Abstract
A logic family is a bunch of logics that belong together in some way. First-order logic is one of the examples. Logics organized into a structure occur in abstract model theory, institution theory and in algebraic logic. Logic families play a role in adopting methods for investigating sentential logics to first-order like logics. We thoroughly discuss the notion of logic families as defined in the recent Universal Algebraic Logic book.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Andréka, H., Z. Gyenis, I. Németi, and I. Sain, Universal Algebraic Logic, Birkhauser, 2022.
Andréka, H., A. Kurucz, I. Németi, and I. Sain, Applying algebraic logic; A general methodology, Lecture Notes of the Summer School “Algebraic Logic and the Methodology of Applying it”, Budapest 1994.
Andréka, H., I. Németi, and I. Sain, Algebraic Logic, in D. M. Gabbay and F. Guenthner, (eds.), Handbook of philosophical logic Vol. II, 2nd edn. Kluwer Academic Publishers, 2001, pp. 133–247.
Barwise, J., Axioms for abstract model theory, Annals of Mathematical Logic 7:221–265, 1974.
Bergman, C.H., Universal Algebra: Fundamentals and Selected Topics, Chapman and Hall, 2011.
Beziau, J.-Y., and M.F. Coniglio, Combining conjunction with disjunction, in B. Prasad (ed.), Proceedings of the 2nd Indian International Conference on Artificial Intelligence (IICAI 2005), Pune, India, IICAI, pp. 1648–1658.
Blok, W., and E. Hoogland, The Beth property in algebraic logic, Studia Logica 83: 49–90, 2006.
Blok,W., and D. Pigozzi, Algebraizable logics, vol. 77, no. 396 of Memoirs of the American Mathematical Society, Providence, Rhode Island, 1989.
Chang, C.C., and H.J. Keisler, Model theory, North���Holland, 1990.
Czelakowski, J., and W. Dziobak, On truth-schemes for intensional logics, Reports on Mathematical Logic 41:151–171, 2006.
Diaconescu, R., Institution-independent model theory, Birkhauser, Basel, Switzerland, 2008.
Diaconescu, R., The axiomatic approach to non-classical model theory,Mathematics 10:3428, 2022.
Enderton, H., A mathematical introduction to logic, Academic Press, 1972.
Font, J.M., Abstract Algebraic Logic. An introductory textbook, College Publications, 2016.
Font, J.M., and R. Jansana, On the Sentential Logics Associated with algebraizable and Semi-nice General Logic, Bulletin of the IGPL 2(1):55–76, 1994.
Goguen, J., and R. Burstall, Institutions: abstract model theory for specification and programming, Journal of the Association for Computing Machinery 39:95–146, 1992.
Gyenis, Z., and Ö. Öztürk, Amalgamation and Robinson property in Universal Algebraic Logic, Logic Journal of IGPL, Online first, 2022.
Gabbay, D., Fibring logics, Clarendon Press, 1998.
Henkin, L., J.D. Monk, and A. Tarski, Cylindric Algebras Parts I, II, North Holland, Amsterdam, 1971, 1985.
Hoogland, E., Algebraic characterizations of various Beth definability properties, Studia Logica 65:91–112, 2000.
Labai, N., and J. Makowsky, Logics with finite Hankel rank, in Fields of logic and computation II: Essays dedicated to Yuri Gurevich on the occasion of his 75th birthday, Springer, 2015, pp. 237–252.
Łos, J. Free product in general algebra, in J.W. Addison, L. Henkink, and A. Tarski, (eds.), The theory of models, Proceedings of the 1963 International Symposium at Berkeley, North-Holland, Amsterdam, 1965, pp. 229–237.
Meseguer, J., General logics, in H.-D. Ebbinghaus, J. Fernandez-Prida, M. Garrido, D. Lascar, and M. Rodriquez Artalejo, (eds.), Logic Colloquium ’87, vol. 129 of Studies in Logic and the Foundations of Mathematics, Elsevier, 1989, pp. 275–329.
Mundici, D., Robinson’s consistency theorem in soft model theory, Transactions of the American Mathematical Society 263:231–241, 1981.
Öztürk, Ö.,On Interpolation in Universal Algebraic Logic, PhD thesis, Eötvös Loránd University, 2024.
Pigozzi, D., Amalgamation, congruence-extension, and interpolation properties in algebras, Algebra Universalis 1:269–349, 1972.
Sannella, D., and A. Tarlecki, Foundations of Algebraic Specifications and Formal Software Development, Springer, 2012.
Tarski, A., and S. Givant, A Formalization of Set Theory without Variables, vol. 41 of Colloquium Publications of the AMS, Providence, Rhode Island, 1987.
Voutsadakis, G., Categorical abstract algebraic logic: computability operators and correspondence theorems, in J. Czelakowski, (ed.) Don Pigozzi on abstract algebraic logic, universal algebra and computer science, Springer, Cham, 2018, pp. 421–454.
Acknowledgements
We wish to express our gratitude towards the anonymous referee for the careful reading of the manuscript and the helpful suggestions. Zalán Gyenis was supported by the grant 2019/34/E/HS1/00044 of the National Science Centre (Poland), and by the grant of the Hungarian National Research, Development and Innovation Office, contract number: K-134275.
Funding
Open access funding provided by HUN-REN Alfréd Rényi Institute of Mathematics.
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.
Presented by Daniele Mundici
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
Andréka, H., Gyenis, Z., Németi, I. et al. Logic Families. Stud Logica (2024). https://doi.org/10.1007/s11225-024-10125-1
Received:
Published:
DOI: https://doi.org/10.1007/s11225-024-10125-1