Abstract
This paper develops De Morgan-Płonka sums, which generalise Płonka sums to contexts in which negation is not topically transparent but still respects De Morgan duality. We give a general theory of De Morgan-Płonka sums, on the model of the general theory of Płonka sums. Additionally, we describe free De Morgan-Płonka sums and apply our construction to give an algebraic proof of completeness for Kit Fine’s truthmaker semantics for Angell’s logic of analytic containment.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Angell, R.B., Deducibility, Entailment and Analytic Containment, in J. Norman, and R. Sylvan, (eds.), Directions in Relevant Logic, Springer, 1989, pp. 119–143.
Berto, F., Topics of Thought: The Logic of Knowledge, Belief, Imagination, Oxford University Press, 2022.
Berto, F., and D. Nolan, Hyperintensionality, in E. N. Zalta, (ed.), The Stanford Encyclopedia of Philosophy (Summer 2021 ed.), Metaphysics Research Lab, Stanford University, 2021; https://plato.stanford.edu/archives/sum2021/ entries/hyperintensionality/.
Bonzio, S., J. Gil-Férez, F. Paoli, and L. Peruzzi, On paraconsistent Weak Kleene logic: axiomatisation and algebraic analysis, Studia Logica 105(2):253–297, 2017.
Bonzio, S., F. Paoli, and M. Pra Baldi, Logics of Variable Inclusion, vol. 59 of Trends in Logic, Springer, 2022.
Bonzio, S., and M. Pra Baldi, Containment logics: Algebraic completeness and axiomatization, Studia Logica 109(5):969–994, 2021.
Burris, S. and H.P. Sankappanavar, A Course in Universal Algebra, vol. 78 of Graduate Texts in Mathematics, Springer, 1981.
Cabrer, L.M., and H.A. Priestley, A general framework for product representations: bilattices and beyond, Logic Journal of the IGPL 23(5):816–841, 2015.
Dolinka, I., and M. Vinčić, Involutorial płonka sums, Periodica Mathematica Hungarica 46(1):17–31, 2003.
Fine, K., Angellic content, Journal of Philosophical Logic 45(2):199–226, 2016.
Fitting, M., Bilattices are Nice Things, in T. Bolander, V. Hendricks, and S.A. Pedersen, (eds.), Self-Reference, CSLI Publications, 2006, pp. 53–78.
Hawke, P., Theories of Aboutness, Australasian Journal of Philosophy 96(4):697–723, 2018.
Hornischer, L., Logics of Synonymy, Journal of Philosophical Logic 49(4):767–805, 2020.
Parry, W.T., Analytic implication; its history, justification and varietiess, in J. Norman, and R. Sylvan, (eds.), Directions in Relevant Logic, Springer, 1989, pp. 101–118.
Płonka, J., On equational classes of abstract algebras defined by regular equations, Fundamenta Mathematicae 64(2):241–247, 1969.
Randriamahazaka, T., A note on the signed occurrences of propositional variables, The Australasian Journal of Logic 19(1), 2022.
Romanowska, A., On free algebras in some equational classes defined by regular equations, Demonstratio Mathematica 11(4):1131–1138, 1978.
Romanowska, A.B., and J.D. Smith, Bisemilattices of subsemilattices, Journal of Algebra 70(1):78–88, 1981.
Yablo, S., Aboutness, Princeton University Press, 2014.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Special Issue: Strong and weak Kleene logics
Edited by Gavin St. John and Francesco Paoli.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Randriamahazaka, T. De Morgan-Płonka Sums. Stud Logica (2024). https://doi.org/10.1007/s11225-024-10111-7
Published:
DOI: https://doi.org/10.1007/s11225-024-10111-7