Aggregation relation (also Decomposition relation, PartOf relation)

This post is part of a series on core relations for structuring representations or models of knowledge.

The aggregation relation is the relation between a whole and its parts. It is the topic of mereology. It is considered to be one of basic abstraction principles [Taivalsaari:1996] in computer science. “Aggregation relation” is synonym to “Decomposition relation”, and “PartOf relation”. They are all names of relations between parts and a whole.

The aggregation relation satisfies the following rules [Borgo+:2009]:

  • Reflexivity: An X is always part of itself.
  • Transitivity: If X is part of Y, and Y is part of Z, then X is part of Z.
  • Antisymmetry: If X is part of Y, and Y is part of X, then X and Y are equal.
  • Extensionality: If X is not part of Y, then there must exist some Z such that Z is part of X and Z is not part of Y.
  • Dissectivity: If Y has a property P and X is part of Y, then X has property P.
  • Additivity: If X has property P and Y has property P, and Z has no parts other than X and Y, then Z has property P.

There are other, alternative sets of rules that you may want aggregation to satisfy; I like the above, because I agree with all but the Dissectivity rule: It is not clear to me how emergent properties (those that a whole has, and none of its parts does) fit in the above, since they seem to violate Dissectivity.

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Ivan Jureta

I hold the Senior Researcher (Chercheur qualifié) position with the Belgian national research fund (Fonds de la Recherche Scientifique – FNRS, Brussels) and am Associate Professor with the Department of Business Administration, University of Namur. My principal research interest is in method engineering and method automation, focusing on the elicitation, modeling and analysis of knowledge that human experts apply in problem solving and decision making, the engineering of ontologies and processes capturing that knowledge, and the automation of the said processes. This interest falls within the various research fields concerned with the transfer, preservation and automation of knowledge. I am the author of “Analysis and Design of Advice” (Springer, 2011) and have published over 50 research papers on these topics within the fields of requirements engineering, business analysis, and conceptual modeling of information systems. I organize and chair the series of International Workshops on Modeling and Reasoning for Business Intelligence (MORE-BI), held in Brussels in 2011 and Florence in 2012. I serve on scientific committees of the IEEE International Requirements Engineering Conference (RE), the International Conference on Advanced Information Systems Engineering (CAiSE), and the International Conference on Conceptual Modeling (ER). In parallel, I am / have been involved with several startups at CxO level and have held lead roles in Product Design for web and digital services that today serve more than 500.000 people every day.