Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoning. (23rd July 2018)

• Record Type: Journal Article
• Authors: Beckmann, Arnold; Preining, Norbert
• Is Part Of: Journal of logic and computation. Volume 28:Number 6(2018)
• Page Start: 1125
• Page End: 1187
• Publication Date: 2018-07-23
• Subjects: Logic programming -- Periodicals; Logic, Symbolic and mathematical -- Periodicals; Computational complexity -- Periodicals; 005.115
• DOI: 10.1093/logcom/exy019
• Languages: English
• ISSNs: 0955-792X

Abstract

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.