Foundations of Semantic Web Technologies

228 Foundations of Semantic Web Technologies

FIGURE 6.4: Examples of simple rule dependency graphs

logics considered in this book.

6

We conclude that rolling-up is only possible

if a variable is “ reachable” by only a single binary predicate.

We now give a more precise characterization of the rules that can be rewrit-

ten as description logic axioms. In order to understand in which cases we can

use the rolling-up method, the key is to consider the dependency graph of

the rule premise. This graph is obtained from the premise by simply taking

variables as nodes, and binary predicates as edges between variables. Note

that (atoms with) constant symbols do ...