The traditional theory of “part of” relations (i.e. mereology) is enriched by adding the formal concept of equivalent and exchangeable parts. Various possible axioms and their roles are discussed. An approach is focused on application to model software structures.


Equivalence Relation Partial Order Proper Part Hasse Diagram Partial Order Relation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Artale, A., Franconi, G., Guarina, E., Pazzi, L.: Part-whole relations in object-centered systems. Data and Knowledge Engineering 20, 347–383 (1996)zbMATHCrossRefGoogle Scholar
  2. 2.
    Casati, R., Varzi, A.C.: Parts and Places. MIT Press, Cambridge (1999)Google Scholar
  3. 3.
    Goodman, N.: The Structure of Appearance. In: Reidel, D. (ed.), 3rd edn. (1977)Google Scholar
  4. 4.
    Grzegorczyk, A.: The System of Leśniewski in Relation to Contemporary Logical Research. Studia Logica 3, 77–95 (1955)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Hoffman, D.M., Weiss, D.M.: Collected Papers by David L. Parnas. Addison-Wesley, Reading (2001)Google Scholar
  6. 6.
    Janicki, R.: Remarks on Mereology of Direct Products and Relations. In: Desharnais, J., Frappier, M., MacCaull, W. (eds.) Relational Methods in Computer Science, pp. 65–84. Methodos Publ. (2002)Google Scholar
  7. 7.
    Janicki, R.: On a mereological system for relational software specifications. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 375–386. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Janicki, R., Khédri, R.: On a Formal Semantics of Tabular Expressions. Science of Computer Programming 39, 189–214 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Janicki, R., Parnas, D.L., Zucker, J.: Tabular Representations in Relational Documents. In: Brink, C., Kahl, W., Schmidt, G. (eds.) Relational Methods in Computer Science, pp. 184–196. Springer, Heidelberg (1997)Google Scholar
  10. 10.
    Khédri, R., Wang, L., Situ, L.: Requirements Specification Decomposition: A System Testing Driven Approach. In: Proc. 7th Int’l Seminar On Relational Methods in Computer Science, Bad Melente, Germany, pp. 97–104 (2003)Google Scholar
  11. 11.
    Leonard, H., Goodman, N.: The calculus of individuals and its uses. Journal of Symbolic Logic 5, 45–55 (1940)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Leśniewski, S.: Grundzüge eines neuen Systems der Grundlagen der Mathematik. Fundamenta Matematicae 24, 1–81 (1929)Google Scholar
  13. 13.
    Polkowski, L., Skowron, A.: Rough Mereology; A New Paradigm for Approximate Reasoning. Journal of Approximate Reasoning 15(4), 316–333 (1997)MathSciNetGoogle Scholar
  14. 14.
    Rosen, K.H.: Discrete Mathematics and its Applications. McGraw-Hill, New York (1991)Google Scholar
  15. 15.
    Salustri, F.A., Lockledge, J.C.: Towards a formal theory of products including mereology. In: Proc. 12th Int’l Conf. on Engn. Design, Munich, pp. 1125–1130 (1999)Google Scholar
  16. 16.
    Simons, P.: On Understanding Leśniewski. Hist. and Phil. of Logic 3, 165–191 (1982)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Simons, P.: Parts. A Study in Ontology. Claredon Press (1987)Google Scholar
  18. 18.
    Szyperski, C.: Component Software. Addison-Wesley, Reading (1997)Google Scholar
  19. 19.
    Srzednicki, J.T.J., Rickey, V.F.: Leśniewski’s Systems. Kluwer, Dordrecht (1984)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ryszard Janicki
    • 1
  1. 1.Department of Computing and SoftwareMcMaster UniversityHamiltonCanada

Personalised recommendations