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Abstract

Based on Formal Concept Analysis the notion of a Temporal Conceptual Semantic System is introduced as a formal conceptual representation for temporal systems with arbitrary discrete or continuous semantic scales. In this paper, we start with an example of a weather map with a moving high pressure zone to explain the basic notions for Temporal Conceptual Semantic Systems. The central philosophical notion of an object is represented as a formal concept or, more flexible, as a tuple of concepts. Generalizing the idea of a volume of an object in physics we introduce the notion of a trace of an object in some space. This space is described as a continuous or discrete concept lattice. Combining the notion of a trace of an object with the notion of a time granule yields the notion of a state of an object at some time granule. This general notion of a state allows for a clear conceptual understanding of particles, waves and Heisenberg’s Uncertainty Relation. Besides these theoretical aspects, Temporal Conceptual Semantic Systems can be used very effectively in practice. That is shown for data of a distillation column using a nested transition diagram.

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References

  1. 1.
    Arbib, M.A.: Theory of Abstract Automata. Prentice Hall, Englewood Cliffs (1970)zbMATHGoogle Scholar
  2. 2.
    Auletta, G.: Foundations and Interpretations of Quantum Mechanics. World Scientific Publishing Co. Pte. Ltd., Singapore (2000)CrossRefzbMATHGoogle Scholar
  3. 3.
    Becker, P.: Multi-dimensional Representation of Conceptual Hierarchies. In: Stumme, G., Mineau, G. (eds.) Proceedings of the 9th International Conference on Conceptual Structures, Supplementary Proceedings, pp. 33–46. Department of Computer Science, University Laval (2001)Google Scholar
  4. 4.
    Becker, P., Hereth Correia, J.: The ToscanaJ Suite for Implementing Conceptual Information Systems. In: Ganter, B., Stumme, G., Wille, R. (eds.) FCA 2005. LNCS (LNAI), vol. 3626, pp. 324–348. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Bertalanffy, L.v.: General System Theory. George Braziller, New York (1969)Google Scholar
  6. 6.
    Butterfield, J. (ed.): The Arguments of Time. Oxford University Press, Oxford (1999)zbMATHGoogle Scholar
  7. 7.
    Butterfield, J., Isham, C.J.: On the Emergence of Time in Quantum Gravity. In: Butterfield, J. (ed.) The Arguments of Time. Oxford University Press, Oxford (1999)Google Scholar
  8. 8.
    Castellani, E. (ed.): Interpreting Bodies: Classical and Quantum Objects in Modern Physics. Princeton University Press, Princeton (1998)Google Scholar
  9. 9.
    Eilenberg, S.: Automata, Languages, and Machines, vol. A. Academic Press, London (1974)zbMATHGoogle Scholar
  10. 10.
    Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer, Heidelberg (1999); German version: Springer, Heidelberg (1996)CrossRefzbMATHGoogle Scholar
  11. 11.
    Kalman, R.E., Falb, P.L., Arbib, M.A.: Topics in Mathematical System Theory. McGraw-Hill Book Company, New York (1969)zbMATHGoogle Scholar
  12. 12.
    Lin, Y.: General Systems Theory: A Mathematical Approach. Kluwer Academic/Plenum Publishers, New York (1999)zbMATHGoogle Scholar
  13. 13.
    Mesarovic, M.D., Takahara, Y.: General Systems Theory: Mathematical Foundations. Academic Press, London (1975)zbMATHGoogle Scholar
  14. 14.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)CrossRefzbMATHGoogle Scholar
  15. 15.
    Neumann, J.v.: Mathematical Foundations of Quantum Mechanics (engl. translation of Neumann, J.v.: Mathematische Grundlagen der Quantenmechanik. Springer, Berlin (1932)). University Press, Princeton (1932)Google Scholar
  16. 16.
    Sowa, J.F.: Conceptual structures: information processing in mind and machine. Addison-Wesley, Reading (1984)zbMATHGoogle Scholar
  17. 17.
    Sowa, J.F.: Knowledge representation: logical, philosophical, and computational foundations. Brooks Cole Publ. Comp., Pacific Grove (2000)Google Scholar
