Probabilistic consequence relations.
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| Title: | Probabilistic consequence relations. |
|---|---|
| Authors: | Égré, Paul1 (AUTHOR), Ripley, Ellie2 (AUTHOR) |
| Source: | Journal of Logic & Computation. Dec2025, Vol. 35 Issue 8, p1-29. 29p. |
| Subjects: | Inference (Logic), Propositional calculus, Conditionals (Logic), Distribution (Probability theory) |
| Abstract: | This paper investigates logical consequence defined in terms of probability distributions, for a classical propositional language using a standard notion of probability. We examine three distinct probabilistic consequence notions, which we call material consequence , preservation consequence and symmetric consequence. While material consequence is fully classical for any threshold, preservation consequence and symmetric consequence are subclassical, with only symmetric consequence gradually approaching classical logic at the limit threshold equal to 1. Our results extend earlier results obtained by J. Paris in a |$\text{Set-Fmla}$| setting to the Set-Set setting, and consider open thresholds beside closed ones. In the Set-Set setting, in particular, they reveal that probability 1 preservation does not yield classical logic, but supervaluationism, and conversely positive probability preservation yields subvaluationism. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 190650840 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Probabilistic consequence relations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Égré%2C+Paul%22">Égré, Paul</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ripley%2C+Ellie%22">Ripley, Ellie</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Logic+%26+Computation%22">Journal of Logic & Computation</searchLink>. Dec2025, Vol. 35 Issue 8, p1-29. 29p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Inference+%28Logic%29%22">Inference (Logic)</searchLink><br /><searchLink fieldCode="DE" term="%22Propositional+calculus%22">Propositional calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Conditionals+%28Logic%29%22">Conditionals (Logic)</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper investigates logical consequence defined in terms of probability distributions, for a classical propositional language using a standard notion of probability. We examine three distinct probabilistic consequence notions, which we call material consequence , preservation consequence and symmetric consequence. While material consequence is fully classical for any threshold, preservation consequence and symmetric consequence are subclassical, with only symmetric consequence gradually approaching classical logic at the limit threshold equal to 1. Our results extend earlier results obtained by J. Paris in a |$\text{Set-Fmla}$| setting to the Set-Set setting, and consider open thresholds beside closed ones. In the Set-Set setting, in particular, they reveal that probability 1 preservation does not yield classical logic, but supervaluationism, and conversely positive probability preservation yields subvaluationism. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=190650840 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1093/logcom/exae076 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 29 StartPage: 1 Subjects: – SubjectFull: Inference (Logic) Type: general – SubjectFull: Propositional calculus Type: general – SubjectFull: Conditionals (Logic) Type: general – SubjectFull: Distribution (Probability theory) Type: general Titles: – TitleFull: Probabilistic consequence relations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Égré, Paul – PersonEntity: Name: NameFull: Ripley, Ellie IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 0955792X Numbering: – Type: volume Value: 35 – Type: issue Value: 8 Titles: – TitleFull: Journal of Logic & Computation Type: main |
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