Computational linguistics and mathematical logic from a computer science point of view

Let us look at a special type of context sensitive grammars, the so-called Definite Clause Grammars, or DCG, as described by Pereira and Warren (l980). The following question seems natural here: every context sensitive language be described by meeins of a definite clause grammar ? The question must be answered in the eiffirmative, as can be seen by simu­ lating Turing machines or better Markov algorithms by means of definite clause grammars. This means that the definite clause grammars have at least the same computational power as the grammars of Chomsky type 0. And hence theoretically speaking they can also handle languages of Chomsky type 1. If we focus on the question which practical methods have been developed to handle context sensitive languages by means of definite clause grammars or similar formalisms then the situation is much more unclear. It seems to be a problem with a considerable actual research effort. We may see the occuring of several new grammar types as the results of exactly this tendency, for instance Gapping Grammars in (Dahl & Abramson 1984, Dcihl 1984) eind Puzzle Grammars (Sabatier 1984). The next natural and fundamental question seems to be the following Does there exist any known problems within the languages that can be described by means of definite clause grammars ? It should be answered in the affirmative, actually there exist many problems. As an example we may look at possibly the most famous problem, the coordination problem. The text that we want to examine consists simply of the Danish sentence