I would not think any Hallidayan would ever posit a 1-to-1 mapping between Semantics and Grammar. That would invalidate the need for Semantics as a separate stratum. …So, the mapping between Semantics and Grammar always needs to be seen as a many-to-many mapping.- language provides multiple forms for realising a particular meaning.- a particular form can express alternative meanings(but yes, "Construing Experience" can be read (misread?) to suggest a one to one mapping between semantic process type selection and Transitivity selection in the grammar. Something I and other have argued against in the past. And not something that I think was intended by the authors, Christian and MAKH).
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[1] To be clear, it is metaphor that motivates semantics as a stratum of content. Halliday & Matthiessen (1999: 237):
If the congruent pattern had been the only form of construal, we would probably not have needed to think of semantics and grammar as two separate strata: they would be merely two facets of the content plane, interpreted on the one hand as function and on the other as form.
[3] This is misleading. On the one hand, PROCESS TYPE is a grammatical system within the larger system of TRANSITIVITY (Halliday & Matthiessen 2014: 219, 354-5), so, in this sense, the notion of a 'one to one mapping' of 'process type selection' to 'transitivity selection' is nonsensical.
On the other hand, in the absence of grammatical metaphor, the process type served by a verbal group is congruent with its semantic value. Moreover, in the case of grammatical metaphor, the incongruence is not between one process type and another, but between a process and some other element, as when a Process is realised grammatically by a Range participant, as he had a bath.
[4] To be clear, O'Donnell misunderstands the system of PROCESS TYPE, largely because he fails to recognise verbal group complexes. See, for example: