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Toward a well-founded theory for multi-level conceptual modeling

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Abstract

Multi-level conceptual modeling addresses the representation of subject domains dealing explicitly with multiple classification levels. Despite the recent advances in multi-level modeling techniques, we believe that the literature in multi-level conceptual modeling would benefit from a theory that: (1) formally characterizes the nature of classification levels and (2) precisely defines the structural relations that may occur between elements of different classification levels. This work aims to fill this gap by proposing an axiomatic theory that can be considered a reference top-level ontology for types in multi-level conceptual modeling. The theory provides the modeler with basic concepts and patterns to articulate domains that require multiple levels of classification as well as to inform the development of well-founded languages for multi-level conceptual modeling. The whole theory is founded on a basic instantiation relation and characterizes the concepts of individuals and types, with types organized in levels related by instantiation. Further, it includes intra-level structural relations that are used to define expressive multi-level models and cross-level relations that allow us to account for and incorporate the different notions of power type in the literature.

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Notes

  1. This discussion is extended in this paper in Sect. 4, where we show how the definitions are related to each other and how they can be given different uses.

  2. We are aware that certain approaches such as RM-ODP distinguish the terms instantiation and instance, but this distinction is not required here, and hence, we use the terms interchangeably.

  3. For the sake of clarity in the presentation, we focus in this section on types that apply necessarily to their instances (the so-called rigid types  [21]). A treatment of dynamic classification (and non-rigidity) is deferred to Sect. 6.2.

  4. Note that in biology there is a long and involved debate on the ontological status of taxa such as species  [15]. One of the interpretations is that biological taxa (e.g., the “Homo sapiens” species, the “Canis Lupus Familiaris” species) represents a group of animals rather than a kind or type of animal. We stay clear of this debate and represent species (and other taxa) as the type that is instantiated by all members of that group (and only by them) (e.g., “Human” and “Dog”).

  5. Datatypes such as String and Integer can be considered first-order types whose instances (e.g., the integer value “1” and the string “xyz”) are “abstract entities” (see  [21], p. 327).

  6. A more comprehensive definition would acknowledge that differences in various regularity attributes simultaneously may cancel each other’s effects on the intension; thus, we could add a ceteris paribus clause to definition D12, which would then state that an attribute a is a regularity attribute iff different values for a with all other things equal would result in a different type.

  7. For the sake of simplicity, we have assumed here that the classes are not abstract. The semantic mapping becomes even more involved in the presence of abstract classes.

  8. The full specification of the theory in Alloy can be found in https://github.com/jpalmeida/mlt-ontology.

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Acknowledgements

This research is partly funded by the Brazilian Research Funding Agencies CAPES, CNPq (Grant Numbers 311313/2014-0, 485368/2013-7, 461777/2014-2) and FAPES (Grant Number 69382549).

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Authors and Affiliations

  1. Ontology and Conceptual Modeling Research Group (NEMO), Federal University of Espírito Santo (UFES), Vitória, ES, Brazil

    Victorio A. Carvalho & João Paulo A. Almeida

  2. Research Group in Applied Informatics, Informatics Department, Federal Institute of Espírito Santo (IFES), Colatina, ES, Brazil

    Victorio A. Carvalho

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  1. Victorio A. Carvalho
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  2. João Paulo A. Almeida
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Correspondence to João Paulo A. Almeida.

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Communicated by Prof. Colin Atkinson, Thomas Kühne, and Juan de Lara.

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Carvalho, V.A., Almeida, J.P.A. Toward a well-founded theory for multi-level conceptual modeling. Softw Syst Model 17, 205–231 (2018). https://doi.org/10.1007/s10270-016-0538-9

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