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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-021-00806-2
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Abstract
Structural reasoning is simply reasoning that is governed exclusively by structural rules. In this context a proof system can be said to be structural if all of its inference rules are structural. A logic is considered to be structuralizable if it can be equipped with a sound and complete structural proof system. This paper provides a general formulation of the problem of structuralizability of a given logic, giving specific consideration to a family of logics that are based on the Dunn–Belnap four-valued semantics. It is shown how sound and complete structural proof systems can be constructed for a spectrum of logics within different logical frameworks.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Jul 1, 2022
Keywords: Structural reasoning; Structural systems; Cut rule; Dunn-Belnap’s four-valued logics; Consequence systems; 03F03; 03F07; 03B35; 03B47; 03B70