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Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning

Arnold Beckmann Orcid Logo, Norbert Preining

Journal of Logic and Computation, Volume: 28, Issue: 6, Pages: 1125 - 1187

Swansea University Author: Arnold Beckmann Orcid Logo

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DOI (Published version): 10.1093/logcom/exy019

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 be...

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Published in: Journal of Logic and Computation
ISSN: 0955-792X 1465-363X
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa40432
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first_indexed 2018-05-27T19:01:25Z
last_indexed 2023-02-15T03:49:48Z
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spelling 2023-02-14T15:38:33.4520536 v2 40432 2018-05-27 Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning 1439ebd690110a50a797b7ec78cca600 0000-0001-7958-5790 Arnold Beckmann Arnold Beckmann true false 2018-05-27 SCS 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. Journal Article Journal of Logic and Computation 28 6 1125 1187 0955-792X 1465-363X 23 7 2018 2018-07-23 10.1093/logcom/exy019 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2023-02-14T15:38:33.4520536 2018-05-27T15:20:12.8145472 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Arnold Beckmann 0000-0001-7958-5790 1 Norbert Preining 2 0040432-27052018152319.pdf Beckmann-Preining-HND-final.pdf 2018-05-27T15:23:19.7370000 Output 717803 application/pdf Accepted Manuscript true 2019-07-23T00:00:00.0000000 true eng
title Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning
spellingShingle Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning
Arnold Beckmann
title_short Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning
title_full Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning
title_fullStr Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning
title_full_unstemmed Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning
title_sort Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning
author_id_str_mv 1439ebd690110a50a797b7ec78cca600
author_id_fullname_str_mv 1439ebd690110a50a797b7ec78cca600_***_Arnold Beckmann
author Arnold Beckmann
author2 Arnold Beckmann
Norbert Preining
format Journal article
container_title Journal of Logic and Computation
container_volume 28
container_issue 6
container_start_page 1125
publishDate 2018
institution Swansea University
issn 0955-792X
1465-363X
doi_str_mv 10.1093/logcom/exy019
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 1
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description 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.
published_date 2018-07-23T03:51:30Z
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score 11.014291

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