Abstract
The aim of this paper is to mathematically introduce negation to concept graphs (which are a mathematical modification of conceptual graphs) as a well-defined syntactical construct. First off, we discuss some questions which arise when negations for conceptual graphs are defined. In our view, a solution for these questions is to express negations by cuts in the sense of Peirce’s theory of existential graphs. A set-theoretical semantics for (nonexistential) concept graphs with cuts is developed in the framework of contextual logic. A modification of Peirce’s alpha-calculus, which is sound and complete, is presented.
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References
Baader, F., Molitur, R., Tobies, S.: The Guarded Fragment of Conceptual Graphs. RWTH LTCS-Report, http://www-lti.informatik.rwth-aachen.de/Forschung/Papers.html
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)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)
Ganter, B., Wille, R.: Contextual attribute logic. In: Tepfenhart, W., Cyre, W. (eds.) Conceptual Structures: Standards and Practices, pp. 377–388. Springer, Berlin (1999)
Lukose, D., Kremer, R.: Knowledge Engineering: PART A, Knowledge Representation, http://www.cpsc.ucalgary.ca/~kremer/courses/CG/
Peirce, C.S.: Reasoning and the Logic of Things. In: Kremer, K.L. (ed.) The Cambridge Conferences Lectures of 1898. Harvard Univ. Press, Cambridge (1992)
Prediger, S.: Kontextuelle Urteilslogik mit Begriffsgraphen. 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.) Conceptual Structures: Theory, Tools and Applications, pp. 225–239. Springer, Berlin (1998)
Prediger, S.: Simple Concept Graphs: A Logic Approach. In: Mugnier, M.-L., Chein, M. (eds.) Conceptual Structures: Theory, Tools and Applications, pp. 225–239. Springer, Berlin (1998)
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.: Conceptual Graphs: Draft Proposed American National Standard. In: Tepfenhart, W., Cyre, W. (eds.) Conceptual Structures: Standards and Practices, pp. 1–65. Springer, Berlin (1999)
Sowa, J.F.: Knowledge Representation: Logical, Philosophical, and Computational Foundations. Brooks Cole Publishing Co., Pacific Grove (2000)
Wermelinger, M.: Conceptual Graphs and First-Order Logic. In: Ellis, G., et al. (eds.) Conceptual Structures: Applications, Implementations and Theory, pp. 323–337. Springer, Berlin (1995)
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Dau, F. (2000). Negations in Simple Concept Graphs. 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_18
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DOI: https://doi.org/10.1007/10722280_18
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