Knowing Facts

She	knows	the fact [[that he is called Peter]]
Senser	Process: mental	Phenomenon

cf:

She	knows	his name
Senser	Process: mental	Phenomenon

Projection Distinction: Hypotaxis Vs Embedding

She	thought		that	he	was called	Peter
a			‘b
Senser	Process: mental			Value	Process: relational	Token

She	liked	(the fact) [[that he was called Peter]]
Senser	Process: mental	Phenomenon: metaphenomenon

In the first case, the hypotactic projection nexus, the mental process of cognition projects a report (he was called Peter) into semiotic existence.

In the second case, the clause simplex, the mental process of emotion ranges over a fact (he was called Peter) presented as already projected by other symbolic processing, mental or verbal.

This is one important semantic distinction made explicit by the grammatical distinction between hypotaxis and embedding.

Identifying Clause As Embedded Fact: Qualified Awareness

She	is	aware (of the fact) [[that he is called Peter]]
Carrier	Process: attributive	Attribute

Dependent And Embedded Clauses As Theme

1. clause complex Theme:

Halliday & Matthiessen (2004: 374):

… the qualifying clause can be placed either before or after the ‘head’ clause … The choice is determined by textual considerations.

if the duke gives anything to my aunt	it'll be that teapot
x b	a
Theme	Rheme

enhancing beta clause Theme:

if the duke	gives anything to my aunt
Theme	Rheme

alpha clause Theme:

it	'll be that teapot
Theme	Rheme

2. embedded clause as Theme:

what the duke gave my aunt	was that teapot
Theme	Rheme

Hypotactic Elaborating Clause Nexus With 'As'

It is a large construction	as can be seen from its 15 cloisters, 13 oratories, 86 staircases, 88 fountains, more than 1,600 paintings, 9 towers and 73 sculptures
a	= b

Cf

It is a large construction, which can be seen from its 15 cloisters, 13 oratories, 86 staircases, 88 fountains, more than 1,600 paintings, 9 towers and 73 sculptures