Abstract
Our classical understanding of objects in spatiotemporal systems is based on the idea that such an object is at each moment at exactly one place. As long as the notions of “moment” and “place” are not made explicit in their granularity the meaning of that idea is not clear. It became clear by the introduction of Conceptual Time Systems with Actual Objects and a Time Relation (CTSOT) using an explicit granularity description for space and time and an object representation such that each object is at each moment in exactly one state – where the states are formal concepts of the CTSOT.
For the purpose of introducing also a granularity tool for the objects the author has defined Conceptual Semantic Systems where relational information is combined with the granularity tool of conceptual scales. That led to a mathematical definition of particles and waves such that the usual notions of particles and waves in physics are covered. Waves and wave packets are “distributed objects” in the sense that they may appear simultaneously at several places.
Now the question arises how to introduce a mathematical notion for the “state of a distributed object”, as for example the state of an electron or the state of an institution, in the general framework of Conceptual Semantic Systems. That question is answered in this paper by the introduction of the notion of the “aspect of a concept \(\textbf{c}\) with respect to some view Q”, in short “the Q-aspect of \(\textbf{c}\)” which is defined as a suitable set of formal concepts. For spatiotemporal Conceptual Semantic Systems the state of an object \(\textbf{p}\) at a time granule \(\textbf{t}\) is defined as the spatial aspect of the infimum of “realizations” of \(\textbf{p}\) and \(\textbf{t}\). The one-element states of “actual objects” in a CTSOT are special cases of these states which may have many elements.
The information units (instances) of a Conceptual Semantic System connect the concepts of different semantical scales, for example scales for objects, space, and time. That allows for defining the information distribution of the Q-aspect of a distributed object \(\textbf{c}\) which leads to a mathematical definition of the “BORN-frequency”; that is defined as a relative frequency of information units which can be understood as a very meaningful mathematical representation of the famous “probability distribution of a quantum mechanical system”.
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References
Bohm, D.: A suggested interpretation of the quantum theory in terms of “hidden” variables. Phys. Rev. 85 (1952)
Born, M.: Die statistische Deutung der Quantenmechanik. Nobelvortrag. In: [Bo63], II, 430-441. English translation: The statistical interpretation of quantum mechanics. Nobel Lecture, December 11 (1954), http://nobelprize.org/physics/laureates/1954/born-lecture.html
Born, M.: Ausgewählte Abhandlungen. Vandenhoeck and Ruprecht, Göttingen (1963)
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)
Dürr, D.: Bohmsche Mechanik als Grundlage der Quantenmechanik. Springer, Berlin (2001)
Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer, Heidelberg (1996); German version: Formale Begriffsanalyse: Mathematische Grundlagen. Springer, Heidelberg (1996)
de Moor, A., Lex, W., Ganter, B. (eds.): ICCS 2003. LNCS, vol. 2746. Springer, Heidelberg (2003)
Kuchar, K.: The Problem of Time in Quantum Geometrodynamics. In: [But99], pp. 169–195
Passon, O.: Bohmsche Mechanik. Eine elementare Einführung in die deterministische Interpretation der Quantenmechanik. Verlag Harri Deutsch, Frankfurt (2004)
Prediger, S., Wille, R.: The lattice of concept graphs of a relationally scaled context. In: Tepfenhart, W.M. (ed.) ICCS 1999. LNCS, vol. 1640, pp. 401–414. Springer, Heidelberg (1999)
Priss, U., Corbett, D.R., Angelova, G. (eds.): ICCS 2002. LNCS (LNAI), vol. 2393. Springer, Heidelberg (2002)
Reichenbach, H.: The Direction of Time. In: Reichenbach, M. (ed.) The Direction of Time, University of California Press, Berkeley (1991); (Originally published in 1956)
Sowa, J.F.: Conceptual structures: information processing in mind and machine. Adison-Wesley, Reading (1984)
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)
Toraldo di Francia, G.: A World of Individual Objects? In: [Ca98], 21–29
Wille, R.: Conceptual Graphs and Formal Concept Analysis. In: Delugach, H.S., Keeler, M.A., Searle, L., Lukose, D., Sowa, J.F. (eds.) ICCS 1997. LNCS (LNAI), vol. 1257, pp. 290–303. Springer, Heidelberg (1997)
Wille, R.: Contextual Logic summary. In: Stumme, G. (ed.) Working with conceptual structures: Contributions to ICCS 2000, pp. 265–276. Shaker-Verlag, Aachen (2000)
Wille, R.: Existential concept graphs of power context families. In: [PCA99], pp. 382–395
Wille, R.: Conceptual Contents as Information - Basics for Contextual Judgment Logic. In: [MLG03], pp. 1–15
Wolff, K.E.: Concepts, States, and Systems. In: Dubois, D.M. (ed.): Computing Anticipatory Systems. In: 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: B. Sanchez, N. Nada, A. Rashid, T. Arndt, M. Sanchez (eds.): Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics, SCI, vol. II: Information Systems Development, International Institute of Informatics and Systemics, pp. 124–132 (2000); ISBN 980-07-6688-X
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: D.M. Dubois (ed.): International Journal of Computing Anticipatory Systems, vol. 11, CHAOS 2002, pp. 398–412 (2002)
Wolff, K.E.: Interpretation of Automata in Temporal Concept Analysis. In: [PCA99], pp. 341–353
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.: States, Transitions, and Life Tracks in Temporal Concept Analysis. Preprint Darmstadt University of Applied Sciences, Mathematics and Science Faculty (2004)
Wolff, K.E.: ‘Particles’ and ‘Waves’ as Understood by Temporal Concept Analysis. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds.) ICCS 2004. LNCS (LNAI), vol. 3127, pp. 126–141. Springer, Heidelberg (2004)
Wolff, K.E., Yameogo, W.: Time Dimension, Objects, and Life Tracks - A Conceptual Analysis. In: [MLG03], pp. 188–200
Wolff, K.E., Yameogo, W.: Turing Machine Representation in Temporal Concept Analysis. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 360–374. Springer, Heidelberg (2005)
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Wolff, K.E. (2005). States of Distributed Objects in Conceptual Semantic Systems. In: Dau, F., Mugnier, ML., Stumme, G. (eds) Conceptual Structures: Common Semantics for Sharing Knowledge. ICCS 2005. Lecture Notes in Computer Science(), vol 3596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11524564_17
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DOI: https://doi.org/10.1007/11524564_17
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