Foundations of Semantic Web Technologies

Ontologies and Rules 223

program we consider. For plain datalog programs that are consistent, it is

always possible to construct models in this particularly simple fashion by just

taking the constant symbols as interpretation domains, and such models are

known as Herbrand models.

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Moreover, it is always possible to find a model

that satisfies as few datalog atoms as possible, such that no other model sat-

isfies fewer datalog facts. The existence of such least Herbrand models is of

great significance and can be exploited for practical implementations – but

for our purposes it is enough to note that this feature provides us with a

conveniently small example ...