  18. 18.
    Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered sets, pp. 445–470. Reidel, Dordrecht (1982); Reprinted in: Ferré, S., Rudolph, S. (eds.): Formal Concept Analysis. ICFCA 2009. LNAI 5548, pp. 314–339. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    Wolff, K.E.: Concepts, States, and Systems. In: Dubois, D.M. (ed.) Proceedings of Computing Anticipatory Systems. American Institute of Physics, Conference, vol. 517, pp. 83–97 (2000)Google Scholar
  21. 21.
    Wolff, K.E.: A Conceptual View of Knowledge Bases in Rough Set Theory. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 220–228. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  22. 22.
    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, pp. 91–107. Stanford University, Palo Alto (2001)Google Scholar
  23. 23.
    Wolff, K.E.: Transitions in Conceptual Time Systems. International Journal of Computing Anticipatory Systems 11, 398–412 (2002)Google Scholar
  24. 24.
    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)CrossRefGoogle Scholar
  25. 25.
    Wolff, K.E.: Concepts in Fuzzy Scaling Theory: Order and Granularity. Fuzzy Sets and Systems 132, 63–75 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    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)CrossRefGoogle Scholar
  27. 27.
    Wolff, K.E.: States, Transitions, and Life Tracks in Temporal Concept Analysis. In: Ganter, B., Stumme, G., Wille, R. (eds.) FCA 2005. LNCS (LNAI), vol. 3626, pp. 127–148. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  28. 28.
    Wolff, K.E.: States of Distributed Objects in Conceptual Semantic Systems. In: Dau, F., Mugnier, M.-L., Stumme, G. (eds.) ICCS 2005. LNCS (LNAI), vol. 3596, pp. 250–266. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  29. 29.
    Wolff, K.E.: A Conceptual Analogue of Heisenberg’s Uncertainty Relation. In: Ganter, B., Kwuida, L. (eds.) Contributions to ICFCA 2006, pp. 19–30. Verlag Allgemeine Wissenschaft (2006)Google Scholar
  30. 30.
    Wolff, K.E.: Conceptual Semantic Systems - Theory and Applications. In: Goncharov, S., Downey, R., Ono, H. (eds.) Mathematical Logic in Asia, pp. 287–300. World Scientific, New Jersey (2006)Google Scholar
  31. 31.
    Wolff, K.E.: Basic Notions in Temporal Conceptual Semantic Systems. In: Gély, A., Kuznetsov, S.O., Nourine, L., Schmidt, S.E. (eds.) Contributions to ICFCA 2007, pp. 97–120. Clermont-Ferrand, France (2007)Google Scholar
  32. 32.
    Wolff, K.E.: Applications of Temporal Conceptual Semantic Systems. In: Zagoruiko, N.G., Palchunov, D.E. (eds.) Knowledge - Ontology - Theory, vol. 2, pp. 3–16. Russian Academy of Sciences. Sobolev Institute for Mathematics, Novosibirsk (2007)Google Scholar
  33. 33.
    Wolff, K.E.: Relational Semantic Systems, Power Context Families, and Concept Graphs. In: Wolff, K.E., Rudolph, S., Ferré, S. (eds.) Contributions to ICFCA 2009, pp. 63–78. Verlag Allgemeine Wissenschaft, Darmstadt (2009)Google Scholar
  34. 34.
    Wolff, K.E.: Relational Scaling in Relational Semantic Systems. In: Rudolph, S., Dau, F., Kuznetsov, S.O. (eds.) ICCS 2009. LNCS (LNAI), vol. 5662, pp. 307–320. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  35. 35.
    Wolff, K.E.: Temporal Relational Semantic Systems. In: Croitoru, M., Ferré, S., Lukose, D. (eds.) ICCS 2010. LNCS (LNAI), vol. 6208, pp. 165–180. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  36. 36.
    Zadeh, L.A.: The Concept of State in System Theory. In: Mesarovic, M.D. (ed.) Views on General Systems Theory, pp. 39–50. John Wiley & Sons, New York (1964)Google Scholar
  37. 37.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Part I: Inf. Science 8, 199–249, Part II: Inf. Science 8, 301–357; Part III: Inf. Science 9, 43–80 (1975)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Karl Erich Wolff
    • 1
  1. 1.Mathematics and Science FacultyDarmstadt University of Applied SciencesDarmstadtGermany

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