Abstract
Mereocat (mereological category), a theory of part-whole relations based on category theory, is proposed and its basic properties are discussed. The concepts of mereological sum is redefined in categorical framework. The theory is then applied to model some properties of component software architecture.
Partly supported by NSERC of Canada Grant.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Allen, R., Garlan, D.: A Formal Basis for Architectural Connection. ACM Transactions on Software Engineering and Methodology 6(3), 213–249 (1997)
Barr, M., Wells, C.: Toposes, Triples and Theories. Springer, Heidelberg (1985)
Barwise, J., Seligman, J.: Information Flow: The Logic of Distributed Systems. Cambridge University Press, Cambridge (1997)
Casati, R., Varzi, A.: Parts and places: the structures of spatial representation. MIT Press, Cambridge (1999)
Fiadeiro, J.L.: Categories for Software Engineering. Springer, Heidelberg (2004)
Forrest, P.: Nonclassical mereology and its application to sets. Notre Dame Journal of Formal Logic 43(2), 79–94 (2002)
Goguen, J.A.: Categorical foundations for general systems theory. In: Pichler, F., Trappl, R. (eds.) Advances in Cybernetics and Systems Research, pp. 121–130, Transcripta Books (1973)
Goguen, J.A., Rosu, G.: Institution morphisms. Formal Aspects Computing 13(3-5), 274–307 (2002)
Goodman, N.: The structure of appearance. Dordrecht (1977)
Grzegorczyk, A.: The system of Leśniewski in relation to contemporary logical research. Studia Logica 3, 77–95 (1955)
Ivers, J., Clements, P., Garlan, D., Nord, R., Schmerl, B., Oviedo, J.: Documenting component and connector views with UML 2.0. Technical Report CMU-CS-2004-TR-008, School of Computer Science, Carnegie Mellon University (April 2004)
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)
Janicki, R.: Basic mereology with equivalence relations. In: Jedrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol. 3618, pp. 507–519. Springer, Heidelberg (2005)
Janicki, R., Khedri, R.: On a formal semantics of tabular expressions. Science of Computer Programming 39(2–3), 189–213 (2001)
Janicki, R., Lê, D.T.M.: Towards a pragmatic mereology. Fundamenta Informaticae 75(1-4), 295–314 (2007)
Jazayeri, M., Ran, A., van der Linden, F.: Software architecture for product families: principles and practice. Addison-Wesley, Reading (2000)
Lawvere, F.W., Rosebrugh, R.: Sets for Mathematics. Cambridge University Press, Cambridge (2003)
Lê, D.T.M., Janicki, R.: On a parthood specification method for component software. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 537–546. Springer, Heidelberg (2006)
Leonard, H.S., Goodman, N.: The calculus of individuals and its uses. Journal of Symbolic Logic 5(2), 45–55 (1940)
Leśniewski, S.: Grundzüge eines neuen systems der grundlagen der mathematik. Fundamenta Mathematicae 24, 1–81 (1929)
Lopes, A., Wermelinger, M., Fiadeiro, J.L.: High-order architectural connectors. ACM Transactions on Software Engineering and Methodology 12(1), 64–104 (2003)
MacLane, S.: Categories for the Working Mathematician. Springer (1998)
Meirav, A.: Wholes, Sums and Unities (Philosophical Studies). Springer (2003)
Motschnig-Pitrik, R., Kaasbøll, J.J.: Part-whole relationship categories and their application in object-oriented analysis. IEEE Transactions on Knowledge and Data Engineering 11(5), 779–797 (1999)
Parnas, D.L.: On the criteria to be used in decomposing systems into modules. Communications of the ACM 15(12), 1053–1058 (1972)
Parnas, D.L.: On a buzzword: Hierarchical structure. In: Proc. of IFIP 1974 Congress, pp. 336–339. North-Holland, Amsterdam (1974)
Pawlak, Z.: Rough Sets. Kluwer Academic Publishers, Dordrecht (1991)
Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning. Journal of Approximate Reasoning 15, 316–333 (1997)
Rumbaugh, J., Eddy, F.: Object-Oriented Modeling and Design. Prentice-Hall, Englewood Cliffs (1991)
Rumbaugh, J., Jacobson, I., Booch, G.: The Unified Modeling Language Reference Manual. Addison-Wesley, Reading (2004)
Salustri, F.A., Lockledge, J.C.: Towards a formal theory of products including mereology. In: Proc. of 12th Int’l Conf. on Engineering Design, pp. 1125–1130 (1999)
Simons, P.: On understanding Leśniewski. History and Philosophy of Logic 3(2), 165–191 (1982)
Simons, P.: Parts: A Study in Ontology. Oxford University Press, Oxford (1987)
Skowron, A., Stepaniuk, J., Peters, J.F.: Rough Sets and Infomorphisms: Towards Approximation of Relations in Distributed Environments. Fundamenta Informaticae 54(1-3), 263–277 (2003)
Smith, B.: Mereotopology: a theory of parts and boundaries. Data and knowledge engineering 20(3), 287–303 (1996)
Srzednicki, J.T.J., Rickey, V.F. (eds.): Leśniewski’s Systems. Kluwer Academic Publishers, Dordrecht (1984)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lê, D.T.M., Janicki, R. (2008). A Categorical Approach to Mereology and Its Application to Modelling Software Components. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets VIII. Lecture Notes in Computer Science, vol 5084. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85064-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-85064-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85063-2
Online ISBN: 978-3-540-85064-9
eBook Packages: Computer ScienceComputer Science (R0)