Clause Without Medium

you	were seen	at the anti-Trump rally
Range	Process	Location

Halliday & Matthiessen (2014: 341):

Except in the special case of the medio–receptive voice, the Medium is obligatory in all processes; and it is the only element that is, other than the process itself. … The Medium is also the only element that is never introduced into the clause by means of a preposition (again with the same exception of medio–receptives); it is treated as something that always participates directly in the process.

Imperial Retaliation

the empire	strikes		back
Medium	Process
Subject	Finite	Predicator	Adjunct
Mood		Residue

Halliday & Matthiessen (2014: 341):

Every process has associated with it one participant that is the key figure in that process; this is the one through which the process is actualised, and without which there would be no process at all.  Let us call this element the Medium, since it is the entity through the medium of which the process comes into existence. … in a material process the Medium is equivalent to the Actor in an intransitive clause and Goal in a transitive clause.

Halliday & Matthiessen (2014: 152n):

Note that if the lexical verb is a phrasal one, the non-verbal part, the adverb and/or preposition, serves as Adjunct, thus falling outside the scope of the Predicator. The combination of Predicator + Adjunct corresponds to the Process.

Embedded Clause Complex Or Ranking Clause Complex With Ellipsis?

(1) Paratactic extending clause complex embedded as Attribute:

The kind of food we eat	depends on		which part of the world we live in or which part of our country we live in
Carrier	Process: causal: condition		Attribute
Theme	Rheme
Subject	Finite	Predicator	Complement
Mood		Residue

which part of the world we live in	or which part of our country we live in
1	+ 2 alternation

(2) Paratactic extending clause complex with ellipsed Carrier and Process:

The kind of food we eat depends on which part of the world we live in	or the kind of food we eat depends on which part of our country we live in
1	+ 2 alternation

The kind of food we eat	depends on		which part of the world we live in
Carrier	Process: causal: condition		Attribute
Theme	Rheme
Subject	Finite	Predicator	Complement
Mood		Residue

or	the kind of food we eat	depends on		which part of our country we live in
	Carrier	Process: causal: condition		Attribute
Rheme
	Subject	Finite	Predicator	Complement
	Mood		Residue

Each analysis construes

• the same Theme: the kind of food we eat,
• the same Subject: the kind of food we eat,
• the same conditional relation between the same Carrier the kind of food we eat and the same Attribute(s) which part of the world we live in (or) which part of our country we live in, and
• the same interdependency (parataxis) and same logico-semantic relation (extension: alternation).

But the first analysis is simpler.