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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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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.
College: Faculty of Science and Engineering
Issue: 6
Start Page: 1125
End Page: 1187