Abstract
In this paper two developments in Conceptual Knowledge Processing are combined, namely Contextual Logic introduced by Rudolf Wille and Temporal Concept Analysis introduced by the author. The basic structures connecting both theories are Relational Semantic Systems (RSS), each consisting of conceptual scales and a Relational Data Systems (RDS) for the representation of relational knowledge. We introduce the notion of a concept graph of a RSS. As opposed to the definition of a concept graph of a power context family the concepts used in the concept graph of a RSS are taken from the conceptual scales and not from the concept lattices of the contexts of k-ary relations. For the graphical representation of relational knowledge in information maps we modify tools from Temporal Concept Analysis and develop relational trace diagrams. Its usefulness is shown in a small example of a Relational Semantic System.
This work is supported by DFG-RFBR project COMO, GZ: 436 RUS 113/829/0-1.
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References
Becker, P., Hereth Correia, J.: The ToscanaJ Suite for Implementing Conceptual Information Systems. In: Ganter, B., Stumme, G., Wille, R. (eds.) Formal Concept Analysis. LNCS (LNAI), vol. 3626, pp. 324–348. Springer, Heidelberg (2005)
Devlin, K.: Logic and Information. Cambridge University Press, Cambridge (1991)
Eklund, P., Groh, B., Stumme, G., Wille, R.: A contextual-logic extension of TOSCANA. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS (LNAI), vol. 1867. Springer, Heidelberg (2000)
Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer, Heidelberg (1999); German version: Springer, Heidelberg (1996)
Hereth, J.: Relational Scaling and Databases. In: Priss, U., Corbett, D.R., Angelova, G. (eds.) ICCS 2002. LNCS (LNAI), vol. 2393, pp. 62–76. Springer, Heidelberg (2002)
Prediger, S.: Kontextuelle Urteilslogik mit Begriffsgraphen. Ein Beitrag zur Restrukturierung der mathematischen Logik. Dissertation, TU Darmstadt 1998. Shaker, Aachen (1998)
Prediger, S., Wille, R.: The lattice of concept graphs of a relationally scaled context. In: Tepfenhart, W.M. (ed.) ICCS 1999. LNCS (LNAI), vol. 1640, pp. 401–414. Springer, Heidelberg (1999)
Sowa, J.F.: Conceptual structures: information processing in mind and machine. Addison-Wesley, Reading (1984)
Sowa, J.F.: Knowledge representation: logical, philosophical, and computational foundations. Brooks Cole Publ. Comp., Pacific Grove (2000)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered sets, pp. 445–470. Reidel, Dordrecht (1982)
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.: Implicational Concept Graphs. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds.) ICCS 2004. LNCS (LNAI), vol. 3127, pp. 52–61. Springer, Heidelberg (2004)
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.: ‘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.: States, Transitions, and Life Tracks in Temporal Concept Analysis. In: Ganter, B., Stumme, G., Wille, R. (eds.) Formal Concept Analysis. LNCS, vol. 3626, pp. 127–148. Springer, Heidelberg (2005)
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)
Wolff, K.E.: Conceptual Semantic Systems - Theory and Applications. In: Goncharov, S.S., Downey, R., Ono, H. (eds.) Mathematical Logic in Asia. Proceedings of the 9th Asian Logic Conference, pp. 288–301. World Scientific, New Jersey (2006)
Wolff, K.E.: Basic Notions in Temporal Conceptual Semantic Systems. In: Kuznetsov, S.O., Schmidt, S. (eds.) ICFCA 2007. LNCS, vol. 4390, pp. 97–120. Springer, Heidelberg (2007)
Wolff, K.E.: Applications of Temporal Conceptual Semantic Systems. In: Zagoruiko, N.G., Palchunov, D.E. (eds.) Knowledge - Ontology - Theory. Russian Academy of Sciences. Sobolev Institute for Mathematics. Novosibirsk, vol. 2, pp. 3–16 (2007)
Wolff, K.E.: Relational Semantic Systems, Power Context Families, and Concept Graphs. In: The Proceedings of the International Conference on Formal Concept Analysis 2009, Darmstadt (accepted for publication, 2009)
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Wolff, K.E. (2009). Relational Scaling in Relational Semantic Systems. In: Rudolph, S., Dau, F., Kuznetsov, S.O. (eds) Conceptual Structures: Leveraging Semantic Technologies. ICCS 2009. Lecture Notes in Computer Science(), vol 5662. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03079-6_24
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DOI: https://doi.org/10.1007/978-3-642-03079-6_24
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