Abstract
The notion of causality is very important in many applications areas. Because of this importance, there are several formalizations of this notion in physics and in AI. Most of these definitions describe causality as a crisp (“yes”-“no”) relation between two events or two processes – cause and effect. However, such descriptions do not fully capture the intuitive idea of causality: first, often, several conditions are needed to be present for an effect to occur, and, second, the effect is often a matter of degree. In this paper, we show how to modify the current description of causality so as to take both these phenomena into account – in particular, by extending the notion of directed acyclic graph to hypergraphs. As a somewhat unexpected side effect of our analysis, we get a natural explanation of why, in contrast to space-time of Special Relativity – in which division into space and time depends on the observer, in cosmological solutions there is a clear absolute separation between space and time.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Belohlavek, R., Dauben, J.W., Klir, G.J.: Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York (2017)
Feynman, R., Leighton, R., Sands, M.: The Feynman Lectures on Physics. Addison Wesley, Boston (2005)
Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River (1995)
Kreinovich, V., Ortiz, A.: Towards a better understanding of space-time causality: Kolmogorov complexity and causality as a matter of degree. In: Proceedings of the Joint World Congress of the International Fuzzy Systems Association and Annual Conference of the North American Fuzzy Information Processing Society IFSA/NAFIPS 2013, Edmonton, Canada, 24–28 June 2013, pp. 1349–1353 (2013)
Kreinovich, V., Kosheleva, O., Ortiz-Muñoz, A.: Need for simplicity and everything is a matter of degree: how Zadeh’s philosophy is related to Kolmogorov complexity, quantum physics, and deep learning. In: Shahbazova, S.N., Abbasov, A.M., Kreinovich, V., Kacprzyk, J., Batyrshin, I.Z. (eds.) Recent Developments and the New Directions of Research, Foundations, and Applications. STUDFUZZ, vol. 422, pp. 203–216. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-20153-0_16
Mendel, J.M.: Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions. Springer, Cham (2017)
Nguyen, H.T., Walker, C.L., Walker, E.A.: A First Course in Fuzzy Logic. Chapman and Hall/CRC, Boca Raton (2019)
Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Boston (1999)
Pearl, J.: Causality: Models, Reasoning and Inference. Cambridge University Press, Cambridge (2009)
Pimenov, R.I.: Kinematic Spaces: Mathematical Theory of Space-Time. Consultants Bureau, New York (1970)
Thorne, K.S., Blandford, R.D.: Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. Princeton University Press, Princeton (2021)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Acknowledgments
This work was supported in part by the National Science Foundation grants 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science), HRD-1834620 and HRD-2034030 (CAHSI Includes), and by the AT &T Fellowship in Information Technology.
It was also supported by the program of the development of the Scientific-Educational Mathematical Center of Volga Federal District No. 075-02-2020-1478, and by a grant from the Hungarian National Research, Development and Innovation Office (NRDI).
The authors are thankful to Art Duval and Razieh Nabi for valuable discussions, and to the anonymous referees for useful suggestions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Joslyn, C., Ortiz-Muñoz, A., Rodriguez Velasquez, E.D., Kosheleva, O., Kreinovich, V. (2023). Causality: Hypergraphs, Matter of Degree, Foundations of Cosmology. In: Cohen, K., Ernest, N., Bede, B., Kreinovich, V. (eds) Fuzzy Information Processing 2023. NAFIPS 2023. Lecture Notes in Networks and Systems, vol 751. Springer, Cham. https://doi.org/10.1007/978-3-031-46778-3_26
Download citation
DOI: https://doi.org/10.1007/978-3-031-46778-3_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-46777-6
Online ISBN: 978-3-031-46778-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)