45804 - Temporal Language

N. Lygeros

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The set of all strings over the alphabet A is denoted A*. With the operation of concatenation, the set A* of strings over A forms a free monoid. If we take the classical definition of a language i.e. a subset of A*, together with the alphabet A, then we have to admit that natural languages are not language in this mathematical sense. Because natural languages change with time, they are in fact temporal languages.
Let’s L(T) be a temporal language. Let’s suppose that the alphabet is stable i.e. temporally invariant. In this case A* is also stable. So the difference is the subset of A* which is temporal. That’s why we have to define some new concepts which are instable, to take account of the influence of Time on natural languages. But in any case, this means that a natural language is unstable and that’s why it can evaluate.