The first relaxation assumes that there is a sort system defined for feature structures that makes it possible to make a distinction between cyclic and non-cyclic attributes (cf. ). For the moment a non-cyclic attribute may be defined as an attribute with a finite number of possible values (i.e. it is not recursive). For example the attributes and will be cyclic whereas will be non-cyclic. The completeness and coherence condition is restricted to cyclic attributes. As the proof procedure can only further instantiate non-cyclic attributes no termination problems occur because there are only a finite number of possibilities to do this. The definition of `equivalence' for feature structures is now slightly changed. To define this properly it is necessary to define the notion non-cyclic extension. A non-cyclic extension of a feature structure only instantiates non-cyclic attributes. This results in the following definition of equivalence:
It will be clear that the usefulness of this definition depends heavily on
the style of grammar writing that is used. Note that it is of course also
possible to declare for each non-cyclic attribute whether the completeness and
coherence requirements hold.