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Permanent link (DOI): https://doi.org/10.7939/R3M90292C

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Paraconsistent Logic for Dialethic Arithmetics Open Access

Descriptions

Other title
Subject/Keyword
Non-standard Models of Arithmetic
Paraconsistent Logic
Logic
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Tedder, Andrew J
Supervisor and department
Bimbo, Katalin (Philosophy)
Examining committee member and department
Pelletier, Jeff (Philosophy)
Hazen, Allen (Philosophy)
Galvani, Valentina (Economics)
Department
Department of Philosophy
Specialization

Date accepted
2014-06-27T14:40:35Z
Graduation date
2014-11
Degree
Master of Arts
Degree level
Master's
Abstract
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.
Language
English
DOI
doi:10.7939/R3M90292C
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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