Martin (1992: 140-1):
At its simplest, a reference chain consists of two items, one presuming, one presumed. For display purposes, the nominal group realising a given participant in a text will be used to name that realisation of the participant in the reference chain. […] For longer texts, these chains can simply be extended, with presuming items shown to be as well presumed; these then form the systemic equivalent of the "participant lines" in the Hartford stratificationalists' reticula […]. The basic descriptive strategy underlying chains formed in this way is to take each phoric item back once to the item which last realised or presumed the information that needs to be recovered.
 This notion of reference chains, as linked instantial participants sharing the same identity, is not consistent with what the model is purported to be: 'reference as semantic choice'. This is because, in SFL, reference is the grammatical system that is the resource for referring (personal and demonstrative co-reference and general and specific comparative reference). In order to be a semantics of reference in SFL, the meanings realised by the grammatical system of reference need to be modelled, specifying how such semantic choices are realised at the level of lexicogrammar.
 Reference chains as linked instantial participants sharing the same identity, are not structures that realise a system of referring. Moreover, reference chains are not structures that realise any of the systems provided in this chapter (pp 102, 105, 106, 110, 112, 114, 118, 120, 124, 126), and, naturally, none of these systems provide realisation statements specifying how their features are realised as structures.