Modal verbs always keep the variable {ON}; we do not say, *we are maying, *we have mayed, or *we have been musting, but there is a way to think about Modal syntax as “modifying” the real time Aspect, that is, variables {ON} or {IN}, {TO}, and {AT}.
REAL TIME
{ON} You read.
{IN} You are reading.
{TO} You have read.
{AT} You have been reading.
MODAL MODIFICATION
You may read.
You may be reading.
You may have read.
You may have been reading.
We can choose to perceive modified real time with real-time frames.
93. You may have read the book, but you haven’t played the grammar computer game. — We know that someone has read a book.
93a. You may have read the book, would you tell? — We guess if someone has read a book.
Without auxiliary HAVE, we may tend towards the open Modal frame, rather than the closed real-time.
93b. I may play the game one day;
93c. I must see the game movie.
Intuitively or common sense as well, we might say the matter is open with a Modal, and it is a thing of a marked boundary in real time. Let us compare examples:
94. She may be reading;
(or doing something else, open Modal frame).
94a. She is reading;
(the phrasing does not bring anything else, closed real-time frame).
Let us now think how our syntax and cognitive time frames might complement one another: Modal verbs would close their frame with auxiliary HAVE, whereas real time frame would open with the auxiliary.
It is logical to ask, if our Modal Net would render the variable {IN} an empty value with a closed Modal frame: auxiliary HAVE becomes an anchor and not a time extent (■CHAPTER 10), whereas in syntactic order, we first have the net and only then the particle ING:
94b. She may / might have been readING.
Our Progressive does not become empty, because it is not a parameter: it is a cognitive variable. Such variables can work in time more than in order, so the Modal net does not nullify ING whatsoever.
For figurative talk and theory generally, we can manage by balancing the variables {ON} and {IN}.