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Contextual Logic and Aristotle’s Syllogistic

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Conceptual Structures: Common Semantics for Sharing Knowledge (ICCS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3596))

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Abstract

This paper is concerned with incorporating negational relationships into the semantics of Contextual Logic by mathematizing Aristotle’s Syllogistic in contextual-logic terms. For preparing this, a short sketch of Aristotle’s Syllogistic is presented. Then it is shown how a contextual semantics for Aristotle’s syllogisms can be developed on the basis of so-called syllogistic contexts. This semantic approach is used to determine implication bases for elementary judgments within syllogistic contexts. Finally, directions of further research are mentioned.

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References

  1. Aristoteles: Lehre vom Schluß oder Erste Analytik. Felix Meiner, Hamburg (1975)

    Google Scholar 

  2. Audi, R. (ed.): The Cambridge dictionary of philosophy. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  3. Brandom, R.B.: Making it explicit. Reasoning, representing, and discursive commitment. Harvard University Press, Cambridge (1994)

    Google Scholar 

  4. Dau, F., Klinger, J.: From Formal Concept Analysis to Contextual Logic. FB4-Preprint, TU Darmstadt (2003)

    Google Scholar 

  5. Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer, Heidelberg (1999); German version: Formale Begriffsanalyse: Mathematische Grundlagen. Springer, Heidelberg (1996)

    Google Scholar 

  6. Ganter, B., Wille, R.: Contextual Attribute Logic. In: Tepfenhart, W., Cyre, W. (eds.) ICCS 1999. LNCS, vol. 1640, pp. 377–388. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  7. Sowa, J.F.: Conceptual structures: Information processing in mind and machine. Adison-Wesley, Reading (1984)

    MATH  Google Scholar 

  8. Stekeler-Weithofer, P.: Grundprobleme der Logik: Elemente einer Kritik der formalen Vernunft. de Gruyter, Berlin (1986)

    Google Scholar 

  9. Thom, P.: Syllogismus; Syllogistik. In: Gründer, K. (Hrsg.) Historisches Wörterbuch der Philosophie. Bd.10. Schwabe, Basel, pp. 687–707 (1998)

    Google Scholar 

  10. 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)

    Google Scholar 

  11. Wille, R.: Boolean Concept Logic. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS, vol. 1867, pp. 317–331. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  12. Wille, R.: Contextual Logic summary. In: Stumme, G. (ed.) Working with conceptual structures: Contributions to ICCS 2000, pp. 265–276. Shaker-Verlag, Aachen (2000)

    Google Scholar 

  13. 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)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, D–64289, Darmstadt

    Rudolf Wille

Authors
  1. Rudolf Wille
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Editor information

Editors and Affiliations

  1. School of Information Systems and Technology, University of Wollongong, Northfields Ave, NSW 2522, Wollongong, Australia

    Frithjof Dau

  2. RCR, LIRMM, UMII, CNRS,  

    Marie-Laure Mugnier

  3. Research Center L3S, Appelstr. 9a, D-30167, Hannover, Germany

    Gerd Stumme

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© 2005 Springer-Verlag Berlin Heidelberg

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Wille, R. (2005). Contextual Logic and Aristotle’s Syllogistic. In: Dau, F., Mugnier, ML., Stumme, G. (eds) Conceptual Structures: Common Semantics for Sharing Knowledge. ICCS 2005. Lecture Notes in Computer Science(), vol 3596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11524564_16

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  • DOI: https://doi.org/10.1007/11524564_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27783-5

  • Online ISBN: 978-3-540-31885-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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