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Paraconsistent Logic for Dialethic Arithmetics

  • Author / Creator
    Tedder, Andrew J
  • Inconsistent and collapse models of arithmetic are presented in the language and semantics of the simple paraconsistent logic LP. I present a logic which extends LP by the addition of a sensible conditional connective and quantifiers. This logic, called A 3 , is specified as a Hilbert style axiom system and a Gentzen-style sequent calculus, and these systems are shown to be equivalent. I show the sequent calculus to be sound and complete for the A3 semantics and prove the elimination theorem. Finally, I specify arithmetical axiom systems for the collapse models and show that these axiom systems capture some salient properties of their associated models.

  • Subjects / Keywords
  • Graduation date
    2014-11
  • Type of Item
    Thesis
  • Degree
    Master of Arts
  • DOI
    https://doi.org/10.7939/R3M90292C
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Philosophy
  • Supervisor / co-supervisor and their department(s)
    • Bimbo, Katalin (Philosophy)
  • Examining committee members and their departments
    • Pelletier, Jeff (Philosophy)
    • Galvani, Valentina (Economics)
    • Hazen, Allen (Philosophy)