Halliday & Matthiessen (1999: 519-20):
Turning now to the logical part of the grammar's ideational resources: this is the part that is concerned not with individual processes but with the relation between one process aid another. In calling this "logical" we are using the term in the sense of natural language logic: that is, grammatical logic, not formal logic — although, of course, this is the source from which formal logic is ultimately derived.