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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Arbib, M.A.: Theory of Abstract Automata. Prentice Hall, Englewood Cliffs, N.J., 1970.
Brauer, W.: Automatentheorie. B.G. Teubner 1984.
Eilenberg, S.: Automata, Languages, and Machines. Vol. A. Academic Press 1974.
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.
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.
Ganter, B., R. Wille: Formal Concept Analysis: mathematical foundations, (translated from the German by Cornelia Franzke) Springer-Verlag, Berlin-Heidelberg 1999.
Ginsburg, S.; Algebraic and automata-theoretic properties of formal languages. North-Holland, Amsterdam, 1975.
Kalman, R.E., Falb, P.L., Arbib, M.A.: Topics in Mathematical System Theory. McGraw-Hill Book Company, New York, 1969.
Lin, Y.: General Systems Theory: A Mathematical Approach. Kluwer Academic/ Plenum Publishers, New York, 1999.
Mesarovic, M.D., Y. Takahara: General Systems Theory: Mathematical Foundations. Academic Press, London, 1975.
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Ordered Sets (ed. I. Rival). Reidel, Dordrecht-Boston 1982, 445–470.
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.
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.
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.
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.
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.
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.
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.
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.
Wolff, K.E.: Objects, Space, and Time-A Conceptual Analysis, (unpublished)
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.
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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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