Abstract
It is shown how Conceptual Graphs and Formal Concept Analysis may be combined to obtain a formalization of Elementary Logic which is useful for knowledge representation and processing. For this, a translation of conceptual graphs to formal contexts and concept lattices is described through an example. Using a suitable mathematization of conceptual graphs, basics of a unified mathematical theory for Elementary Logic are proposed.
Preview
Unable to display preview. Download preview PDF.
References
K.-O. Apel: Das Apriori der Kommunikationsgemeinschaft und die Grundlagen der Ethik. In: Transformation der Philosophie. Band 2: Das Apriori der Kommunikationsgemeinschaft. Suhrkamp Taschenbuch Wissenschaft 165, Frankfurt 1976.
W. Brugger (Hrsg.): Philosophisches Wörterbuch. Herder, Freiburg 1976.
M. Chein, M.-L. Mugnier: Conceptual Graphs: fundamental notions. Revue d'Intelligence Artificielle 6 (1992), 365–406.
M. Chein, M.-L. Mugnier: Représenter des connaissances et raisonner avec des graphes. R.R.LIRMM 003-95. Université Montpellier 1995.
B. Ganter, R. Wille: Formale Begriffsanalyse: Mathematische Grundlagen. Springer, Berlin-Heidelberg 1996.
K. J. Grau: Grundriß der Logik. Teubner, Leipzig und Berlin 1918.
J. Habermas: Theorie kommunikativen Handelns. Band 1. Suhrkamp, Frankfurt 1981.
I. Kant: Logic. Dover, New York 1988.
F. Lehmann, R. Wille: A triadic approach to formal concept analysis. In: G. Ellis, R. Levinson, W. Rich, J. F. Sowa (eds.): Conceptual Structures: Applications, Implementations and Theory. Springer, Berlin-Heidelberg-New York 1995, 32–43.
B. Nebel: Reasoning and revision in hybrid representation systems. Springer, Berlin-Heidelberg-New York 1990.
Ch. S. Peirce: Phänomen und Logik der Zeichen. Suhrkamp Taschenbuch Wissenschaft 425, Frankfurt 1983.
S. Prediger: Symbolische Datenanalyse und ihre begriffsanalytische Einordnung. Staatsexamensarbeit. FB Mathematik, TH Darmstadt 1996.
The Smithonian Guide to Historic America. Stewart, Tabori & Chang Inc., New York 1989.
J. F. Sowa: Conceptual structures: information processing in mind and machine. Adison-Wesley, Reading 1984.
J. F. Sowa: Conceptual Graphs summary. In: T. E. Nagle, J. A. Nagle, L. L. Gerholz, P. W. Eklund (eds.): Conceptual Structures: Current Research and Practice. Ellis Horwood, 1992, 3–51.
J. F. Sowa: Syntax, semantics, and pragmatics of contexts. In: G. Ellis, R. Levinson, W. Rich, J. F. Sowa (eds.): Conceptual Structures: Applications, Implementations and Theory. Springer, Berlin-Heidelberg-New York 1995, 1–15.
J. F. Sowa: Knowledge representation: logical, philosophical, and computational foundations. PWS Publishing Co., Boston (to appear)
R. Wille: Restructuring lattice theory: an approach based on hierarchies of concepts. In: I. Rival (ed.): Ordered Sets. Reidel, Dordrecht-Boston 1982, 445–470.
R. Wille: Concept lattices and conceptual knowledge systems. Computers & Mathematics with Applications. 23 (1992), 493–515.
R. Wille: Begriffsdenken: Von der griechischen Philosophie bis zur Künstlichen Intelligenz heute. Diltheykastanie, Ludwig-Georgs-Gymnasium Darmstadt 1995, 77–109.
R. Wille: Restructuring mathematical logic: an approach based on Peirce's pragmatism. In: A. Ursini, P. Agliano (eds.): Logic and Algebra. Marcel Dekker, New York 1996, 267–281.
R. Wille: Conceptual structures of multicontexts. In: P. W. Eklund, G. Ellis, G. Mann (eds.): Conceptual Structures: Knowledge Representation as Interlingua. Springer, Berlin-Heidelberg-New York 1996, 23–39.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wille, R. (1997). Conceptual graphs and formal concept analysis. In: Lukose, D., Delugach, H., Keeler, M., Searle, L., Sowa, J. (eds) Conceptual Structures: Fulfilling Peirce's Dream. ICCS 1997. Lecture Notes in Computer Science, vol 1257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027878
Download citation
DOI: https://doi.org/10.1007/BFb0027878
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63308-2
Online ISBN: 978-3-540-69424-3
eBook Packages: Springer Book Archive