Components of Ontology: Concepts

Earlier, in Evaluation of the C2IEDM as an Interoperability-Enabling Ontology we defined a concept as "anything that has addressable properties". Although this is a loose definition, it fits our usage. Within our formal ontology, concepts exist for several purposes - giving definition and identity to other concepts (which may be compounded of several entailing concepts), giving definition and identity to entities, and finally giving definition and identity to relationships. As these three purposes are very similar (all involve the endowment of definition and identity), they should be considered as part of a class. We will call members of that class compounds. Compounds are defined explicitly as any of the components within our ontology that are composed of several concepts in identity. This includes all of our ontology, with the exception of atomic concepts, and of course the rules (which are not composed of concepts, but are instead applied against concepts and compounds of concepts).

We have earlier mentioned that the various characteristics of concepts are defined as "properties". This is true, but when examined further it is easily seen that these "properties" are actually other concepts. To continue, without confusing the earlier term, we will call these concepts "property exhibiting concepts", or "properties" for short.

It is important to see that although a concept that exhibits a property might be attached to a compound, it is not necessary that the property have the same “value” at all times. For instance, if the concept “location” were to be correctly attributed to an entity, that concept is always linked to that entity, although the value of that concept may change, over time. This changing aspect of a “property exhibiting concept” is called, for convenience, a property value.

The Dimensions of Concepts

For evaluating the "concepts" component of a formal ontology, it becomes helpful to think of concepts in two dimensions.

1. First, each concept has a horizontal applicability, which consists of all the compounds to which a particular concept can possibly belong. This, we call the domain of a concept. The domain of a concept also contains all of the possible property values that it might exhibit. Very specific concepts will have a small domain (they apply to only a small number of compounds). Broadly applicable concepts will have a very large domain. As an example of this idea, think of the concept "red coloring". There are many, many red things, red is a concept with a very large domain. On the other hand, consider the concept "comprised of antimony". There are not too many things that we can think of that are comprised of antimony, hence that concept has a small domain.
   



2. Second, each concept has a vertical applicability, where the concept and a collection of other concepts together define a compound. This we consider the range of concepts that define a compound. The range of concepts that a compound has also contains all of the possible property values that the concepts in that range might have in relation to the compound. Any compound that is even moderately complex, and is non-trivially defined, will have a large range (meaning, that it will take a large number of defining concepts to describe all of the aspects of such a compound). A compound that is either non-complex, or defined in a non-complex manner, will have a small range of concepts defining it.
   

A Method for Concept Evaluation

For this component (concepts) of a formal ontology to be evaluated for completeness, then both aspects have to be considered.

1. First, the domain of concepts must be considered. There should be a mix of both general concepts (those with a large domain) and specific concepts (those with a small domain) for an ontology to be effective. If there are too many concepts that have a very small domain, then it will be difficult to compose rules for the formation of relationships between entities (all of the rules will be based on very small concept domains, therefore be very specific in nature, and not easy to wantify or analyze). On the other hand, if there are not enough concepts with a small domain, then it might become difficult to identify very specific entities, and composing rules becomes very easy, but very difficult to apply with precision.
   
   
   As an example of this, suppose that the only concepts describing the size of vehicles were this "Motorcycle sized, or smaller" and "Larger than a motorcycle". With this simple set of concepts describing the characteristic size, it becomes very difficult to determine rules about relating a “vehicle” with “the ability to cross a certain bridge”. As the number of vehicles "larger than a motorcycle" is very large, and there is a great range of weights and widths of those vehicles, it can be seen that basing "bridge crossing ability" rules on this (with any sort of precision) is not possible without further subdivision of the size concept.
   


2. 
   Second, the ranges of concepts have to be considered. We have described the range of concepts that an entity can have in two broad terms - those concepts exhibiting internal properties, and those exhibiting external properties. These two terms can apply to all compounds, but they are of particular interest in the area of entities. The terms deserve greater explanation, and they seem easy enough to define. Internal properties are those properties that give the compound self-identity. External properties are those properties that define how the entity affects, and is affected by, other entities within the ontology (via relationships).
   

For an example showing the applicability of internal and external properties, consider the entity granny smith apple. A granny smith apple is an entity that has (among others) the internal properties of being the fruit of a certain tree, having height and weight within a certain range, having a certain color and taste, etc. It also has a number of external properties, such as edible source of nutrition for herbivores and omnivores. If we have the n-ary tuple -

school boy => eating => granny smith apple

We see that we have the entity school boy related to the entity eating. As granny smith apple has the external property listed above, and school boy has the internal characteristic of omnivore, and the entity eating has the property of an act describing the ingesting of edibles, then it becomes clear how all these properties work together allowing for the ontological description of school boy eating granny smith apple.

In evaluating the ranges of concepts that exist for the compounds of a formal ontology, it is important to understand to what purpose the ontological description will be put. If it is to support all possible communications within a universe of discourse, then the sorts of interactions between entities, defined by the possible relationships and rules governing their application, must be considered. At that point, each range of concepts must be evaluated to ensure that it has sufficient coverage of external properties to accommodate all of the possibly required relationships between entities. Secondly, for each level of detail resolution that a formal ontology requires its entities to be considered at, there must be sufficient internal properties for the range of concepts for the entities to be considered sufficiently at that level of detail resolution. If a formal ontology is to be able to support the consideration of entities at several (or many) different levels of resolution, then the requirements of the range of concepts for the entities supporting those levels of resolution must be present.

It is apparent, now, that the evaluation of the concepts of a formal ontology is based heavily in the use that the ontology is to serve within the universe of discourse. This is unavoidable, unless the entire domain and range of all possible concepts were to be described as part of the formal ontology. We also see the basing of evaluation within the realm of "intended use" as being a good thing - it allows an application of detail to exist where it is needed.

Earlier article on concepts

Tags: ontology