• DocumentCode
    728999
  • Title

    Hyper Natural Deduction

  • Author

    Beckmann, Arnold ; Preining, Norbert

  • Author_Institution
    Swansea Univ., Swansea, UK
  • fYear
    2015
  • fDate
    6-10 July 2015
  • Firstpage
    547
  • Lastpage
    558
  • 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 Gödel 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.
  • Keywords
    formal logic; Avron hypersequent calculus; Gentzen natural deduction system; hypernatural deduction system; infinite-valued propositional Gödel logic; Calculus; Cost accounting; Electronic mail; Linearity; Programming; Semantics; Gödel Logic; Hyper Natural Deduction; Hyper Sequent Calculus; Natural Deduction; Normalisation;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Logic in Computer Science (LICS), 2015 30th Annual ACM/IEEE Symposium on
  • Conference_Location
    Kyoto
  • ISSN
    1043-6871
  • Type

    conf

  • DOI
    10.1109/LICS.2015.57
  • Filename
    7174911
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=728999