The first thing I would say about modal verbs is that their usage extends over many different contexts and so any general rules are bound to fail when taken out of context.
Outline
- Use of 'will' and 'would' to express belief
- Other uses
- The answer
1. Use of 'will' and 'would' to express belief
(Credit for this section should go to @snailboat)
To illustrate the difference in use of 'will' and 'would' for expressing certainty, snailboat suggested the following sentences at the ELL chat room:
1A. I'm sure they have been looking for those bank robbers.
1B. I'm sure they will have been looking for those bank robbers.
2A. I'm sure they had been looking for those bank robbers.
2B. I'm sure they would have been looking for those bank robbers.
In sentences 1A (they have been) and 2A (they had been) the speaker knows they have/had been looking for those bank robbers. The main difference is that the use of present perfect in 1A (they have been) indicates that the search has lasted at least until now.
In sentences 1B (they will have been) and 2B (they would have been) the speaker expresses a belief:
in sentence 1B (they will have been), the speaker expresses the belief that they have been looking for those bank robbers.
in sentence 2B (they would have been) the speaker expresses the belief that they had been looking for those bank robbers.
2. Other uses
Again, a word of caution, the interpretation above is not unique and can change if the context changes. This section shows other possible uses of will have been and would have been.
3. The answer
Let's now consider the example in your question:
A： We saw a police helicopter yesterday morning.
B： I'm sure they would have been looking for those bank robbers.
To be able to use "will have been" is necessary to change the context as described in the first section of this answer:
A： We have seen a police helicopter.
B： I'm sure they will have been looking for those bank robbers.
All four of these are expressing some degree of sadness or wistfulness that a trip was cancelled. There might be very little difference in meaning between them, although:
I'm sorry that the trip was cancelled.
could be indicating some apology on behalf of the speaker. For example, if a travel agent was calling a customer with bad news – that arranged travel plans would need to be cancelled for some reason – the agent would be more likely to use "I'm sorry that..." than any of your other three options.
However, suppose the would-be traveler announces at her weekly bridge game that her trip had to be cancelled. Her fellow bridge players could easily go around the table and say:
I'm sorry that your trip was cancelled.
It's too bad that your trip was cancelled.
Such a shame that your trip was cancelled.
and they all pretty much mean the same thing:
It's so sad that your trip was cancelled.
Among friends, "I'm sorry that..." often means, "I'm sorry to hear that..." However, in the case of the travel agent, "I'm sorry that..." means, "I apologize for saying this, but..."
As for any other nuances, I'd be inclined to say that "It's a pity that..." sounds a bit old-fashioned, or perhaps a little stilted for everyday conversation. That said, all of them can be used as expressions of empathy.
Best Answer
Early and earlier (and also late/later) can all be used as adjectives, but whilst earlier and later are usually used to describe the relative occurance of an event to another (perhaps implied) event, early and late are used to describe the absolute occurance of an event on a (often implied) timeline.
For example, when considering a collection of paintings:
This statement states that the author prefers paintings that were created before the current painting. This contrasts with the statement:
This statement on the other hand states that the author prefers paintings that were painted early on the unspecified but implied timeline of the artist's entire career.
Similarly, suppose the theatre has showings at 8 AM, 11 AM, 2:00 PM, 5 PM, 10PM, 11 PM and midnight. Then
In this case, the tickets procured must be for the midnight showing, since this is the only showing that is later than 11PM.
On the other hand,
In this case, the first clause is merely descriptive; tickets could not be obtained for the 11PM showing. The second clause stands alone stating that tickets could be obtained for a late showing, and hence the tickets might be for the midnight one OR the 10PM showing, since both are objectively "late showings". The 10PM showing is a late showing even though it is earlier than the 11PM showing.
When no separate comparative event is provided earlier and later mean the same as early and late, but are just less idiomatic; assuming no other context, the following two sentences are equivalent:
Be aware that late as an adjective also has the meaning dead that the adjective later does not have:
And finally there are certain idioms where the choice of "late/later" and "early/earlier" is fixed. In these cases, you should not substitute late for later or early for earlier (or vv):