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Classical implication for three-valued logic

Classical implication for three-valued logic
Classical implication for three-valued logic
The article proposes a new implication for three-valued logical systems. The tautologies of this implication are exactly the same as for the classical implication in the two-valued Boolean logic. In the setting of this new implication, the conjunction and disjunction can be viewed as binary modalities. The article studies the definability and complete axiomatisation of the three versions of these modalities capturing Kleene’s, weak Kleene’s, and short-circuit versions of the connectives.
Axiomatisation, Completeness, Three-valued logic
Li, Zhuyu
1e9d3625-ec62-492f-b9c5-2de81db494bc
Naumov, Pavel
8b6c40fb-b199-44d5-a8e2-0ebd021566b0
Li, Zhuyu
1e9d3625-ec62-492f-b9c5-2de81db494bc
Naumov, Pavel
8b6c40fb-b199-44d5-a8e2-0ebd021566b0

Li, Zhuyu and Naumov, Pavel (2025) Classical implication for three-valued logic. Journal of Logic, Language, and Information. (doi:10.1007/s10849-025-09436-w).

Record type: Article

Abstract

The article proposes a new implication for three-valued logical systems. The tautologies of this implication are exactly the same as for the classical implication in the two-valued Boolean logic. In the setting of this new implication, the conjunction and disjunction can be viewed as binary modalities. The article studies the definability and complete axiomatisation of the three versions of these modalities capturing Kleene’s, weak Kleene’s, and short-circuit versions of the connectives.

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More information

Accepted/In Press date: 14 May 2025
Published date: 18 June 2025
Additional Information: Publisher Copyright: © The Author(s) 2025.
Keywords: Axiomatisation, Completeness, Three-valued logic
Learn more about Agents, Interactions and Complexity research

Identifiers

Local EPrints ID: 502304
URI: http://eprints.soton.ac.uk/id/eprint/502304
DOI: doi:10.1007/s10849-025-09436-w
PURE UUID: 3e36e3f0-07e2-4acb-bf7b-5926a24fc000
ORCID for Pavel Naumov: ORCID iD orcid.org/0000-0003-1687-045X

Catalogue record

Date deposited: 20 Jun 2025 16:53
Last modified: 22 Aug 2025 02:34

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Contributors

Author: Zhuyu Li
Author: Pavel Naumov ORCID iD

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