Journal article 908 views 251 downloads
Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning
Journal of Logic and Computation, Volume: 28, Issue: 6, Pages: 1125 - 1187
Swansea University Author: Arnold Beckmann
-
PDF | Accepted Manuscript
Download (792.88KB)
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...
Published in: | Journal of Logic and Computation |
---|---|
ISSN: | 0955-792X 1465-363X |
Published: |
2018
|
Online Access: |
Check full text
|
URI: | https://cronfa.swan.ac.uk/Record/cronfa40432 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
first_indexed |
2018-05-27T19:01:25Z |
---|---|
last_indexed |
2023-02-15T03:49:48Z |
id |
cronfa40432 |
recordtype |
SURis |
fullrecord |
<?xml version="1.0"?><rfc1807><datestamp>2023-02-14T15:38:33.4520536</datestamp><bib-version>v2</bib-version><id>40432</id><entry>2018-05-27</entry><title>Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning</title><swanseaauthors><author><sid>1439ebd690110a50a797b7ec78cca600</sid><ORCID>0000-0001-7958-5790</ORCID><firstname>Arnold</firstname><surname>Beckmann</surname><name>Arnold Beckmann</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2018-05-27</date><deptcode>SCS</deptcode><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><type>Journal Article</type><journal>Journal of Logic and Computation</journal><volume>28</volume><journalNumber>6</journalNumber><paginationStart>1125</paginationStart><paginationEnd>1187</paginationEnd><publisher/><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0955-792X</issnPrint><issnElectronic>1465-363X</issnElectronic><keywords/><publishedDay>23</publishedDay><publishedMonth>7</publishedMonth><publishedYear>2018</publishedYear><publishedDate>2018-07-23</publishedDate><doi>10.1093/logcom/exy019</doi><url/><notes/><college>COLLEGE NANME</college><department>Computer Science</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SCS</DepartmentCode><institution>Swansea University</institution><apcterm/><funders/><projectreference/><lastEdited>2023-02-14T15:38:33.4520536</lastEdited><Created>2018-05-27T15:20:12.8145472</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Computer Science</level></path><authors><author><firstname>Arnold</firstname><surname>Beckmann</surname><orcid>0000-0001-7958-5790</orcid><order>1</order></author><author><firstname>Norbert</firstname><surname>Preining</surname><order>2</order></author></authors><documents><document><filename>0040432-27052018152319.pdf</filename><originalFilename>Beckmann-Preining-HND-final.pdf</originalFilename><uploaded>2018-05-27T15:23:19.7370000</uploaded><type>Output</type><contentLength>717803</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2019-07-23T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807> |
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 |
active_str |
0 |
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 |
_version_ |
1763752532118601728 |
score |
11.016235 |