Metamodel

A Metamodel is a model that can be used to define other more constrained models.

• AKA: Model of Models, Model Template, Modeling Framework.
• Context:
  • It can typically be defined as a modeling language for specifying model structures.
  • It can typically be created by a metamodel creation task (metamodeling).
  • It can typically contain one or more free model parameters that enable model instantiation.
  • It can typically define metamodel elements that represent model components.
  • It can typically specify metamodel constraints that govern model generation.
  • It can often establish metamodel relationships between metamodel elements.
  • It can often incorporate model variables for representing dynamic system aspects.
  • It can often support model transformation through metamodel mappings.
  • It can often enable model validation via metamodel rules.
  • It can often facilitate supervised learning tasks through model family specification.
  • It can range from being an Informal Metamodel to being a Formal Metamodel, depending on its metamodel specification rigor.
  • It can range from being a Simple Metamodel to being a Complex Metamodel, depending on its metamodel element count.
  • It can range from being a Domain-Specific Metamodel to being a General-Purpose Metamodel, depending on its metamodel application scope.
  • ...
• Examples:
  • Computational Metamodels, such as:
    • UML Metamodel for software design modeling.
    • BPMN Metamodel for business process modeling.
    • Process Metamodel for workflow structure modeling.
  • Mathematical Metamodels, such as:
    • Equation-based Metamodel for mathematical relationship modeling.
    • Statistical Model Family for statistical analysis modeling.
    • Probabilistic Graphical Model Family for uncertainty representation modeling.
  • Learning-Based Metamodels, such as:
    • Automated Predictive Modeling Metamodel for predictive task modeling.
    • Supervised Model-based Learning Metamodel for pattern recognition modeling.
  • Information Metamodels, such as:
    • Metadata Model for data description modeling.
    • Lexinfo Metadata Modeling Language for linguistic annotation modeling.
    • Ontology Metamodel for knowledge representation modeling.
  • ...
• Counter-Examples:
  • Data Models, which represent specific data structures rather than model templates.
  • Function Familys, which define specific mathematical function sets rather than model-defining frameworks.
  • Model Instances, which implement concrete models without metamodel abstraction capability.
  • AI-based System implementations, which use metamodels but are not themselves metamodels.
• See: Abstract Entity, Model-Driven Engineering, Meta-Metamodel, AI-based System Development Framework, Model Transformation.

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References

2011

• http://en.wikipedia.org/wiki/Metamodeling
  • 'Metamodeling, or meta-modeling in software engineering and systems engineering among other disciplines, is the analysis, construction and development of the frames, rules, constraints, models and theories applicable and useful for modeling a predefined class of problems. As its name implies, this concept applies the notions of meta- and modeling.

    "Metamodeling" is the construction of a collection of "concepts" (things, terms, etc.) within a certain domain. A model is an abstraction of phenomena in the real world; a metamodel is yet another abstraction, highlighting properties of the model itself. A model conforms to its metamodel in the way that a computer program conforms to the grammar of the programming language in which it is written.

2004

• (Amatriain, 2004) ⇒ Xavier Amatriain. (2004). “An Object-Oriented Metamodel for Digital Signal Processing with a focus on Audio and Music." PhD Thesis.
  • http://www.iua.upf.es/~xamat/Thesis/html/node2.html
  • Model: A model can be understood as the formal abstract representation of a given system. A single system can be represented through different models, depending on the level of abstraction required and foreseen use.

    Metamodel: A model that explains a set of related model[s.

1974

• (Baird, 1974) ⇒ Yonathan Bard. (1974). “Nonlinear Parameter Estimation." Academic Press. ISBN:0120782502
  • QUOTE: We refer to the relations which supposedly describe a certain physical situation, as a model. Typically, a model consists of one or more equations. The quantities appearing in the equations we classify into variables and parameters. The distinction between these is not always clear cut, and it frequently depends on the context in which the variables appear. Usually a model is designed to explain the relationships that exist among quantities which can be measured independently in an experiment; these are the variables of the model. To formulate these relationships, however, one frequently introduces “constants" which stand for inherent properties of nature (or of the materials and equipment used in a given experiment). These are the parameters.

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