There are a number of situations in which it is helpful to have a formal representation of the concepts that are in play in some business or organization; a concept model.

For example, in business reporting or management information systems, a concept model can ensure that the information in those reports and interfaces consistently reflects the business concepts that are being reported on. Concept models are also important in information systems development, where they provide a computationally-independent view of the subject matter that is to be represented in data and manipulated by applications. Similarly, in data integration a concept model can represent a common, enterprise-wide view of the meanings of the data in different sources and system outputs.

What Is a Concept Model

What do we mean by a concept? This can be anything in some real or possible world.

What do we mean by a model? A model is any formal, structured representation of something other than itself.

Every element or feature in the model has a relationship to something that it represents.

It is important to note that this is independent of the underlying model formalism, whether it is a graphically-rich Computer Aided Design (CAD) model such as a UML Class Model, a sheet of musical notation, or a structured vocabulary. What the model represents and how it represents it are two separate matters.

The aim of a concept model is to formally define what it means to be a given kind of thing. This includes, as a minimum, addressing the two questions: "What kind of thing is it?" and "What distinguishes it from other things?" These provide the necessary (or necessary and sufficient) conditions and are known as the intension (with an 's') for that kind, or class, of thing.

For example, we may say that

• there is a set of things that is a mammal (itself a kind of vertebrate and so on)

and

• it is necessarily the case that, to be a member of this particular set, a thing must have floppy ears, a tail that wags, and a wet nose.

This is a (somewhat informal) intension of all the things that are a dog. Note that we did not need to rely on the word 'dog' in order to define that kind of thing in the world.

In set theoretic terms, the set of things that matches the criteria set out in the intension form the extension of that set. The concept model tells you what it means to be that kind of thing. This is the case whether any things of that kind exist or not, for example if they are described in order to avoid them or to predict them.

These intensional definitions will necessarily make reference to other kinds of thing that are defined in the same model. In this way, the concept model provides an internally-consistent account of the things that the business cares about.

In order to make rules, declarations, or definitions about what can or should be, those rules cannot refer to data or to words — they may only refer to concepts. A concept model makes that possible by providing the predicates for those rules and statements.

Concept Models and Ontologies

This kind of concept model is often referred to as an ontology.

Any model that frames a formal set of intensional definitions of things is, by definition, an ontology — just as those things with wet noses are, by definition, a dog. This is regardless of what underlying formalism we use to make those intensional statements, provided only that the formalism is able to unambiguously make those kinds of intensional statement.

Some model formalisms are better suited to saying this kind of thing than others. Many ontologies use Description Logic (DL) or First Order Logic (FOL) expressed using textual expressions with special symbols such as ∀ or ∃. A structured business vocabulary, for example in SBVR, can also do this since it uses words that are themselves formally defined to provide the necessary kinds of formal expression.

This should not be confused with the kind of ontology that is used to represent meanings in linked data or knowledge graphs, for example using the Web Ontology Language (OWL) from the W3C. Those are also a kind of ontology but are not concept models since they represent data. In principle, OWL can also be used to express a concept model since it expresses the same formalisms as Description Logic. However, when this is done it should be made very clear that the things that it represents are real things, and the way it is constructed will be very different to an ontology used to reason over data.

Concept Models in the Business Domain

Note that a concept model is not derived by taking a logical data model, crossing out all the 'complicated' bits, and presenting this to the business. That is one use of the term 'conceptual model' common in IT, which is why we use the term 'concept model' here. A concept model is not an abstraction of a logical data model; it is a concrete representation of reality.

One kind of artifact commonly used by business to perform the role of a concept model is the business glossary. However, models based on words alone are no substitute for logical representations of concepts, and a business glossary is not a concept model. The exception to this is SBVR, which works because the concepts defined in an SBVR Structured Business Vocabulary are represented using logically-unambiguous intensional statements.

In summary, a concept model is a representation of possible things in the world, or things that are to be considered, avoided, allowed, and so on. It represents those things unambiguously using formal logic. As such, a concept model also provides the building blocks for higher orders of logical expression about things in the business domain.

References

Description Logic (DL): https://en.wikipedia.org/wiki/Description_logic

First Order Logic (FOL): https://en.wikipedia.org/wiki/First-order_logic

Semantics of Business Vocabulary and Business Rules (SBVR): https://www.omg.org/spec/SBVR/

Web Ontology Language (OWL): https://www.w3.org/TR/owl-ref/

# # #