Abstract
A qualitative mathematical framework for a granular representation of relational information about general objects, as for examples particles, waves, persons, families, institutions or other systems in discrete or continuous “space-time” is introduced. That leads to a common description of particles and waves in physics, such that the intuitive physical notion of “wave packet” can be captured by the mathematical notion of a general object or a packet in a spatio-temporal Conceptual Semantic System. In these systems particles and waves are defined as special packets. It is proved, that “classical objects” and “classical waves” can be represented as, respectively, particles and waves in spatio-temporal Conceptual Semantic Systems.
The underlying mathematical framework is Formal Concept Analysis and its subdiscipline Temporal Concept Analysis. That allows for describing continuously fine or arbitrarily coarse granularity in the same conceptual framework. The central idea for a “symmetric” description of objects, space, and time is the introduction of “instances” representing information units of observations, connecting the granules for objects, 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
Preview
Unable to display preview. Download preview PDF.
References
Bechstein, L.: Der Wettlauf zwischen dem Hasen und dem Igel. In: Ludwig Bechsteins Märchenbuch. F.W. Hendel Verlag Leipzig, pp. 260–264 (1926)
Butterfield, J. (ed.): The Arguments of Time. Oxford University Press, Oxford (1999)
Castellani, E. (ed.): Interpreting Bodies: Classical and Quantum Objects in Modern Physics. Princeton University Press, Princeton (1998)
Einstein, A.: Zur Elektrodynamik bewegter Körper. Annalen der Physik 17, 891–921 (1905)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)
Gabbay, D.M., Hodkinson, I., Reynolds, M.: Temporal Logic - Mathematical Foundations and Computational Aspects, vol. 1. Clarendon Press, Oxford (1994)
Reichenbach, H.: The Direction of Time. Edited by M. Reichenbach. University of California Press, Berkeley (1991) (Originally published in 1956)
Strahringer, S., Wille, R.: Towards a Structure Theory for Ordinal Data. In: Schader, M. (ed.) Analysing and Modelling Data and Knowledge, pp. 129–139. Springer, Heidelberg (1992)
di Toraldo di Francia, G.: A World of Individual Objects? In: Castellani, E. (ed.) Interpreting Bodies: Classical and Quantum Objects in Modern Physics, pp. 21–29. Princeton University Press, Princeton (1998)
van Benthem, J.: Temporal Logic. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 4, Epistemic and Temporal Reasoning, pp. 241–350. Clarendon Press, Oxford (1995)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, Reidel, Dordrecht-Boston, pp. 445–470 (1982)
Wille, R.: Introduction to Formal Concept Analysis. In: Negrini, G. (ed.) Modelli e modellizzazione. Models and modelling. Consiglio Nazionale delle Ricerche, Instituto di Studi sulli Ricerca e Documentatione Scientifica, Roma, pp. 39–51 (1997)
Wille, R.: Contextual Logic summary. In: Stumme, G. (ed.) Working with Conceptual Structures. Contributions to ICCS 2000, pp. 265–276. Shaker, Aachen (2000)
Wolff, K.E.: A first course in Formal Concept Analysis - How to understand line diagrams. In: Faulbaum, F. (ed.) SoftStat 1993, Advances in Statistical Software 4, pp. 429–438. Gustav Fischer Verlag, Stuttgart (1994)
Wolff, K.E.: Concepts, States, and Systems. In: Dubois, D.M. (ed.) Computing Anticipatory Systems. CASYS 1999 - Third International Conference, Liège, Belgium, 1999, American Institute of Physics, Conference Proceedings 517, pp. 83–97 (2000)
Wolff, K.E.: Towards a Conceptual System Theory. In: Sanchez, B., Nada, N., Rashid, A., Arndt, T., Sanchez, M. (eds.) Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics, SCI 2000, Information Systems Development, International Institute of Informatics and Systemics, vol. II, pp. 124–132 (2000)
Wolff, K.E.: Temporal Concept Analysis. In: Mephu Nguifo, E., et al. (eds.) ICCS- 2001 International Workshop on Concept Lattices-Based Theory, Methods and Tools for Knowledge Discovery in Databases, Stanford University, Palo Alto (CA), pp. 91–107 (2001)
Wolff, K.E.: Transitions in Conceptual Time Systems. In: Dubois, D.M. (ed.) International Journal of Computing Anticipatory Systems, CHAOS 2002, vol. 11, pp. 398–412 (2002)
Wolff, K.E.: Interpretation of Automata in Temporal Concept Analysis. In: Priss, U., Corbett, D.R., Angelova, G. (eds.) ICCS 2002. LNCS (LNAI), vol. 2393, pp. 341–353. Springer, Heidelberg (2002)
Wolff, K.E., Yameogo, W.: Time Dimension, Objects, and Life Tracks - A Conceptual Analysis. In: Ganter, B., de Moor, A., Lex, W. (eds.) ICCS 2003. Lecture Notes in Computer Science (LNAI), vol. 2746, pp. 188–200. Springer, Heidelberg (2003)
Wolff, K.E.: Towards a Conceptual Theory of Indistinguishable Objects. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 180–188. Springer, Heidelberg (2004)
Wolff, K.E.: Temporal Concept Analysis - States, Transitions, Life Tracks. Preprint Darmstadt University of Applied Sciences, Mathematics and Science Faculty (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wolff, K.E. (2004). ‘Particles’ and ‘Waves’ as Understood by Temporal Concept Analysis. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds) Conceptual Structures at Work. ICCS 2004. Lecture Notes in Computer Science(), vol 3127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27769-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-27769-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22392-4
Online ISBN: 978-3-540-27769-9
eBook Packages: Springer Book Archive