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Towards Mathematical Morpho-Logics

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Technologies for Constructing Intelligent Systems 2

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 90))

Abstract

In this paper, we suggest a new way to process information represented in a logical framework based on mathematical morphology. We show how the basic morphological operations can be expressed in a logical setting. We give some properties, show some links with revision and fusion, and ideas illustrate possible use of morpho-logics to approximation, reasoning and decision.

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References

  1. C. E. Alchourrón, P. Gärdenfors, and D. Makinson. On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. Journal of Symbolic Logic, 50: 510–530, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  2. O. Bailleux and P. Marquis. DISTANCE-SAT: Complexity and Algorithms. In National Conference on Artificial Intelligence AAAI’99, pages 642–647, 1999.

    Google Scholar 

  3. I. Bloch. On Links between Mathematical Morphology and Rough Sets. Pattern Recognition, 33 (9): 1487–1496, 2000.

    Article  MathSciNet  Google Scholar 

  4. I. Bloch. Using Mathematical Morphology Operators as Modal Operators for Spatial Reasoning. In ECAI 2000, Workshop on Spatio-Temporal Reasoning, pages 73–79, Berlin, Germany, 2000.

    Google Scholar 

  5. I. Bloch and H. Maître. Fuzzy Mathematical Morphologies: A Comparative Study. Pattern Recognition, 28 (9): 1341–1387, 1995.

    Article  MathSciNet  Google Scholar 

  6. M. Dalal. Investigations into a Theory of Knowledge Base Revision: Preliminary Report. In AAAI’88, pages 475–479, 1988.

    Google Scholar 

  7. D. Dubois, F. Esteva, P. Garcia, L. Godo, and H. Prade. A Logical Approach to Interpolation based on Similarity Relations. International Journal of Approximate Reasoning, 17 (1): 1–36, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  8. F. Esteva, P. Garcia, and L. Godo. A Modal Account of Similarity-Based Reasoning. International Journal of Approximate Reasoning, 16: 235–260, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  9. M. L. Ginsberg, A. J. Parkes, and A. Roy. Supermodels and Robustness. In Fifteenth National Conference on Artificial Intelligence AAAI’98, pages 334339, Madison, Wisconsin, July 1998.

    Google Scholar 

  10. G. E. Hughes and M. J. Cresswell. An Introduction to Modal Logic. Methuen, London, UK, 1968.

    MATH  Google Scholar 

  11. H. Katsuno and A. O. Mendelzon. Propositional Kowledge Base Revision and Minimal Change. Artificial Intelligence, 52: 263–294, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  12. S. Konieczny and R. Pino-Pérez. On the Logic of Merging. In 6th International Conference on Principles of Knowledge Representation and Reasoning,pages 488–498, Trento, Italy, 1998.

    Google Scholar 

  13. S. Konieczny and R. Pino-Pérez. Merging with Integrity Constraints. In A. Hunter and S. Parsons, editors, ECSQARU’99, volume 1638 of LNCS, pages 232–244, London, July 1999. Springer.

    Google Scholar 

  14. C. Lafage and J. Lang. Représentation logique de préférences pour la décision de groupe. In RFIA 2000, volume III, pages 267–276, Paris, France, February 2000.

    Google Scholar 

  15. C. Lantuejoul and F. Maisonneuve. Geodesic Methods in Image Analysis. Pattern Recognition, 17 (2): 177–187, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  16. G. Matheron. Eléments pour une théorie des milieux poreux. Masson, Paris, 1967.

    Google Scholar 

  17. G. Matheron. Random Sets and Integral Geometry. Wiley, New-York, 1975.

    MATH  Google Scholar 

  18. R. Pino-Pérez and C. Uzcâtegui. Jumping to Explanations versus jumping to Conclusions. Artificial Intelligence, 111: 131–169, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  19. M. Schmitt and J. Mattioli. Morphologie mathématique. Masson, Paris, 1994.

    Google Scholar 

  20. J. Serra. Image Analysis and Mathematical Morphology. Academic Press, London, 1982.

    MATH  Google Scholar 

  21. J. Serra. Image Analysis and Mathematical Morphology, Part II: Theoretical Advances. Academic Press (J. Serra Ed. ), London, 1988.

    Google Scholar 

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Author information

Authors and Affiliations

  1. ENST-TSI, CNRS URA 820, 46 rue Barrault, 75013, Paris, France

    Isabelle Bloch

  2. IRIT-UPS, 118 route de Narbonne, 31062, Toulouse, France

    Jérôme Lang

Authors
  1. Isabelle Bloch
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  2. Jérôme Lang
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Editor information

Editors and Affiliations

  1. CNRS, LIP6, Université Paris VI, 8 rue du Capitaine Scott, 75015, Paris, France

    Bernadette Bouchon-Meunier

  2. Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo, 28660, Boadilla del Monte, Madrid, Spain

    Julio Gutiérrez-Ríos

  3. Escuela Técnica Superior de Ingenieros de Telecomunicación, Universidad Politécnica de Madrid, Ciudad Universitaria s/n, 28040, Madrid, Spain

    Luis Magdalena

  4. Machine Intelligence Institute, Iona College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2002 Springer-Verlag Berlin Heidelberg

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Bloch, I., Lang, J. (2002). Towards Mathematical Morpho-Logics. In: Bouchon-Meunier, B., Gutiérrez-Ríos, J., Magdalena, L., Yager, R.R. (eds) Technologies for Constructing Intelligent Systems 2. Studies in Fuzziness and Soft Computing, vol 90. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1796-6_29

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  • DOI: https://doi.org/10.1007/978-3-7908-1796-6_29

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2504-6

  • Online ISBN: 978-3-7908-1796-6

  • eBook Packages: Springer Book Archive

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