Extensions of Hałkowska–Zajac's three-valued paraconsistent logic

Archive for Mathematical Logic 41 (3):299-307 (2002)
  Copy   BIBTEX

Abstract

As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we prove that extensions of the logic involved form a four-element chain, the only proper consistent extensions being the least non-paraconsistent extension of it and the classical logic. RID=""ID="" Mathematics Subject Classification (2000): 03B50, 03B53, 03G10 RID=""ID="" Key words or phrases: Many-valued logic – Paraconsistent logic – Extension – Prevariety – Distributive lattice

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,202

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

Ideal Paraconsistent Logics.O. Arieli, A. Avron & A. Zamansky - 2011 - Studia Logica 99 (1-3):31-60.
Finitely many-valued paraconsistent systems.Roman Tuziak - 1997 - Logic and Logical Philosophy 5:121-127.
How to avoid deviance (in logic).Walter Sinnott-Armstrong & Amit Malhotra - 2002 - History and Philosophy of Logic 23 (3):215--36.
Introducción a las lógicas no clásicas.Lorenzo Peña - 1993 - Universidad Nacional Autónoma de México.
Paraconsistency Everywhere.Greg Restall - 2002 - Notre Dame Journal of Formal Logic 43 (3):147-156.

Analytics

Added to PP
2013-11-23

Downloads
15 (#889,556)

6 months
7 (#339,156)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Subquasivarieties of implicative locally-finite quasivarieties.Alexej P. Pynko - 2010 - Mathematical Logic Quarterly 56 (6):643-658.
N-valued maximal paraconsistent matrices.Adam Trybus - 2019 - Journal of Applied Non-Classical Logics 29 (2):171-183.

Add more citations

References found in this work

Add more references