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THE EXTERNAL VERSION OF A SUBCLASSICAL LOGIC

Part of: Philosophical aspects of logic and foundations Algebraic logic

Published online by Cambridge University Press:  12 November 2025

MASSIMILIANO CARRARA Open the ORCID record for MASSIMILIANO CARRARA [Opens in a new window]  and
MICHELE PRA BALDI Open the ORCID record for MICHELE PRA BALDI [Opens in a new window]
MASSIMILIANO CARRARA
Affiliation:
DEPARTMENT OF PHILOSOPHY, SOCIOLOGY, PEDAGOGY, AND APPLIED PSYCHOLOGY UNIVERSITY OF PADUA ITALY E-mail: massimiliano.carrara@unipd.it
MICHELE PRA BALDI*
Affiliation:
DEPARTMENT OF PHILOSOPHY, SOCIOLOGY, PEDAGOGY, AND APPLIED PSYCHOLOGY UNIVERSITY OF PADUA ITALY E-mail: massimiliano.carrara@unipd.it
*
E-mail: michele.prabaldi@unipd.it
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Abstract

A three-valued logic is subclassical when it is defined by a single matrix having the classical two-element matrix as a subreduct. In this case, the language of can be expanded with special unary connectives, called external operators. The resulting logic is called the external version of , a notion originally introduced by D. Bochvar in 1938 with respect to his weak Kleene logic. In this paper we study the semantic properties of the external version of a three-valued subclassical logic . We determine sufficient and necessary conditions to turn a model of into a model of . Moreover, we establish some distinctive semantic properties of .

Keywords

three-valued logicsBochvar external logicalgebraic logic

MSC classification

Primary: 03A05: Philosophical and critical 03G25: Other algebras related to logic

Information

Type
Research Article
Information
The Review of Symbolic Logic , First View , pp. 1 - 17
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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