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Interpretation of Automata in Temporal Concept Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2393))

Abstract

The purpose of this paper is to relate the notions of states and transitions in Automata Theory to the conceptual descriptions of states, situations, and transitions in Temporal Concept Analysis. The first key for that relation is that states and situations can be described as formal concepts of formal contexts whose objects are points of time. The second key is the introduction of certain subsystems (interpreted as persons or agents). We prove that labeled transition systems with attributes (a recently introduced generalization of automata) can be represented as state-transition-systems of conceptual time systems.

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References

  1. Arbib, M.A.: Theory of Abstract Automata. Prentice Hall, Englewood Cliffs, N.J., 1970.

    Google Scholar 

  2. Brauer, W.: Automatentheorie. B.G. Teubner 1984.

    Google Scholar 

  3. Eilenberg, S.: Automata, Languages, and Machines. Vol. A. Academic Press 1974.

    Google Scholar 

  4. Ganter, B., S. Rudolph: Formal Concept Analysis Methods for Dynamic Conceptual Graphs. In: Delugach, H.S., G. Stumme: Conceptual Structures: Broadening the Base. ICCS 2001, Lecture Notes in Artificial Intelligence 2120, pp. 143–156, 2001.

    Google Scholar 

  5. Ganter, B., R. Wille: Conceptual Scaling. In: F. Roberts (ed.) Applications of combinatorics and graph theory to the biological and social sciences, 139–167. Springer Verlag, New York, 1989.

    Google Scholar 

  6. Ganter, B., R. Wille: Formal Concept Analysis: mathematical foundations, (translated from the German by Cornelia Franzke) Springer-Verlag, Berlin-Heidelberg 1999.

    MATH  Google Scholar 

  7. Ginsburg, S.; Algebraic and automata-theoretic properties of formal languages. North-Holland, Amsterdam, 1975.

    Google Scholar 

  8. Kalman, R.E., Falb, P.L., Arbib, M.A.: Topics in Mathematical System Theory. McGraw-Hill Book Company, New York, 1969.

    MATH  Google Scholar 

  9. Lin, Y.: General Systems Theory: A Mathematical Approach. Kluwer Academic/ Plenum Publishers, New York, 1999.

    MATH  Google Scholar 

  10. Mesarovic, M.D., Y. Takahara: General Systems Theory: Mathematical Foundations. Academic Press, London, 1975.

    MATH  Google Scholar 

  11. Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Ordered Sets (ed. I. Rival). Reidel, Dordrecht-Boston 1982, 445–470.

    Google Scholar 

  12. Wille, R.: Introduction to Formal Concept Analysis. In: G. Negrini (ed.): Modelli e modellizzazione. Models and modelling. Consiglio Nazionale delle Ricerche, Instituto di Studi sulli Ricerca e Documentatione Scientifica, Roma 1997, 39–51.

    Google Scholar 

  13. Wolff, K.E.: A first course in Formal Concept Analysis-How to understand line diagrams. In: Faulbaum, F. (ed.): SoftStat’ 93, Advances in Statistical Software 4, Gustav Fischer Verlag, Stuttgart 1994, 429–438.

    Google Scholar 

  14. Wolff, K.E.: Concepts, States, and Systems. In: Dubois, D.M. (ed.): Computing Anticipatory Systems. CASYS’99-Third International Conference, Liège, Belgium, 1999, American Institute of Physics Conference Proceedings 517, 2000, pp. 83–97.

    Google Scholar 

  15. 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 2000, Vol. II: Information Systems Development, International Institute of Informatics and Systemics, 2000, p.124–132.

    Google Scholar 

  16. Wolff, K.E.: Conceptual Descriptions of Systems: Data and Laws. Accepted for publication in: D.M. Dubois (ed.) Computing Anticipatory Systems-CASYS’2000, Conference Proceedings. American Institute of Physics.

    Google Scholar 

  17. Wolff, K.E.: Temporal Concept Analysis. In: E. Mephu Nguifo & al. (eds.): ICCS-2001 International Workshop on Concept Lattices-Based Theory, Methods and Tools for Knowledge Discovery in Databases, Stanford University, Palo Alto (CA), 91–107.

    Google Scholar 

  18. Wolff, K.E.: Process Representation in Temporal Concept Analysis. In: G.W. Mineau (ed.): Conceptual Structures: Extracting and Representing Semantics. Contributions to ICCS 2001, The 9th International Conference on Conceptual Structures, Stanford University, California, USA, 211–213.

    Google Scholar 

  19. Wolff, K.E.: Transitions in Conceptual Time Systems. Accepted for publication in: D.M. Dubois (ed.): Computing Anticipatory Systems CASYS’2001, American Institute of Physics Conference Proceedings.

    Google Scholar 

  20. Wolff, K.E.: Objects, Space, and Time-A Conceptual Analysis, (unpublished)

    Google Scholar 

  21. Zadeh, L.A.: The Concept of State in System Theory. In: M.D. Mesarovic: Views on General Systems Theory. John Wiley & Sons, New York, 1964, 39–50.

    Google Scholar 

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© 2002 Springer-Verlag Berlin Heidelberg

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Wolff, K.E. (2002). Interpretation of Automata in Temporal Concept Analysis. In: Priss, U., Corbett, D., Angelova, G. (eds) Conceptual Structures: Integration and Interfaces. ICCS 2002. Lecture Notes in Computer Science(), vol 2393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45483-7_26

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  • DOI: https://doi.org/10.1007/3-540-45483-7_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43901-1

  • Online ISBN: 978-3-540-45483-0

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