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Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning
Arnold Beckmann 
,
Norbert Preining
,
Norbert Preining
Journal of Logic and Computation, Volume: 28, Issue: 6, Pages: 1125 - 1187
Swansea University Author:
Arnold Beckmann
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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...
| Published in: | Journal of Logic and Computation |
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| ISSN: | 0955-792X 1465-363X |
| Published: |
2018
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa40432 |
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| 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. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
6 |
| Start Page: |
1125 |
| End Page: |
1187 |