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UNIVOCITY OF INTUITIONISTIC AND CLASSICAL CONNECTIVES

Part of: General logic Proof theory and constructive mathematics

Published online by Cambridge University Press:  26 December 2024

RODOLFO C. ERTOLA-BIRABEN Open the ORCID record for RODOLFO C. ERTOLA-BIRABEN [Opens in a new window]  and
BRANDEN FITELSON Open the ORCID record for BRANDEN FITELSON [Opens in a new window]
RODOLFO C. ERTOLA-BIRABEN
Affiliation:
CENTRE FOR LOGIC EPISTEMOLOGY AND THE HISTORY OF SCIENCE (CLE) UNIVERSIDADE ESTADUAL DE CAMPINAS (UNICAMP) SÉRGIO BUARQUE DE HOLANDA 251 PO BOX 13083-859 CAMPINAS, SP BRAZIL E-mail: rcertola@unicamp.br
BRANDEN FITELSON*
Affiliation:
DEPARTMENT OF PHILOSOPHY AND RELIGION NORTHEASTERN UNIVERSITY 360 HUNTINGTON AVENUE BOSTON, MA 02115 USA
*
E-mail: b.fitelson@northeastern.edu
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Abstract

This paper investigates the univocity (or uniqueness) of connectives in intuitionistic and classical sentential logic. Specifically, unlike Gentzen systems, Hilbert systems for (various fragments of) intuitionistic and classical logic do not always determine univocal (or unique) conditional connectives. This paper explains when univocal conditional connectives are achieved in Hilbert systems for intuitionistic and classical sentential logic (and when they are not). In the final section, we discuss the (non-)univocity of the Sheffer stroke in Hilbert vs. Gentzen systems for classical sentential logic.

Keywords

univocal connectivesintuitionistic logicclassical logic

MSC classification

Primary: 03F03: Proof theory, general 03B05: Classical propositional logic 03B20: Subsystems of classical logic (including intuitionistic logic)

Information

Type
Article
Information
Bulletin of Symbolic Logic , Volume 31 , Issue 3 , September 2025 , pp. 488 - 497
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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