In the architecture of MiMo2 to be proposed here, (monolingual) relations between phonological representations and semantic representations are defined by constraint-based grammars of the type introduced in chapter 2. However, constraint-based grammars can also be used to define other relations between (parts of) linguistic signs. In particular it is possible, as discussed by  for FUG, to use constraint-based grammars to define transfer rules. In the model I propose a translation relation between two languages is defined as the composition of three reversible relations. Each of these relations is defined by a constraint-based grammar. The first grammar defines the relation between source language utterances and source language dependent semantic representations. The second grammar defines the relation between source language dependent semantic representations and target language dependent semantic representations, the third grammar defines the relation between target language dependent semantic representations and target language utterances. The resulting MT system is reversible iff each of the grammars is reversible, as I showed in section 1.3).
For example, to compute the relation between Dutch and Spanish phonological representations construct the series of the programs for the Dutch grammar, the Dutch-Spanish transfer grammar and the Spanish grammar. Each translation relation that can be defined is necessarily reversible if each of the grammars that are used defines an reversible relation. See figure 5.3 for an illustration.
The reasons for a constraint-based formalism for transfer rules are the following.
In section 5.5 I discuss how to ensure that a transfer grammar is reversible. We show that, as long as translation is compositional in a sense to be made precise, it is possible to guarantee that transfer grammars are reversible. On the other hand such grammars are still powerful enough to handle certain non-compositional translations. For this reason we argue that reversible constraint-based grammars provide for an interesting compromise between expressive power and computability.
As far as the system is concerned, there may be a different logic for natural language semantics for each language. A transfer component for two languages thus functions as an interface to relate the two logics used to define semantic representations with. This makes it possible that grammars are developed quite independently of each other. On the other hand, if languages define similar semantic representations the transfer grammars will generally be simpler and easier to write.
In a transfer model the subset problem, as discussed in the previous section, is in principle present in a slightly different format, because the transfer component need not be `complete' (cf. figure 5.4). The point at which grammars are connected gives in principle rise to an instantiation of the subset problem. However, in practice it turns out that in the proposed architecture the problem hardly surfaces at all. This is so, because the transfer grammars are explicitly tuned to each of the monolingual grammars. Clearly, that was the reason to have transfer grammars in the first place. Therefore, it seems warranted to neglect this problem.