Halliday & Matthiessen (1999: 45):
We shall mention four such challenges briefly here.
(i) The first representational challenge is the need to handle the dimension of instantiation.As a process, instantiation can be represented as involving traversal of the system network and activation of realisation statements. The instance is thus a set of features (semantic types) selected, with associated realisational specifications — an instantial pattern over the semantic potential.However, instantiation also defines a scale between the potential and the instance, with intermediate patterns of instantiation. We will introduce these later as register-specific domain models. Such patterns of instantiation will need to be represented: perhaps as systemic probabilities, or as domain-partitions within the overall ideation base.(ii) The second representational challenge is the need to model how the overall ideation base is expanded by grammatical metaphor. It must be shown how metaphor adds junctional types to the ordinary types …
(iii) The third representational challenge comes from outside the account of the ideation base itself: the ideation base has to be related to the other metafunctional modes of meaning, the interaction base and the text base. The interaction base will include alternative 'projections' of the ideation base to account for the relationship between speaker and addressee. …
(iv) The fourth representational challenge concerns the non-discreteness of the various systems that construe semantic space. The semantic types represented by the features of systems in the system network do not constitute discrete Aristotelian categories; they are values on semantic clines — core regions, to use the metaphor of semantic space. We can bring this out by adopting a topological view on meaning; we can also explore the possibility of interpreting features as names of fuzzy sets.