4.4 The Web Ontology Language 83
Inference for a theory is conceptually simple. If a statement is true in every
possible world, then it is a fact. If a statement is true in some worlds, but not
in others, then one cannot say that it is either true or false: it is not a fact,
at least not yet. A statement that is true in every possible world compatible
with a theory is said to beentailedby the theory. Although the notion of
entailment is simple and intuitive, it is not very practical. After all, there will
always be infinitely many possible worlds so it is not possible to examine
every one. In practice, some other technique is necessary to determine what
statements are entailed.
The most commonly used technique for determining entailment is to use
rules. This is similar to how inference is done in RDF, but there is an impor-
tant difference. Applying RDF rules in any particular RDF document will
always eventually terminate. If one does the same for OWL, then it will not
terminate because OWL models are always infinite. In other words, one can
infer infinitely many facts. To perform inference with OWL one must fo-
cus on a particular question that one would like to answer. For example,
one might ask for all known diseases that are characterized by the ICE syn-
drome (i.e., all known instances of the ICE-Syndrome class). A more subtle
question would be whether two diseases are the same. By focusing on a par-
ticular question, the rule engine can restrict attention to facts and rules that
are relevant. The resulting inference process can be very efficient in practice.
Relational databases and XML differ from the Semantic Web with respect
to how each interprets the meaning of the known facts about the world. We
have already seen some examples of this distinction in the previous section
where someone made a mistake and stated that a Medline citation is owned
by “rhodopsin.” The “owned by” relationship links a citation to the institu-
tion that owns it. A relational database or an XML processor would give an
error message in this case because “rhodopsin” is not an institution. An RDF
processor, on the other hand, would infer that “rhodopsin” is an institution.
Databases and XML are said to be assuming aclosed world. The Semantic
Web, on the other hand, is assuming anopen world.
Logicians refer to this distinction asmonotonicity. A logical system that
assumes anopen worldis monotonic, while a logical system that assumes
aclosed worldis nonmonotonic. To understand why one refers to a mono-
tonic system as open, consider another example. Suppose that the “occursIn”
property gives the species of an entity such as a gene or chromosome. It is
reasonable to require that every gene occurs in at least one species. In OWL
this would be written as follows: