TH connects words that take "that [clause]" complements with the word "that". These include verbs ("I assured him that..."), nouns ("The idea that...") and adjectives ("We are certain that...").
+---TH----+
| |
I assured her that I would finish the project
The idea that we would hire John is preposterous
I'm certain that she could do a good job
The word "that" therefore has TH- & Ce+. The
Ce+
connects to the subject of a following clause.
Verbs that can take "that"+clause have TH+ disjoined with their other complement connectors ( O+, TO+, etc.). With many such verbs, the "that" is optional; they thus carry (TH+ or Ce+), allowing a direct connection to the subject of the subordinate clause. Some verbs can take object+"that" ("I told him that I was angry"); such verbs have (O+ & {TH+}). Adjectives like "certain" have TH+ disjoined with other complement connectors. Nouns like "idea", "opinion", and "argument" have TH+ conjoined with {@M+} (used in prepositional phrases) but disjoined with {R+ & B+} (used in relative clauses); this is somewhat arbitrary.
THb+ connectors are used to connect forms of "be" to "that". The reason for this is that only certain nouns can serve as the subject in such cases: "The problem is that John is coming", "*The dog is that John is coming". To enforce this, we give such nouns Ss*t+ connectors instead of the usual Ss+. We then insist in post-processing that a group containing a THb must contain an Ss#t.
THi+ connectors occur on certain adjectives ("important") which may only take "that+clause" when "filler-it" is the subject. This distinction involves post-processing. See "SF: Filler-it" for further explanation.
THc is used with comparatives; see "MV: Comparatives VI".