Abstract
In this paper, a contextual semantics for nested concept graphs shall be presented, that has especially two aims: We will propose a situation-based semantics that fits with Sowa’s understanding of contexts and draw the connection to formal concept analysis by founding on formal contexts, more precisely triadic power context families. Its basic idea is to understand interpreted nested concept graphs as situation-based judgements in triadic power context families. With it, the logical th eory can be well developed and inferences can be characterized in three ways: By semantical entailment, by means of a standard model and by a sound and complete calculus.
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References
Barwise, J., Perry, J.: Situations and Attitudes. MIT Press, Cambridge (1983)
Chein, M., Mugnier, M.-L.: Positive Nested Conceptual Graphs. In: Delugach, H.S., Keeler, M.A., Searle, L., Lukose, D., Sowa, J.F. (eds.) ICCS 1997. LNCS (LNAI), vol. 1257, pp. 95–109. Springer, Heidelberg (1997)
Chein, M., Mugnier, M.-L., Simonet, G.: Nested Graphs: A Graph-based Knowledge Representation Model with FOL Semantics, Rapport de Recherche, LIRMM, Université Montpellier II (1998)
Devlin, K.: Logic and Information. Cambridge University Press, Cambridge (1991)
Lehmann, F., Wille, R.: A triadic approach to formal concept analysis. In: Ellis, G., et al. ((Hrsg.) ICCS 1995. LNCS, vol. 954, pp. 32–43. Springer, Heidelberg (1995)
McCarthy, J.: Notes on Formalizing Context. In: Proceedings of the IJCAI, pp. 555–560 (1993)
Mugnier, M.-L., Chein, M.: Représenter des Connaissances et Raisonner avec des Graphes, Revue d’Intelligence Artificielle 10, 7–56 (1996)
Preller, A., Mugnier, M.-L., Chein, M.: A Logic for Nested Graphs, Research Report 95038, LIRMM, Université Montpellier II (1995)
Prediger, S.: Kontextuelle Urteilslogik mit Begriffsgraphen. Ein Beitrag zur Restrukturierung der mathematischen Logik, Dissertation, FB Mathematik, TU Darmstadt. Shaker Verlag, Aachen (1998)
Prediger, S.: Simple Concept Graphs: A Logic Approach. In: Mugnier, M.-L., Chein, M. (eds.) ICCS 1998. LNCS (LNAI), vol. 1453. Springer, Heidelberg (1998)
Prediger, S., Wille, R.: The Lattice of Concept Graphs of a Relationally Scaled Context. In: Tepfenhart, W., Cyre, W. (eds.) ICCS 1999. LNCS (LNAI), vol. 1640, pp. 401–414. Springer, Heidelberg (1999)
Simonet, G.: Une sémantique logique pour les graphes emboités, Research Report 96047, LIRMM, Université Montpellier II (1996)
Sowa, J.F.: Conceptual Structures: Information Processing in Mind and Machine. Addison-Wesley, Reading (1984)
Sowa, J.F.: Peircean Foundation for a Theory of Context. In: Lukose, D., et al. (eds.) ICCS 1997. LNCS (LNAI), vol. 1257, pp. 41–64. Springer, Heidelberg (1997)
Wille, R.: The Basic Theorem of Triadic Concept Analysis. Order 12, 149–158 (1995)
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.: Triadic Concept Graphs. In: Mugnier, M.-L., Chein, M. (eds.) ICCS 1998. LNCS (LNAI), vol. 1453, pp. 198–208. Springer, Heidelberg (1998)
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Prediger, S. (2000). Nested Concept Graphs and Triadic Power Context Families. In: Ganter, B., Mineau, G.W. (eds) Conceptual Structures: Logical, Linguistic, and Computational Issues. ICCS 2000. Lecture Notes in Computer Science(), vol 1867. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722280_17
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DOI: https://doi.org/10.1007/10722280_17
Publisher Name: Springer, Berlin, Heidelberg
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