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I was taught long time ago that when using the prepositions 'for' and 'of' to connect two nouns, the general guidelines would be:
1) use 'of' to indicate some sort of belonging or relationship between the two nouns, such as the handle of the umbrella;
2) use 'for' to indicate the purpose or function of the first noun, such as "a machine for slicing bread".

However, sometimes the two prepositions seem to be exchangeable. In the US, the head responsible for energy administration is called "the Secretary OF Energy"; while in the UK, it is called "the Secretary of State FOR Energy". In this case, I would guess that when using 'of', it means the duties of the secretary belongs to the ambit of energy; and when using 'for', it means the function of the secretary is for energy administration.

In this regard, although I have asked somebody else, I am still not quite understand the rationale behind the selection of prepositions for the following sentence:
"The investigation report of/for the incident indicated that nobody should be liable."

People told me that 'of' should be used. I think I understand as it indicates that the 'incident' has some sort of relationship with the 'report'. What puzzles me is that why 'for' could not be used. What is in my mind is that when using 'for', it tells people the function of the 'report' is for the 'incident'.
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This is a distinction that, as a native speaker, I have never thought much about, but your relationship vs. function distinction seems to be a pretty useful rule. In the example you give, I would say that the report is not "for" the incident - after all, the incident was over before the report ever existed, so the report is not serving any function for the incident. You could say "preparation for the incident," or "plans for the incident". The report is "of" the incident in the sense of "about" the incident. If you wanted to use "the report for..." I think you would need something like, "the report for the investigating committee will be ready in two days."

As for the Secretary OF/FOR Energy, I believe that in the U.S. "the Secretary of Energy" is short for "The Secretary of the Department of Energy." I do think that in some cases the choice of "of" or "for" is just a matter of habitual use and can't be analysed too closely.

Hope this helps some. I love questions like this that make me try to find the logic behind the things I say automatically. (My family, however, is getting a little tired of my starting every dinner conversation with something like "There was an interesting question about "of" and "for" in English Forums today...")
Thank you.

In that case, am I correct that the following two sentences are in order?

1. The plan OF the carnival scheduled for April 20 is great. (the 'of' is to indicate relationship between the plan and the carnival)
2. The plan FOR the carnival scheduled for April 20 is great. (the 'for' is to indicate function of the plan).

In addition, whether could I use 'scheduled for' to refer to time only without date? For instance:
3. The meeting is scheduled for 2:00 pm.
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Hi.

Here's my two cents.

1. The plan OF X ....: X is a plan organizer. You may rephrase it as X's plan.
Ex)The plan OF our accounting department leaves nothing to be desired.

2. The plan FOR Y ...: Y is something for which the plan is needed.
Ex)The plan FOR our wedding still remains sketchy.

In expressions with a 'schedule' concept, you need 'for' instead of the prepositions normally used in expressions with a 'non-schedule' concept. You don't need to restrict the object of 'for' to dates. Any kinds of time-concept words or phrases will qualify for the object.

be scheduled for 2:00 p.m./this Friday/next week/April 30/next year

Other examples falling into this category are:

be slated for October
make a reservation of a room for August 10
leave a call for 6:00 tomorrow morning (asking for a wake-up call at a hotel)
set my alarm clock for 5:00 a.m.

I can't think of more than this at the moment.
Hi komuntain,

Could I extend your rationale to debate that the previous sentence of "The investigation report OF the incident indicated that nobody should be liable" is incorrect as the object after 'OF' should be the report writer rather than an incident?

If not, that is the matter that puzzles me a lot - why in some cases the preposition 'of' just indicates a relationship between two objects (such as 'the report of the incident'); but in other cases it indicates that the object behind is the owner of the preceding object (such as 'the plan of Mr. X).

Is there a general rule in applying and distinguishing the use of 'of' and 'for' in sentences where two nouns/objects are to be connected together by virtue of their relationship, purpose, etc.?
Wein,

In spite of the fact that there are sometimes rules of thumb for the selection of prepositions, these are often better thought of as completely idiosyncratic and arbitrary. Only by reading a great deal and imitating what you read can you eventually become comfortable with these pesky little words! In the real world of speaking and writing, especially speaking, you have no time to speculate upon whether "of" or "for" should be used in given situation, so detailed analysis of this sort is only of limited use (unfortunately).

That said, realize that in the case of deverbal nouns the preposition which follows the noun is the same as that which follows the corresponding verb. When the verb takes no preposition, the noun probably takes "of". Even these guidelines can leave you high and dry at times!

to plan for an event: the plan for the event
to search for my umbrella: the search for my umbrella
to report an accident: the report of an accident
to thank someone for a gift: thanks for a gift
to seize the money: the seizure of the money
to meet with friends: a meeting with friends
to discover a mistake: the discovery of a mistake
to blame for misconduct: the blame for the misconduct
to discover a new planet: the discovery of a new planet
to deliver something to a customer: the delivery to that customer

And then there are often cases where more than one preposition can be used.

In the specific case of "investigation report", I am not familiar with this unusual combination. It seems it should be either "investigation" or "report", but not both. I think this may be interfering with the judgment of the proper choice of preposition.

My dictionary has 28 definitions for "for". The definition which I think applies best in "the report for the incident" is "accompanying, paired with".

-- What happened on the corner of Elm and Oak last night?
-- If you want all the details, the report for the incident can be found in this file cabinet here.
-- What about this set of files over here?
-- No, those files are reports for incidents in another part of town.

"report of" could also have been used, and many people prefer it.

CJ

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Broadly speaking,
'of' connotes 1)belonging or possession and 2)about;
'for' has senses of 1)purpose and 2)desire

The report of the incident .... is corerct. I would not choose 'for' in place of 'of.'
Many thanks for your 'high and dry' guidelines!