Abstract
In this paper the authors develop a logic of concepts within a mathematical linguistic theory. In the set of concepts defined in a belief system, the order relationship and Boolean algebra of the concepts are considered. This study is designed to obtain a tool, which is the metatheoretical base of this type of theory.
Similar content being viewed by others
References
Aristotle. (1967). The categories. On interpretation. Prior analytics. The Loeb Classical Library. Harvard University Press.
Aristotle. (2009). Aristotle’s Prior Analytics book I: Translated with an introduction and commentary by Gisela Striker. Oxford University Press.
Burris, S. N., & Sankappanavar, H. P. (1982). A Course in Universal Algebra. Berlin: Springer.
Crawley, P., & Dilworth, R. P. (1973). Algebraic Theory of Lattices. Englewood Cliffs, NJ: Prentice-Hall.
Davey, B. A., & Priestley, H. A. (2002). Introduction to lattices and order (2nd ed.). Cambridge: Cambridge University Press.
Erné, M. (2000). Prime ideal theory for general algebras. Applied Categorical Structures,8, 115–144.
Givant, S., & Halmos, P. (2009). Introduction to Boolean algebras. Undergraduate Texts in Mathematics. Berlin: Springer.
Hjelmslev, L. (1968). Structure fondamentale du langage. Paris: Ed. De Minuit. (In French).
Jipsen, P., & Rose, H. (1992). Varieties of lattices (Vol. 1533)., Lecture Notes in Mathematics Berlin: Springer.
Joos, M. (Ed.). (1966). Readings in linguistics I: The development of descriptive Linguistics in America 1925–56 (4th ed.). Chicago, IL: University of Chicago Press.
Nescolarde-Selva, J., & Usó-Doménech, J. (2013). Topological structures of complex belief systems. Complexity,19(1), 46–62.
Nescolarde-Selva, J., & Usó-Doménech, J. L. (2014a). Semiotic vision of ideologies. Foundations of Science,19(3), 263–282.
Nescolarde-Selva, J., & Usó-Doménech, J. L. (2014b). Reality, systems and impure systems. Foundations of Science,19(3), 289–306.
Nescolarde-Selva, J., Usó-Doménech, J. L., & Gash, H. (2014). A theoretical point of view of reality, perception and language. Complexity,20(1), 27–37.
Nescolarde-Selva, J., Usó-Doménech, J. L., & Sabán, M. J. (2015). Linguistic knowledge of reality: A metaphysical impossibility? Foundations of Science,20(1), 27–58.
Newmeyer, F. J. (1991). Functional explanation in linguistics and the origins of language. Language & Communication,11(1–2), 3–28.
O’Brien, J. (2011). The production of reality: Essays and readings on social interaction. Pine Forge Press, an Imprint of SAGE Publications Inc.
Russell, B. (1976). The problems of philosophy. (Reprint ed.). London, Oxford, NY: Oxford University Press.
Whorf, B. L. (1956). Science and Linguistics. In J. B. Carroll (Ed.), Language, thought and reality. Cambridge: Cambridge University Press, MIT Press.
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.
Rights and permissions
About this article
Cite this article
Usó-Doménech, J.L., Nescolarde-Selva, J.A. Mathematical Logic of Notions and Concepts. Found Sci 24, 641–655 (2019). https://doi.org/10.1007/s10699-019-09604-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10699-019-09604-9