A most frustrating problem often encountered by people, with experience in relational databases when they are introduced to OWL ontologies, is that OWL ontology reasoners seem to ignore constraints. In this post I give examples of this problem, explain why they happen and I provide ways to deal with each example.
A typical example encountered in relational databases is that of modeling orders with orderlines, which can be modeled via
Orderlines tables where the
Orderlines table has a foreign key constraint to the
Orders table. A related OWL ontology is given in Figure 1. It creates as expected
Orderline classes with a
hasOrder object property. That individuals of
Orderline are necessarily associated with one order is enforced by
Orderline being a subclass of
exactly 1 owl:Thing
Two frustrating and most surprising errors given the Order ontology are: (1) if an
Orderline individual is created for which no associated
Order individual exists, the reasoner will not give an inconsistency, and (2) if an
Orderline individual is created for which two or more
Order individuals exist, the reasoner will also not give an inconsistency.
Missing Association Problem
Say we create an individual
orderline123 of type
Orderline, which is not associated with an individual of type Order, in this case the reasoner will not give an inconsistency. The reason for this is due to the open world assumption. Informally it means that the only inferences that the reasoner can make from an ontology is based on explicit information stated in the ontology or what can derived from explicit stated information.
When you state
orderline123 is an
Orderline, there is no explicit information in the ontology that states that
orderline123 is not associated with an individual of
Order via the
hasOrder property. To make explicit that
orderline123 is not in such a relation, you have to define
orderline123 as in Figure 2.
hasOrder max 0 owl:Thing states that it is known that
orderline123 is not associated with an individual via the
Too Many Associated Individuals Problem
Assume we now change our definition of our
orderline123 individual to be associated via
hasOrder to two individuals of
Order as shown in Figure 3. Again, most frustratingly the reasoner does not find that the ontology is inconsistent. The reason for this is that OWL does not make the unique name assumption. This means that individuals with different names can be assumed by the reasoner to represent a single individual. To force the reasoner to see
order2 as necessarily different, you can state
order1 is different from
order2 by adding
order1 (or similarly for
Constraint Checking versus Deriving Inferences
The source of the problems described here is due to the difference between the
purposes of a relational database and an OWL reasoner. The main purpose of a
relational database is to enable view and edit access of the data in such a way that the integrity of the data is maintained. A relational database will ensure that the data adheres to the constraints of its schema, but it cannot make any claims beyond what is stated by the data it contains. The main purpose of an OWL reasoner is to derive inferences from statements and facts. As an example, from the statement
Class: Dog SubclassOf: Animal and the fact
Individual: pluto Type: Dog it can be derived that
pluto is an
Animal, even though the ontology nowhere states explicitly that
pluto is an
Many newcomers to OWL ontologies get tripped up by the difference in purpose of relational databases and OWL ontologies. In this post I explained these pitfalls and how to deal with them.
If you have an ontology modeling problem, you are welcome leaving a comment detailing the problem.