Abstract
Traditional logic can be understood as the investigation of the three main essential functions of thinking – concepts, judgements and conclusions. In the last years, in a new research field termed Contextual Logic, a mathematical theory of this logic is elaborated. Concepts have already been mathematically elaborated by Formal Concept Analysis. Judgements and Conclusions can be expressed by so-called Concept Graphs, which are built upon families of formal contexts.
There are two approaches to concept graphs: A semantical approach, which investigates the theory of concept graphs in an algebraic manner, and a logical approach, which focuses on derivation rules for concept graphs, relying on a separation between syntax and semantics. In [24], Wille introduced two forms of complex implications (object implications and concept implications) to the semantical approach. In this paper it is investigated how these implications can be incorporated into the logical approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Brandom, R.B.: Making it explicit. Reasoning, representing, and discursive commitment. Harvard University Press, Cambridge (1994); Suhrkamp (2001)
Dau, F.: The Logic System of Concept Graphs with Negation. LNCS (LNAI), vol. 2892. Springer, Heidelberg (2003) ISBN 3- 540-20607-8
Dau, F.: Concept Graphs without Negations: Standardmodels and Standardgraphs. In: Ganter, B., de Moor, A., Lex, W. (eds.) ICCS 2003. LNCS (LNAI), vol. 2746, p. 243. Springer, Heidelberg (2003) (This paper is a part of [2] as well) ISBN 3-540-40576-3
Dau, F., Klinger, J.: From Formal Concept Analysis to Contextual Logic. To appear in the Proceedings of the First International Conference on Formal Concept Analysis (2003)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin (1999)
Klinger, J.: Semiconcept Graphs: Syntax and Semantics. Diploma thesis, TU Darmstadt (2001)
Klinger, J.: Simple Semiconcept Graphs: A Boolean Logic Approach. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, p. 101. Springer, Heidelberg (2001)
Klinger, J.: Semiconcept Graphs with Variables. In: Priss, U., Corbett, D.R., Angelova, G. (eds.) ICCS 2002. LNCS (LNAI), vol. 2393, p. 369. Springer, Heidelberg (2002)
Nicholson, M.: The pocket Aussie fact book. Penguin Books, Australia (1999)
Pollandt, S.: Relational Constructions on Semiconcept Graphs. In: Ganter, B., Mineau, G. (eds.) Conceptual Structures: Extracting and Representing Semantics. Contributions to ICCS, Stanford (2001)
Pollandt, S.: Relation Graphs: A Structure for Representing Relations in Contextual Logic of Relations. In: Priss, U., Corbett, D.R., Angelova, G. (eds.) ICCS 2002. LNCS (LNAI), vol. 2393, p. 34. Springer, Heidelberg (2002)
Prediger, S.: Kontextuelle Urteilslogik mit Begriffsgraphen. In: Ein Beitrag zur Restrukturierung der mathematischen Logik, 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, pp. 225–239. Springer, Heidelberg (1998)
Schoolmann, L., Wille, R.: Concept Graphs with Subdivision: A Semantic Approach. In: Ganter, B., de Moor, A., Lex, W. (eds.) ICCS 2003. LNCS (LNAI), vol. 2746, Springer, Heidelberg (2003)
Sowa, J.F.: Conceptual Structures: Information Processing in Mind and Machine. Addison Wesley Publishing Company, Reading (1984)
Sowa, J.F.: Conceptual Graphs Summary. In: Nagle, T.E., Nagle, J.A., Gerholz, L.L., Eklund, P.W. (eds.) Conceptual Structures: current research and practice, pp. 3–51. Ellis Horwood (1992)
Sowa, J.F.: Knowledge Representation: Logical, Philosophical, and Computational Foundations. Brooks Cole Publishing Co., Pacific Grove (2000)
Wille, R.: Plädoyer für eine Philosophische Grundlegung der Begrifflichen Wissensverarbeitung. In: Wille, R., Zickwolff, M. (eds.) Begriffliche Wissensverarbeitung: Grundfragen und Aufgaben, pp. 11–25. B.I.–Wissenschaftsverlag, Mannheim (1994)
Wille, R.: Restructuring Mathematical Logic: An Approach Based on Peirce’s Pragmatism. In: Ursini, A., Agliano, P. (eds.) Logic and Algebra, pp. 267–281. Marcel Dekker, New York (1996)
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, Aachen (2000)
Wille, R.: Lecture Notes on Contextual Logic of Relations. FB4-Preprint, TUDarmstadt (2000)
Wille, R.: Existential Concept Graphs of Power Context Families. In: Priss, U., Corbett, D.R., Angelova, G. (eds.) ICCS 2002. LNCS (LNAI), vol. 2393, p. 382. Springer, Heidelberg (2002)
Wille, R.: Conceptual Contents as Information – Basics for Contextual Judgement Logic. In: Ganter, B., de Moor, A., Lex, W. (eds.) ICCS 2003. LNCS (LNAI), vol. 2746, Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dau, F. (2004). Background Knowledge in Concept Graphs. In: Eklund, P. (eds) Concept Lattices. ICFCA 2004. Lecture Notes in Computer Science(), vol 2961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24651-0_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-24651-0_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21043-6
Online ISBN: 978-3-540-24651-0
eBook Packages: Springer Book Archive