The definition of DL interpretation forgets to say that the domain of interpretation must be non empty. Also, it says that the domain is a set of individuals, while individuals are also defined as symbols used in DL axioms. This may not significantly impact the semantics, but it is usually not imposed that the domain contains individuals. I suggest replacing "The domain of interpretation is a set of individuals" with "The domain of interpretation is a non empty set".
The definition of DL interpretation forgets to say that the domain of interpretation must be non empty. Also, it says that the domain is a set of individuals, while individuals are also defined as symbols used in DL axioms. This may not significantly impact the semantics, but it is usually not imposed that the domain contains individuals. I suggest replacing "The domain of interpretation is a set of individuals" with "The domain of interpretation is a non empty set".