Abstract
We define a concept of truthmaker function, and prove the functional completeness, w.r.t. truthmaker functions in this sense, of a set of four-valued functions corresponding to standard connectives of the system of relevance logic known as First-Degree Entailment or Belnap–Dunn logic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Availability of Data and Materials
Not applicable.
References
Arieli, O., & Avron, A. (2017). Four-valued paradefinite logics. Studia Logica, 105, 1087–1122.
Batchelor, R. (2022). Directional Deduction. arXiv:2208.03925.
Bodnarchuk, V. G., Kaluzhnin, L. A., Kotov, V. N., & Romov, B. A. (1969). Galois theory for Post algebras. Cybernetics, 5, 243–252 (Part I) & 531–539 (Part II).
East, J., Egri-Nagy, A., & Mitchell, J. D. (2017). Enumerating transformation semigroups. Semigroup Forum, 95, 109–125.
Ferguson, T. M. (2016). Faulty Belnap computers and subsystems of FDE. Journal of Logic and Computation, 26, 1617–1636.
Fine, K. (2016). Angellic content. Journal of Philosophical Logic, 45, 199–226.
Lau, D. (2006). Function Algebras on Finite Sets: A Basic Course on Many-Valued Logic and Clone Theory. Springer.
Omori, H., & Wansing, H. (2017). 40 years of FDE: An introductory overview. Studia Logica, 105, 1021–1049.
Post, E. L. (1941). The Two-Valued Iterative Systems of Mathematical Logic. Princeton University Press.
Zach, R. (2023). An epimorphism between Fine and Ferguson’s matrices for Angell’s AC. Logic and Logical Philosophy, 32, 161–179.
Funding
None.
Author information
Authors and Affiliations
Contributions
Not applicable.
Corresponding author
Ethics declarations
Ethical Approval
Not applicable.
Competing Interests
None.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Batchelor, R. First-Degree Entailment and Truthmaker Functions. J Philos Logic 53, 373–390 (2024). https://doi.org/10.1007/s10992-023-09734-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-023-09734-3