Adding definite relations

In this section I will apply the construction defined by [32] to the constraint language defined in the preceding section to obtain $\cal {R}$($\cal {L}$). It is shown in [32] how the nice properties of logic programming languages carry over to a whole class of formalisms built on top of arbitrary constraint languages. The idea is to distinguish between the underlying constraint language (for example $\cal {E}$, where $\cal {E}$ consists of conjunctions of equations between first-order terms) and the definite relations that are defined using constraints from the underlying constraint language. In the case of $\cal {E}$ this results in $\cal {R}$($\cal {E}$), which is just first-order logic. From the resulting logic we then take definite clauses, and in the case of $\cal {E}$ we thus end up with (pure) Prolog. The constraint language $\cal {L}$ can be seen as another instance of such a constraint language. To this constraint language I apply the construction sketched above, resulting in $\cal {R}$($\cal {L}$); $\cal {R}$($\cal {L}$) is thus rather similar to pure Prolog, but equations between first order terms are replaced by the path equations introduced in the previous section. Instead of first order terms, our data structures are feature structures. Furthermore, unlike PATR II I will not restrict the formalism by requiring that phrases are built by concatenation. In figure 2.3 it is shown how the different formalisms are related.

Figure 2.3: Overview of the different formalisms