Boolean negation and non-conservativity III: the Ackermann constant

Logic Journal of the IGPL 29 (3):370-384 (2021)
  Copy   BIBTEX

Abstract

It is known that many relevant logics can be conservatively extended by the truth constant known as the Ackermann constant. It is also known that many relevant logics can be conservatively extended by Boolean negation. This essay, however, shows that a range of relevant logics with the Ackermann constant cannot be conservatively extended by a Boolean negation.

Categories

Keywords

Reprint years

DOI

10.1093/jigpal/jzaa021

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,881

External links

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

Through your library

My notes

Similar books and articles

Constant Domain Quantified Modal Logics Without Boolean Negation.Greg Restall - 2005 - Australasian Journal of Logic 3:45-62.
Boolean Conservative Extension Results for some Modal Relevant Logics.Edwin D. Mares & Koji Tanaka - 2011 - Australasian Journal of Logic 8 (5):31-49.
An Admissible Semantics for Propositionally Quantified Relevant Logics.Robert Goldblatt & Michael Kane - 2010 - Journal of Philosophical Logic 39 (1):73-100.
Completeness and conservative extension results for some Boolean relevant logics.Steve Giambrone & Robert K. Meyer - 1989 - Studia Logica 48 (1):1 - 14.
Converse Ackermann property and constructive negation defined with a negation connective.Gemma Robles & José M. Méndez - 2006 - Logic and Logical Philosophy 15 (2):113-130.
Conservativity of Heyting implication over relevant quantification.Robert Goldblatt - 2009 - Review of Symbolic Logic 2 (2):310-341.
A Routley-Meyer semantics for relevant logics including TWR plus the disjunctive syllogism.Gemma Robles & José M. Méndez - 2011 - Logic Journal of the IGPL 19 (1):18-32.
Three-valued Kripke-style Semantics For Pseudo- And Weak-boolean Logics.Eunsuk Yang - 2012 - Logic Journal of the IGPL 20 (1):187-206.
Simplified semantics for relevant logics (and some of their rivals).Greg Restall - 1993 - Journal of Philosophical Logic 22 (5):481 - 511.
Residuated fuzzy logics with an involutive negation.Francesc Esteva, Lluís Godo, Petr Hájek & Mirko Navara - 2000 - Archive for Mathematical Logic 39 (2):103-124.
Where gamma fails.Robert K. Meyer, Steve Giambrone & Ross T. Brady - 1984 - Studia Logica 43 (3):247 - 256.
A Canonical Model Construction For Substructural Logics With Strong Negation.N. Kamide - 2002 - Reports on Mathematical Logic:95-116.
Admissibility of Ackermann's rule δ in relevant logics.Gemma Robles - 2013 - Logic and Logical Philosophy 22 (4):411-427.
Negation introduced with the unary connective.Gemma Robles - 2009 - Journal of Applied Non-Classical Logics 19 (3):371-388.
Lewis Dichotomies in Many-Valued Logics.Simone Bova - 2012 - Studia Logica 100 (6):1271-1290.

Analytics

Added to PP
2020-07-14

Downloads
41 (#388,316)

6 months
13 (#194,844)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Tore Fjetland Øgaard
University of Bergen

Citations of this work

Add more citations

References found in this work

Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
Begründung einer strengen Implikation.Wilhelm Ackermann - 1956 - Journal of Symbolic Logic 21 (2):113-128.
Classical relevant logics II.Robert K. Meyer & Richard Routley - 1974 - Studia Logica 33 (2):183 - 194.
Simplified semantics for relevant logics (and some of their rivals).Greg Restall - 1993 - Journal of Philosophical Logic 22 (5):481 - 511.

View all 16 references / Add more references