In (a) the clause that Caesar was dead is projected as an ‘idea’ by Mark Antony thought. It is therefore a separate, hypotactic clause; and hence
(i) it cannot be preceded by the fact;
(ii) it cannot be replaced by Caesar’s death;
(iii) it can be quoted: ‘Caesar is dead,’ thought Mark Antony;
(iv) it can be replaced by the substitute so: Mark Antony thought so.
In (b), however, the clause that Caesar was dead, although it is a projection, is not projected by Mark Antony regretted, which is a clause of emotion not of cognition. It is not an idea but a fact; hence it is embedded, and hence
(i) it can be preceded by a ‘fact’ noun;
(ii) it can be replaced by a nominal group Caesar’s death;
(iii) it cannot readily be quoted: Mark Antony regretted, ‘Caesar is dead’ is very forced; and
(iv) it can be replaced by the reference item it, but not by the substitute so: Mark Antony regretted it (not so).
The form Mark Antony dreaded that Caesar was dead is an example of a type that allows both interpretations, and hence is ambiguous: as idea (hypotactic), ‘he thought (and wished otherwise)’, or as fact (embedded), ‘he was afraid because’.
In the case of Mark Antony regretted, ‘Caesar is dead’, the projection ‘Caesar is dead’ is an idea (ranking clause), not a fact (embedded clause). Here the verb regretted serves as a cognitive — rather than emotive — mental Process, the lexical choice adding an 'emotive' feature to the cognition. This is the same principle as lexical choice adding a behavioural feature to a verbal Process, as in 'Caesar is dead', mumbled Cassius.