Q is used in questions, in several different ways. It is used to connect to auxiliaries in simple s-v inversion questions, when there is no preceding object. In some cases the auxiliary connects to the wall (ex. 1 below). In other cases it connects to a question-word like "when", "where", or "why" (ex. 2).
+--Qd-+ | | ///// Are you going to to the movie +--W-+-Qw-+ | | | ///// Why did you goIn noun-focused questions, either object-type or subject-type, the question-word connects to the verb ("What did you buy", "Who bought that"). In the former case, there is s-v inversion, but no Q connection is made. Thus the Q- is optional on auxiliaries.
Post-processing ensures that when a question-word is used in object-type or when-where-why questions (not subject-type questions), the outer group of the sentence contains some kind of SI; this is because in all such cases, a Wq is used to connect to the wall, and this requires an SI in the same group. Post-processing further ensures that SI links can only be used when a Wq is present (see "SI"). However, in simple yes-no questions, question inversion must occur, yet no question word is present. Thus the Q+ on the wall is subscripted Qd, and this is added to Wq on the list of link-types that permit s-v inversion.
(Note that the Q- on auxiliaries is conjoined with SI+, but disjoined with S-; by link logic it can only be used with SI+. Post-processing tightly constrains the use of SI, preventing it from occurring in indirect questions, relative clauses, etc.; the use of Q is thus automatically constrained as well.)
Q is also used for questions with prepositions: "IN which room WERE you working", "TO whom WERE you speaking". See JQ and J.
The Qd link, because it connects to auxilliaries, effectively indicates a truth-query.
The Qw link is used to connect verbs the the WH-word. This allows the verb to be marked as a head-verb (via the WV connector) forming a cycle with the W connector between the WH-word and the wall.
Qe is used to connect adverbs to following auxiliaries in adverbial questions:
+---I---+ +EEh-+--Qe--+-SI+ | | | | | | How quickly did you runQe can only be used in questions ("*Very quickly did you run"). This is enforced by the fact that the sentence must connect to the wall, and can only do so through "how". Again, the use of Qe in indirect questions is prevented because Q- on auxiliaries is conjoined with SI, whose use is constrained by post-processing.
One false positive must be addressed here, however:
+------------B-------+ | +----I---+ | +--Qe--+-SI-+ | | | | | | * Who quickly did Jane hitWe prohibit this in post-processing by requiring that a group containing a Qe must contain an EEh - a link-type occurring only on the word "how".
Grammar Documentation Page.