Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning.
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| Title: | Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning. |
|---|---|
| Authors: | Beckmann, Arnold1 a.beckmann@swansea.ac.uk, Preining, Norbert2 |
| Source: | Journal of Logic & Computation. Sep2018, Vol. 28 Issue 6, p1125-1187. 63p. |
| Subjects: | Natural deduction (Logic), Reasoning, Mathematical formulas, Communication, Mathematical logic |
| Abstract: | We introduce a system of Hyper Natural Deduction for Gödel Logic as an extension of Gentzen’s system of Natural Deduction. A deduction in this system consists of a finite set of derivations which uses the typical rules of Natural Deduction, plus additional rules providing means for communication between derivations. We show that our system is sound and complete for infinite-valued propositional Gödel Logic, by giving translations to and from Avron’s Hypersequent Calculus. We provide conversions for normalization extending usual conversions for Natural Deduction and prove the existence of normal forms for Hyper Natural Deduction for Gödel Logic. We show that normal deductions satisfy the subformula property. [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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 131588406 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Beckmann%2C+Arnold%22">Beckmann, Arnold</searchLink><relatesTo>1</relatesTo><i> a.beckmann@swansea.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Preining%2C+Norbert%22">Preining, Norbert</searchLink><relatesTo>2</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Logic+%26+Computation%22">Journal of Logic & Computation</searchLink>. Sep2018, Vol. 28 Issue 6, p1125-1187. 63p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Natural+deduction+%28Logic%29%22">Natural deduction (Logic)</searchLink><br /><searchLink fieldCode="DE" term="%22Reasoning%22">Reasoning</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+formulas%22">Mathematical formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Communication%22">Communication</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+logic%22">Mathematical logic</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We introduce a system of Hyper Natural Deduction for Gödel Logic as an extension of Gentzen’s system of Natural Deduction. A deduction in this system consists of a finite set of derivations which uses the typical rules of Natural Deduction, plus additional rules providing means for communication between derivations. We show that our system is sound and complete for infinite-valued propositional Gödel Logic, by giving translations to and from Avron’s Hypersequent Calculus. We provide conversions for normalization extending usual conversions for Natural Deduction and prove the existence of normal forms for Hyper Natural Deduction for Gödel Logic. We show that normal deductions satisfy the subformula property. [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=131588406 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1093/logcom/exy019 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 63 StartPage: 1125 Subjects: – SubjectFull: Natural deduction (Logic) Type: general – SubjectFull: Reasoning Type: general – SubjectFull: Mathematical formulas Type: general – SubjectFull: Communication Type: general – SubjectFull: Mathematical logic Type: general Titles: – TitleFull: Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Beckmann, Arnold – PersonEntity: Name: NameFull: Preining, Norbert IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2018 Type: published Y: 2018 Identifiers: – Type: issn-print Value: 0955792X Numbering: – Type: volume Value: 28 – Type: issue Value: 6 Titles: – TitleFull: Journal of Logic & Computation Type: main |
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