Conditionals and consequences

Kyburg, Henry E.; Teng, Choh-Man; Wheeler, Gregory

doi:10.1016/j.jal.2006.03.014

Cited by 21 publications

(12 citation statements)

References 29 publications

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“…This idea is mooted by Kyburg, Teng, and Wheeler [12], but we can go further. We get another connection, this time between the family P and a family weaker than O that has appeared in the literature on several occasions under various names.…”

Section: Observation 33mentioning

confidence: 99%

The Quantitative/Qualitative Watershed for Rules of Uncertain Inference

Hawthorne

Makinson

2007

Stud Logica

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Abstract.We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as 'preface' and 'lottery' rules.

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Section: Observation 33mentioning

confidence: 99%

The Quantitative/Qualitative Watershed for Rules of Uncertain Inference

Hawthorne

Makinson

2007

Stud Logica

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“…The properties of reasoning with such extreme probability statements were studied in [1,39,44] and turned out to be the properties of nonmonotonic reasoning laid bare in System P. In fact, the calculus of infinitesimal conditional probabilities of this form is equivalent to System P [7,39]. And degraded forms of inference rules of System P hold with standard conditional probabilities [23,27,38]. Remark 5 The above setting for plausible inference has been challenged on the ground that it conflicts with the idea of acceptance viewed as high probability: if in a given context Pr(A) and Pr(B) are close to 1, then it does not imply that Pr(AB) is close to 1 at all.…”

Section: Proposition 3 In System P If B |∼ K a Then Ab |∼ K C If Anmentioning

confidence: 99%

“…Remark 5 The above setting for plausible inference has been challenged on the ground that it conflicts with the idea of acceptance viewed as high probability: if in a given context Pr(A) and Pr(B) are close to 1, then it does not imply that Pr(AB) is close to 1 at all. It questions the deductive closure of accepted beliefs [38,48]. This is the basis of the lottery paradox of Kyburg [37] (buying a lottery ticket that loses is very likely, but one is sure that there is at least one winner).…”

Section: Proposition 3 In System P If B |∼ K a Then Ab |∼ K C If Anmentioning

confidence: 99%

Qualitative and quantitative conditions for the transitivity of perceived causation:

Bonnefon

Neves

Dubois

et al. 2012

Ann Math Artif Intell

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If A caused B and B caused C, did A cause C? Although laypersons commonly perceive causality as being transitive, some philosophers have questioned this assumption, and models of causality in artificial intelligence are often agnostic with respect to transitivity. We consider two formal models of causation that differ in the way they represent uncertainty. The quantitative model uses a crude probabilistic definition, arguably the common core of more sophisticated quantitative definitions; the qualitative model uses a definition based on nonmonotonic consequence relations. Different sufficient conditions for the transitivity of causation are laid bare by the two models: The Markov condition on events for the quantitative model, and a so-called saliency condition (A is perceived as a typical cause of B) for the qualitative model. We explore the formal and empirical relations between these sufficient conditions, and between the underlying definitions of perceived causation. These connections shed light on the range of applicability of each model, contrasting commonsense causal reasoning (supposedly qualitative) and scientific causation 312 J.-F. Bonnefon et al.(more naturally quantitative). These speculations are supported by a series of three behavioral experiments.

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“…The more you can say, the less you can do. Non-logical problem domainssuch as natural language-compound this problem because they very often are much richer than even the most expressive formal languages [16,27]. Hence, in nearly all applications of logic, one must select what features of the problem domain to represent within the framework and what features to ignore.…”

Section: On the Application Of Logicmentioning

confidence: 99%

“…For instance, there are good reasons to think that classical statistical inference forms do not satisfy the [And], [Or], and [Cautious Monotonicity] axioms of System P [16]. And there are logically interesting probabilistic logics that are weaker than System P. Among the weakest systems is System Y [34], which is built from 1-monotone capacities but nevertheless preserves greatest lower bound interval estimates on particular sequences of joins and meets of probabilistic events.…”

Section: System P and Aggregationmentioning

confidence: 99%

Applied Logic without Psychologism

Wheeler

2008

Stud Logica

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Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan's impossibility results for non-monotonic logic, David Makinson's normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson's proposed formal constraints on rational acceptance.

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Conditionals and consequences

Cited by 21 publications

References 29 publications

The Quantitative/Qualitative Watershed for Rules of Uncertain Inference

The Quantitative/Qualitative Watershed for Rules of Uncertain Inference

Qualitative and quantitative conditions for the transitivity of perceived causation:

Applied Logic without Psychologism

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