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

  • Logic
  • Non-standard Models of Arithmetic
  • Paraconsistent Logic

• Graduation date

  Fall 2014

• 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.