A General Non-Probabilistic Theory of Inductive Reasoning

Spohn, Wolfgang

doi:10.1016/b978-0-444-88650-7.50017-2

Cited by 99 publications

(69 citation statements)

References 6 publications

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“…Shackle also introduces a notion of conditional possibility, whereby the degree of surprise of a conjunction of two events A and B is equal to the maximum of the degree of surprise of A, and of the degree of surprise of B, should A prove true. The disbelief notion introduced later by Spohn [130] employs the same type of convention as potential surprise, but using the set of natural integers as a disbelief scale; his conditioning rule uses the subtraction of natural integers.…”

Section: Historical Backgroundmentioning

confidence: 99%

“…A possibility measure is also a special case of a Shafer plausibility function [126]. Following a very different approach, possibility theory can account for probability distributions with extreme values, infinitesimal [130] or having big steps [16]. There are finally close connections between possibility theory and idempotent analysis [113].…”

Section: Quantitative Possibility Theorymentioning

confidence: 99%

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Possibility Theory and Its Applications: Where Do We Stand?

Dubois

Prade

2015

Springer Handbook of Computational Intelligence

148

101

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This paper provides an overview of possibility theory, emphasizing its historical roots and its recent developments. Possibility theory lies at the crossroads between fuzzy sets, probability and non-monotonic reasoning. Possibility theory can be cast either in an ordinal or in a numerical setting. Qualitative possibility theory is closely related to belief revision theory, and common-sense reasoning with exception-tainted knowledge in Artificial Intelligence. Possibilistic logic provides a rich representation setting, which enables the handling of lower bounds of possibility theory measures, while remaining close to classical logic. Qualitative possibility theory has been axiomatically justified in a decision-theoretic framework in the style of Savage, thus providing a foundation for qualitative decision theory. Quantitative possibility theory is the simplest framework for statistical reasoning with imprecise probabilities. As such it has close connections with random set theory and confidence intervals, and can provide a tool for uncertainty propagation with limited statistical or subjective information.

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Section: Historical Backgroundmentioning

confidence: 99%

Section: Quantitative Possibility Theorymentioning

confidence: 99%

Possibility Theory and Its Applications: Where Do We Stand?

Dubois

Prade

2015

Springer Handbook of Computational Intelligence

148

101

View full text Add to dashboard Cite

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“…This presupposes a model of supposition, which is nontrivial in cases where the supposition is counterdoxastic or counterfactual. This presupposes, in turn, deploying a grading of events incompatible with the current state K. This grading admits multiple interpretations, including a notion of similarity (Lewis 1973), when the conditional is interpreted ontologically; an epistemic notion of plausibility, (Spohn 1988); or an interpretation in terms of informational value, (Levi 1980;. The result of supposing p with respect to K, therefore, might be represented as the most plausible (most similar, etc.)…”

Section: Future Directionsmentioning

confidence: 99%

Two types of thought: Evidence from aphasia

Davidoff

2005

Behav Brain Sci

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Abstract:The distinction between rules and similarity is central to our understanding of much of cognitive psychology. Two aspects of existing research have motivated the present work. First, in different cognitive psychology areas we typically see different conceptions of rules and similarity; for example, rules in language appear to be of a different kind compared to rules in categorization. Second, rules processes are typically modeled as separate from similarity ones; for example, in a learning experiment, rules and similarity influences would be described on the basis of separate models. In the present article, I assume that the rules versus similarity distinction can be understood in the same way in learning, reasoning, categorization, and language, and that a unified model for rules and similarity is appropriate. A rules process is considered to be a similarity one where only a single or a small subset of an object's properties are involved. Hence, rules and overall similarity operations are extremes in a single continuum of similarity operations. It is argued that this viewpoint allows adequate coverage of theory and empirical findings in learning, reasoning, categorization, and language, and also a reassessment of the objectives in research on rules versus similarity.Keywords: categorization; cognitive explanation; language; learning; reasoning; rules; similarity Emmanuel Pothos received his D.Phil. in Experimental Psychology from the University of Oxford in 1998. Since then he has been a lecturer of psychology at the University of Wales at Bangor and at the University of Edinburgh; he is currently at the University of Crete. His research activity includes computational models in unsupervised categorization and statistical methods for disambiguating rules and similarity in learning. Additionally, he is looking at applications of learning models in the study of addictive behavior. A focal point of his work is the a priori comparability of theoretical accounts and explanatory concepts in cognitive psychology.partly because they uniquely have in common a particular set of properties or features, as research in basic level categorization and spontaneous classification shows (Pothos & Chater 2002;Rosch & Mervis 1975). I postulate that the object properties relevant in deciding how to categorize it amongst a number of candidate categories are the properties uniquely common to the instances of each category (cf. Aha & Goldstone 1992). For example, in order to decide whether my car keys are a member of the category 'things to take out of my house when it is on fire," I will have to consider only whether car keys match the uniquely common properties of the other members of that category ("credit cards," "my cat," "my university diploma") (Barsalou 1991). Note that the present proposal does not involve any commitment about the form of features or properties (cf. Marr 1982). We simply require that at some level it is possible to represent objects in terms of discrete entities (perceptual features, abstract proper...

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“…We decided to use qualitative order-of-magnitude probabilities based on the kappa calculus [Spohn, 1988;Pearl, 1989]. The kappa calculus can be described in terms of surprise; the kappa values correspond to the level of surprise.…”

Section: Qualitative Probabilistic Matchingmentioning

confidence: 99%

Type Uncertainty in Ontologically-Grounded Qualitative Probabilistic Matching

Poole

Smyth

2005

Lecture Notes in Computer Science

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Abstract. This paper is part of a project to match real-world descriptions of instances of objects to models of objects. We use a rich ontology to describe instances and models at multiple levels of detail and multiple levels of abstraction. The models are described using qualitative probabilities. This paper is about the problem of type uncertainty; what if we have a qualitative distribution over the types. For example allowing a model to specify that a meeting is always scheduled in a building, usually in a civic building, and never a shopping mall can help an agent find a meeting even if it is unsure about the address.

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A General Non-Probabilistic Theory of Inductive Reasoning

Cited by 99 publications

References 6 publications

Possibility Theory and Its Applications: Where Do We Stand?

Possibility Theory and Its Applications: Where Do We Stand?

Two types of thought: Evidence from aphasia

Type Uncertainty in Ontologically-Grounded Qualitative Probabilistic Matching

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