Twist-Valued Models for Three-Valued Paraconsistent Set Theory

Logic and Logical Philosophy:1 (forthcoming)
  Copy   BIBTEX

Abstract

We propose in this paper a family of algebraic models of ZFC based on the three-valued paraconsistent logic LPT0, a linguistic variant of da Costa and D’Ottaviano’s logic J3. The semantics is given by twist structures defined over complete Boolean agebras. The Boolean-valued models of ZFC are adapted to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. This allows for inconsistent sets w satisfying ‘not (w = w)’, where ‘not’ stands for the paraconsistent negation. Finally, our framework is adapted to provide a class of twist-valued models generalizing Löwe and Tarafder’s model based on logic (PS 3,∗), showing that they are paraconsistent models of ZFC. The present approach offers more options for investigating independence results in paraconsistent set theory.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,168

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Finitely many-valued paraconsistent systems.Roman Tuziak - 1997 - Logic and Logical Philosophy 5:121-127.
Heyting-valued interpretations for constructive set theory.Nicola Gambino - 2006 - Annals of Pure and Applied Logic 137 (1-3):164-188.
Ideal Paraconsistent Logics.O. Arieli, A. Avron & A. Zamansky - 2011 - Studia Logica 99 (1-3):31-60.
N-valued maximal paraconsistent matrices.Adam Trybus - 2019 - Journal of Applied Non-Classical Logics 29 (2):171-183.
Truth and the Liar in De Morgan-Valued Models.Hannes Leitgeb - 1999 - Notre Dame Journal of Formal Logic 40 (4):496-514.
Self-Extensional Three-Valued Paraconsistent Logics.Arnon Avron - 2017 - Logica Universalis 11 (3):297-315.

Analytics

Added to PP
2020-08-13

Downloads
7 (#1,044,287)

6 months
4 (#183,048)

Historical graph of downloads
How can I increase my downloads?