Construction of Concepts and Decomposition of Objects

Day - Time: 19 October 2010, h.11:00
Place: Area della Ricerca CNR di Pisa - Room: C-29

Elvira Immacolata Locuratolo


The seminar aims to present the research results achieved in transporting to the concept theory algorithms for mapping graphs of classes supported by semantic data models to graphs of classes supported by object systems. The concept theory comprises the distinction between the intensional and extensional aspects of concepts. The former is referred to the information contents of concepts, whereas the latter is referred to the sets of objects which fall under the concepts. These two aspects of concepts define two different levels of representation, called intensional/concept level and extensional/set-theoretical level, respectively. It is correct to go from the concept level to the set-theoretical level, but not vice versa.

The partitioning algorithms employed in computer science and information engineering have been defined at the set-theoretical level.

These algorithms cannot be applied to the concept level; however, they can be transported to this level. Really, our approach, which is based on the construction of concepts and on the decomposition of objects, allows:

  • Defining the process of concept construction.
  • Providing a network of concepts enclosing:
    • All and only the concepts related with a Universe of Discourse and basic concepts
    • All and only the intensional inclusion relations.
  • Recognizing the concepts that can be mapped to the extensional level.
  • Organizing the set of classes at the extensional level into a graph of object classes.
  • Transforming it into a graph of semantic classes.

Differently from other approaches, which can be found in information modeling and knowledge bases, and in formal context analysis, our approach makes it possible to relate each extension with all and only the concepts which can be constructed starting from a Universe of Discourse and basic concepts. Possible application fields of our approach are outlined.