Implications of Open World Assumption in Ontology Applications
Looking at newbies’ questions in OWL forums [1], I came to notice that most computer science guys usually makes wrong assumptions about inference on ontologies. This is because we are used to work with relational databases and inference methods that assume that all possible information is known (closed-world assumption), which in fact possed the challenge of information integration in the first place.
In Description Logics (DL) knowledge bases (KBs), i.e. information represented through ontological formats and exploited through a concept reasoner, the Open World Assumption (OWA) makes that conclussions not only depend on information contained in the knowledge base, but also on unknown/missing and plausible information. This is, using information contained on it we can conclude that certain statement (query) holds, but we cannot simply deny it if there is no enough evidence. This is because the information that might draw the conclusion false might not be contained in the KB.
The concrete example discussed in the forum was: there are defined two partitions for a class on which the first one identifies individuals with at least one value for the property P (P min 1), meanwhile the second one identifies those individuals that do not have any value for P (P exactly 0). Both are cardinality constraints on property P.
Meanwhile reasoners can easily classify individuals in the first partition, they are not capable of classifying an individual in the second partition when an individual lacks of relations through P. The reason is that the reasoner assumes that that information might be missing in the KB. Then, how can be classified an individual in the second partition? The answer is simple, assert it directly in the KB:
I = P exactly 0 && …
This isn’t intuitive for people that has been educated on relational databases, but is quit clear for Ontology experts and concept reasoners can easily handle this kind of assertions.
An example
In order to clarify the matter you can see the following example, where people is divided in two partitions: those with children (Parent) and those without any children (NoParent). There are two persons, Joseph and Jesus, such that the second is son of the first and he has no children. In the following Protege snapshots you can see how are classified both of them. Note the declaration of the second individual: Jesus = Person && hasChild exactly 0. Inferences are shown with a yellow background and dashed lines.
 Person with children (Parent) |
 Person without children (NoParent) |
Other alternatives have been proposed for solving this problem. For instance, it has been introduced an epistemic operator [2] that allows to specify: given that all about property P is known. In this way you specify in the NoParent concept that information regarding children is completely known in the knowledge base. Nevertheless, as far as I know, concept reasoners do not support this operator yet.
You can find more information about OWA and hor to help your concept reasoner to decide on more complex partitions in [3]. The example is a little unclear as long as authors define Sex as a class and Male and Female as its subclasses. If instead of Sex they would use Animal, the example would make more sense. This is, an animal is male or female, but not both at once.
References
