Finally, it formulates derivation rules based on the types found, in the manner of the rules of a context-free grammar. The program can present the grammatical structure found in several ways, as well as use it to parse other sentences or generate new ones. The formal languages used in description logics are very close to modal languages. This similarity was first noticed by Schild, who used it as a bridge to transfer complexity results and axiomatizations from modal logics to description logics. But as Schild himself noticed, the link between basic modal logics and description logics can only be established at the level of concept satisfiability.
Hybrid languages are modal languages which allow explicit reference to the states in a model.
In addition, we can take advantage for recent result to provide characterizations in terms of both complexity and expressive power. In such an axiomatization, the theory's predictions can be derived as theorems by the inference rules of the logic. In practice, only very few theories from the empirical sciences have been formalized in first order logic. One of the reasons is that the calculations involved in formalizing scientific theories quickly defy manual processing. The availability of automated reasoning tools allows us to transcend these limitations.