Martin (1992: 132-3):
The issue then is whether possessive Deictics are the deixis of the participant they possess. Is the possessed participant identified through its possessor, or does the possessive Deictic neutralise the participant's phoricity (as with the neutralised reference in the grammar of little texts)? Du Bois' data indicates [sic] that a frog of his or a friend of John's do not alternate with his frog or John's friend to introduce participants (1980:243-245); pending further investigation this suggests that the interpretation of possessive Deictics as the deixis of the participants they possess is correct. Accordingly, possessive nominal groups will only be coded once for phoricity below, even though they realise two participants. This is after all literally what the grammar of the English nominal group argues: "recover the identity of the possessed participant here through its possessor".
 The notion of a "possessed participant" confuses clause participant with nominal group Thing. A possessive Deictic modifies the Thing of a nominal group. The entire nominal group realises a participant, even in Martin's restricted definition of participant.
 This misunderstands deixis. To be clear, a possessive Deictic structurally realises features of the system of nominal group DEIXIS.
 The notion of "the participant's phoricity" confuses the Thing of a nominal group, misunderstood as a clause participant, with the items that make phoric reference. This confusion derives from misinterpreting textual reference as ideational denotation, as explained in many previous posts.
 This is misleading, because it misrepresents Du Bois (1980: 243-5), who is concerned with possession being expressed either through verbs or noun phrases:
For clothes as for body parts, no descriptive mode initial mentions bear possessive adjectives — that is, a shirt of his does not occur — or otherwise indicate possession in the noun phrase. In virtually all cases possession is already expressed (have) or implied (have on, etc.) in the verb or preposition. In other words, when a "human" frame element (a body part or item of clothing) is mentioned, possession will ordinarily be expressed in one way or another. If the descriptive mode is selected, the verb serves to express possession, but if the narrative mode is selected, possession must be expressed in the noun phrase.
 Given the above, this is a non-sequitur, inferred from a misrepresented citation, in support of a misunderstanding of deixis.
 This confuses nominal groups with reference items.
 Such nominal groups realise only one participant, even on Martin's definition of participant (as nominal group functioning as Medium or Agent).
 There is nothing "literal" about a grammar "arguing".
 This confuses nominal groups with reference items, and Things with participants, and presents the confusion as a quote, as if it were a widely accepted maxim.