This is a rough first draft, and corrections would be very welcome - (there probably do need to be some, so pinch of salt still required :-)

Draft FAQ: OF 1.8 Filter options and their search language equivalents:

Showing the option label used in the GUI (spaces removed) and (if different) the corresponding filter identifier in the OF 1.8 Applescript suite.

I hope that this may be helpful, and possibly shed some additional light on exactly what each filter does/means.

[Once there seems to be consensus that these search language equivalents are more or less correct, I will add this list to the default abbreviations file in the Where in OF script for OF 1.8]

PlanningMode:Sidebar

[Remaining-projects]->((status is active) or (status is on hold) and ((effectively hidden of its folder is false) or (its folder is missing value)))
[Active-projects]->((status is active) and ((effectively hidden of its folder is false) or (its folder is missing value)))
[Stalled-projects]->((number of tasks is number of completed tasks) and (status is active) and (singleton action holder is false) and ((effectively hidden of its folder is false) or (its folder is missing value)))
[Pending-projects]->((singleton action holder is false) and (status is active) and (start date > now) and ((effectively hidden of its folder is false) or (its folder is missing value)))
[OnHold-projects]|[on-hold-projects]->((status is on hold) and ((effectively hidden of its folder is false) or (its folder is missing value)))
[Dropped-projects]->((status is dropped) or (effectively hidden of its folder is true))
[Completed-projects]->(status is done)

PlanningMode|ContextMode:Status

[Remaining]|[incomplete]->(completed is false)
[NextAction]|[next]->(next is true)
Available: tasks which are neither waiting their turn in a sequential project, nor already completed, nor deferred by a future start date (either of their own or inherited from a project or Single Action list), nor out of action because their project or context is on hold or dropped.
[Available]->(blocked is false) and (completed is false) and ((start date is missing value) or (start date < now)) and ((its containing project is missing value) or (status of its containing project is active) and ((start date of its containing project < now) or (start date of its containing project is missing value))) and ((its context is missing value) or ((allows next action of its context is true) and (hidden of its context is false)))
[Completed]|[complete]->(completed is true)

PlanningMode|ContextMode:Flagged

[Flagged]->(flagged is true)
[Unflagged]->(flagged is false)

PlanningMode|ContextMode:Duration

[5min]|[5m]->(estimated minutes <= 5)
[15min]|[15m]->(estimated minutes <= 15)
[30min]|[30m]->(estimated minutes <= 30)
[1hour]|[60m]->(estimated minutes <= 60)
[>1hour]|[long]->(estimated minutes > 60)
[Unestimated]->(estimated minutes is missing value)

ContextMode:Sidebar

[Remaining-Contexts]|[available-contexts]->(effectively hidden is false)
[Active-Contexts]->(remaining task count > 0)
[Stalled-Contexts]|[inactive-contexts]->(remaining task count is 0)
[OnHold-Contexts]|[on-hold-contexts]->(status is on hold)
[Dropped-Contexts]|[unavailable-contexts]->(effectively hidden is true)


ContextMode:Due (within Flagged menu)
The value of 'soon' below depends on the setting in OF Preferences > Data > "Due Soon" is in the next N days. Code defining 'soon' is given in the next post in this thread.

[DueSoon]|[due]->(due date ≤ soon)
[DueOrFlagged]|[due-or-flagged]->((due date ≤ soon) or (flagged is true))
[DueAndFlagged]|[due-and-flagged]->((due date ≤ soon) and (flagged is true))

--

I have amended the search language definitions which refer to 'soon' in the FAQ above.

Whereas they previously used the expression:

today + <num> * days

they now simply use the variable name:

soon

Which can be defined in Applescript with code like:

tell application id "com.omnigroup.omnifocus"
	tell default document
		set soon to (current date) + ((value of setting id "DueSoonInterval") as integer)
	end tell
end tell

[I have also added the keyword 'soon' to the search language recognized by my Where in OF script. The expression 'today + <num> * days' can also be used in Where in OF searches and shortcuts, and is resolved by a dialog asking the user to enter a number for <num>]

(Note that 'soon' is the current moment + N * 24 hours, which I understand to be the calculation used by OF, whereas the 'today' in today + <num> * days uses a base time of "00:00" this morning, rather than the time of the search.)

Updated the definition of [Available] tasks.
(Above)

The help file's comment on the Availability filter is that Available actions are:

"things you can actually do, because they aren’t blocked by earlier actions in a sequential project"

but the fuller picture is more like:

tasks which are neither waiting their turn in a sequential project, nor already completed, nor deferred by a future start date (either of their own or inherited from a project or Single Action list), nor out of action because their project or context is on hold or dropped.

--