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### 4.4 Qualified Number Restrictions

We now study reasoning in $A L C Q ℐ$ knowledge bases by exhibiting an encoding from $A L C Q ℐ$ knowledge bases to $A L C ℱ ℐ *$ knowledge bases [De Giacomo and Lenzerini 1995b , De Giacomo 1995]. The encoding is based on the notion of reification (see later). As the encoding is polynomial, we get as a result the EXPTIME-decidability of reasoning in $A L C Q ℐ$ knowledge bases. However, ...

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