Object identification and retrieval in a CAST library

  • Charles Rattray
  • Marion Marsden
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 585)

Abstract

The classification and recognition problems are fundamental to an understanding of object identification and retrieval in a CAST library or repository.

In this paper, we have attempted to provide a framework in the guise of categories of approximations and categorical shape theory, in which to consider these problems. In doing so, we have chosen to specify CAST objects in terms of well-defined mathematical entities, namely, sketches. Crucial to classification and recognition in this context is the need to match sketches. By emphasising their geometric aspects we have suggested that a graph theoretic view of matching might be fruitful.

Much more work needs to be done, of course, to exploit categorical shape theory and the theory of sketches in this area. The geometric matching algorithm, too, must be generalised to deal properly with cones and cocones, and to deal with partial matching of sketches. This is not trivial and may benefit from the generalised matching algorithm design approach of Srinivas, based on sheaf theory [32].

Keywords

Equivalence Class Object Identification System Requirement Graph Theoretic Approach Derivational Analogy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M Barr, C Wells: Topos, Triples, and Theories, Springer-Verlag, New York, 1985.Google Scholar
  2. [2]
    M Barr: “Models of Sketches”, Cahiers de Topologie et Géométrie Difféntielle Catégoriques, XXVII, 2, 1986.Google Scholar
  3. [3]
    M Barr, C Wells: Category Theory for Computing Science, Prentice-Hall International Series in Computer Science, London, 1990.Google Scholar
  4. [4]
    F L Bauer, M Wirsing: “Crypt-Equivalent Algebraic Specifications”, Acta Informatica, 25, 1988.Google Scholar
  5. [5]
    K Borsuk: Theory of Shape, Monografie Matematyczne, 59, Warsaw, 1975.Google Scholar
  6. [6]
    J G Carbonell: “Derivational Analogy and Its Role in Problem-Solving”, Proceedings AAAI-83, Washington, 1983.Google Scholar
  7. [7]
    J-M Cordier, T Porter: “Pattern Recognition and Categorical Shape Theory”, UCNW Pure Maths Preprint 86.16, University of Wales, Bangor, UK, 1986.Google Scholar
  8. [8]
    J-M Cordier, T Porter: Shape Theory: categorical approximation methods, Ellis Horwood Ltd., 1990.Google Scholar
  9. [9]
    A Deleanu, P Hilton: “On the Categorical Shape of a Functor”, Fundamenta Mathematicae, XCVII, 3, 1977.Google Scholar
  10. [10]
    C Ehresmann: “Esquisses et Types des Structures Algébriques”, Bull. Instit. Polit., Iasi, XIV, 1968.Google Scholar
  11. [11]
    H Ehrig, B Mayr: Fundamentals of Algebraic Specification, Vol. I: Equations and Initial Semantics, Springer-Verlag, 1985.Google Scholar
  12. [12]
    H-D Ehrich, A Sernadas, C Sernadas; “Objects, Object Types, and Object Identification”, Lecture Notes in Computer Science, 393, 1989.Google Scholar
  13. [13]
    D Eichmann, J Atkins: “Design of a Latticed-Based Faceted Classification System”, 2nd International Conference on Software Engineering and Knowledge Engineering, Skokie, Illinois, June 21–23 1990.Google Scholar
  14. [14]
    W Gaube, H C Mayr, P C Lockemann: “Retrieval in a Module Library Using Formal Specifications: preliminary search using syntactic properties”, Preprint, Institut für Informatik II, Universität Karlsruhe, 1985.Google Scholar
  15. [15]
    R Gould: Graph Theory, Benjamin Cummings Publ., 1988.Google Scholar
  16. [16]
    J W Gray: “Categorical Aspects of Data Type Constructors”, Theoretical Computer Science, 50, 2, 1987.Google Scholar
  17. [17]
    R Guitart, C Lair: “Calcul syntaxique des modèles et formules internes”, Diagrammes, 4, 1980.Google Scholar
  18. [18]
    R Guitart, C Lair: “Limites et co-limites pour représenter les formules”, Diagrammes, 7, 1982.Google Scholar
  19. [19]
    D Kapur, H Zhang: “An overview of RRL: Rewrite Rule Laboratory”, 9th International Conference on Automated Deduction, Lecture Notes in Computer Science, 355, 1989.Google Scholar
  20. [20]
    C Lair: “Etude Générale de la Categorie des Esquisses”, Esquisses Math., 23, Amiens, 1975.Google Scholar
  21. [21]
    C Lair: “Catégories qualifiables et catégories esquissables”, Diagrammes, 17, 1987.Google Scholar
  22. [22]
    C Lair: “Trames et Sémantiques Catégoriques des Systèmes de Trames”, Diagrammes, 18, Paris, 1987.Google Scholar
  23. [23]
    S K Lellali: “Categorical Abstract Data Types (CADT)”, Digrammes, 21 1989.Google Scholar
  24. [24]
    S MacLane: Categories for the Working Mathematician, Springer-Verlag, New York, 1971.Google Scholar
  25. [25]
    M Makai, R Paré: Accessible Categories: the Foundations of Categorical Model Theory, Contemporary Mathematics, 104, American Mathematics Society Publication, 1989.Google Scholar
  26. [26]
    R Prieto-Diaz, P Freeman: “Classifying Software for Reusability”, IEEE Software, 1987.Google Scholar
  27. [27]
    C Rattray, J McInnes, A C Reeves, M Thomas: “Software Re-Usability in a Knowledge-Based Environment”, Proceedings of 3rd Annual Knowledge-Based Assistant Conference, Rome Air Development Center, Utica, 1988.Google Scholar
  28. [28]
    C Rattray: “Systems Factories and CAST”, in Cybernetics and Systems '90 (R Trappl: editor), World Scientific Publ. Co., 1990.Google Scholar
  29. [29]
    C Rattray, J McInnes, A C Reeves, M Thomas: “A Knowledge-Based Model for Software Re-Usability”, in Artificial Intelligence and Software Engineering (D Partridge: editor), Ablex Publ. Co., New York, 1990.Google Scholar
  30. [30]
    P Rowlinson: personal communication, 1991.Google Scholar
  31. [31]
    G-C Rota, D H Sharp, R Sokolowski: “Syntax, Semantics, and the Problem of the Identity of Mathematical Objects”, J Phil of Science, 55, 3, 1988.Google Scholar
  32. [32]
    Y V Srinivas: “Pattern Matching: a Sheaf-Theoretic Approach”, 2nd International Conference on Algebraic Methodology and Software Technology (AMAST'91), Workshops in Computing Series, Springer-Verlag, 1992.Google Scholar
  33. [33]
    Tanvir Ahmed: PhD thesis, Department of Computer Science, University of Strathclyde, UK, 1991.Google Scholar
  34. [34]
    Y S Yang: personal communication, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Charles Rattray
    • 1
  • Marion Marsden
    • 1
  1. 1.Department of Computing ScienceUniversity of StirlingStirlingScotland

Personalised recommendations