Hyper Natural Deduction

descriptionPublicationkeyboard_double_arrow_right Article , Conference object 01 Jul 2015 United Kingdom Publisher:IEEEJournal:2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

Authors: Arnold Beckmann; Norbert Preining;

doi: 10.1109/lics.2015.57

Hyper Natural Deduction

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Abstract

We introduce a Hyper Natural Deduction system as an extension of Gentzen's Natural Deduction system. A Hyper Natural Deduction consists of a finite set of derivations which may use, beside typical Natural Deduction rules, additional rules providing means for communication between derivations. We show that our Hyper Natural Deduction system is sound and complete for infinite-valued propositional Godel Logic, by giving translations to and from Avron's Hyper sequent Calculus. We also provide conversions for normalisation and prove the existence of normal forms for our Hyper Natural Deduction system.

Country

United Kingdom

Related Organizations

Japan Advanced Institute of Science and Technology
Japan
Swansea University
United Kingdom

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