Abstract
We present and discuss a diagrammatic visualization and reasoning language coming about by augmenting Euler diagrams with higraphs. The diagrams serve (hierarchical as well as trans-hierarchical) classification and specification of various logical relationships between classes. The diagrams rely on a well-defined underlying class-relationship logic, called CRL, being a fragment of predicate logic. The inference rules at the level of diagrams take form of simple diagrammatic ipso facto rules. The diagrams are intended for computerization by offering navigation and zooming facilities as known from road maps. As such they may facilitate ontological engineering, which often involves larger amounts of data. The underlying inference process is expressible in function-free definite clauses, datalog. We also discuss the relationship to similar diagram and logic proposals.
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References
Allwein, G., Barwise, J.: Logical Reasoning with Diagrams. Oxford University Press, London (1996)
Armstrong, D.: A Theory of Universals. Cambridge University Press, Cambridge (1978)
Barwise, J., Hammer, E.: Diagrams and the concept of a logical system. In: [1]
Brink, C., et al.: Peirce algebras. Form. Asp. Comput. 6(3), 339–358 (1994)
Dau, F., Fish, A.: Conceptual spider diagrams. In: Proceedings of the 16th International Conference on Conceptual Structures. Lecture Notes in Computer Science, vol. 5113, pp. 104–118. Springer, Berlin (2008)
Fischer Nilsson, J.: A conceptual space logic. In: Kawaguchi, E., et al. (eds.) Information Modelling and Knowledge Bases XI. 9th European-Japanese Conferences on Information Modelling and Knowledge Bases, Iwate, Japan, May 24–28, 1999, pp. 26–40. IOS Press, Amsterdam (2000)
Fischer Nilsson, J.: Ontological constitutions for classes and properties. In: Int. Conference on Conceptual Structures. Lecture Notes in Computer Science, vol. 4068, pp. 37–53. Springer, Berlin (2006)
Fischer Nilsson, J.: On reducing relationships to property ascriptions. In: Kiyoki, Y., et al. (eds.) Information Modelling and Knowledge Bases XX. Frontiers in Artificial Intelligence and Applications, vol. 190, pp. 245–252. IOS Press, Amsterdam (2008)
Fischer Nilsson, J.: Querying class-relationship logic in a metalogic framework. In: Flexible Query Answering Systems FQAS 2011. Lecture Notes in Computer Science, vol. 7022 (2011)
Fischer Nilsson, J., Palomäki, J.: Towards computing with intensions and extensions of concepts. In: Charrel, P.-J., et al. (eds.) Information Modelling and Knowledge Bases IX, pp. 100–114. IOS Press, Amsterdam (1998)
Fish, A., Flower, J., Howse, J.: The semantics of augmented constraint diagrams. J. Vis. Lang. Comput. 16(6), 541–573 (2005)
Gabbay, D.M., Woods, J. (eds.): Handbook of the History of Logic, vol. 3, The Rise of Modern Logic: From Leibniz to Frege. Elsevier, Amsterdam (2004)
Gärdenfors, P.: Conceptual Spaces: On the Geometry of Thought. MIT Press, Cambridge (2000)
Gil, J., Howse, J., Kent, S.: Towards a formalization of constraint diagrams. In: Proceedings of the IEEE 2001 Symposia on Human Centric Computing Languages and Environments (HCC’01) (2001)
Grosof, B.N., Horrocks, I., Volz, R., Decker, S.: Description logic programs: combining logic programs with description logic. In: Proceedings of the Twelfth International World Wide Web Conference, WWW2003, Budapest, Hungary, 2003, pp. 48–57. ACM, New York (2003)
Hamfelt, A., Fischer Nilsson, J.: Towards a logic programming methodology based on higher-order predicates. New Gener. Comput. 15(4), 421–448 (1997)
Hammer, E.M.: Logic and Visual Information. CSLI, Stanford (1995)
Harel, D.: On visual formalisms. Commun. ACM 31(5), 514–530 (1988)
Howse, J.: Diagrammatic reasoning systems. In: Proceedings of the 16th International Conference on Conceptual Structures: Knowledge Visualization and Reasoning. Lecture Notes in Artificial Intelligence, vol. 5113, pp. 1–20 (2008)
Howse, J., et al.: Euler diagram-based notations. University of Brighton and University of Kent, UK
Merrill, G.H.: Ontological realism: methodology or misdirection? Appl. Ontol. 5(2), 79–108 (2010)
Oliver, I., Howse, J., Stapleton, G., Nuutila, E., Törmä, S.: A proposed diagrammatic logic for ontology specification and visualization. In: 8th International Semantic Web Conference (Posters and Demos) (2009)
Sánchez Valencia, V.: The algebra of logic. In: [12]
Shin, S.-J.: The Iconic Logic of Peirce’s Graphs. MIT Press, Cambridge (2002)
Smith, B.: Against fantalogy. In: Reicher, M.E., Marek, J.C. (eds.) Experience and Analysis, pp. 153–170 (2005)
Smith, B., Rosse, C.: The Role of Foundational Relations in the Alignment of Biomedical Ontologies, MEDINFO 2004, pp. 444–448. IOS Press, Amsterdam (2004)
Sowa, J.: Knowledge Representation: Logical, Philosophical and Computational Foundations. Brooks Cole, Pacific Grove (2000)
van Benthem, J.: Essays in Logical Semantics. Reidel, Dordrecht (1986)
Acknowledgements
Many thanks to Sun-Joo Shin and Bartlomiej Szymczak, and to the anonymous reviewers for helpful comments and suggestions.
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Fischer Nilsson, J. (2013). Diagrammatic Reasoning with Classes and Relationships. In: Moktefi, A., Shin, SJ. (eds) Visual Reasoning with Diagrams. Studies in Universal Logic. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0600-8_6
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DOI: https://doi.org/10.1007/978-3-0348-0600-8_6
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