confidence: 99%

How do Beliefs Simplify Reasoning?

Staffel

2018

Nous

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According to an increasingly popular epistemological view, people need outright beliefs in addition to credences to simplify their reasoning. Outright beliefs simplify reasoning by allowing thinkers to ignore small error probabilities. What is outright believed can change between contexts. It has been claimed that thinkers manage shifts in their outright beliefs and credences across contexts by an updating procedure resembling conditionalization, which I call pseudo‐conditionalization (PC). But conditionalization is notoriously complicated. The claim that thinkers manage their beliefs via PC is thus in tension with the view that the function of beliefs is to simplify our reasoning. I propose to resolve this puzzle by rejecting the view that thinkers employ PC. Based on this solution, I furthermore argue for a descriptive and a normative claim. The descriptive claim is that the available strategies for managing beliefs and credences across contexts that are compatible with the simplifying function of outright beliefs can generate synchronic and diachronic incoherence in a thinker's attitudes. Moreover, I argue that the view of outright belief as a simplifying heuristic is incompatible with the view that there are ideal norms of coherence or consistency governing outright beliefs that are too complicated for human thinkers to comply with.

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“…The devising of inconsistency measures has been influenced by a set of rationality postulates proposed by Hunter and Konieczny [25]. Among these basic requirements, the postulates of (Independence) and (Dominance) have been subject to debate [8,27,11]. The postulate of (Independence) is strongly related to minimal inconsistent sets as the primitive conflict characterisation [8,11], and such a link may be undesirable sometimes.…”

Section: Our Approachmentioning

confidence: 99%

Localising iceberg inconsistencies

Bona

Hunter

2017

Artificial Intelligence

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In artificial intelligence, it is important to handle and analyse inconsistency in knowledge bases. Inconsistent pieces of information suggest questions like "where is the inconsistency?" and "how severe is it?". Inconsistency measures have been proposed to tackle the latter issue, but the former seems underdeveloped and is the focus of this paper. Minimal inconsistent sets have been the main tool to localise inconsistency, but we argue that they are like the exposed part of an iceberg, failing to capture contradictions hidden under the water. Using classical propositional logic, we develop methods to characterise when a formula is contributing to the inconsistency in a knowledge base and when a set of formulas can be regarded as a primitive conflict. To achieve this, we employ an abstract consequence operation to "look beneath the water level", generalising the minimal inconsistent set concept and the related free formula notion. We apply the framework presented to the problem of measuring inconsistency in knowledge bases, putting forward relaxed forms for two debatable postulates for inconsistency measures. Finally, we discuss the computational complexity issues related to the introduced concepts.

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Measuring inconsistency in probabilistic logic: rationality postulates and Dutch book interpretation

Cited by 27 publications

References 40 publications

Analysing inconsistent information using distance-based measures

Analysing inconsistent information using distance-based measures

How do Beliefs Simplify Reasoning?

Localising iceberg inconsistencies

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