1. Entailments and inferences
Logical entailment
Many terrorists in Fallujah were killed.[ Some terrorists in Fallujah were killed.
Presupposition
Kerry realized that the campaign was in trouble.
Kerry did not realize that the campaign was in trouble.
Conversational inference
Bush was able to convince McCain to campaign for him.
… but Bush chose not to do it.
Many terrorists in Fallujah were killed. Some terrorists in Fallujah were not killed.
… in fact all of them.
Plausible inference
Many terrorists were shot. Many terrorists were killed.
Trustworthy source
Reuters reports that Congress has passed the use of force resolution.
(to avoid contamination with quality of background knowledge)

2. Strong Implicatives
In affirmative sentences, strong positive implicatives such as manage entail that the embedded proposition is true, while strong negative implicatives such as fail entail that the embedded proposition is false. In negative sentences, the polarity of the entailment is reversed. Strong implicatives also carry presuppositions. (Otherwise they would be devoid of any meaning.)
Kerry managed to hold on to his seat.
Entails: Kerry held on to his seat.
Presupposes: It was difficult for Kerry to hold on to his seat.
Bush didn’t manage to find any oil.
Entails: Bush didn't find any oil.
Presupposes: It was difficult for Bush to find oil.
The administration failed to track down the perpetrators.
Entails: The administration didn't track down the perpetrators.
Presupposes: The administration tried or should have tried to track down the perpetrators.
Bush didn’t fail to read a report warning of al-Qaida attacks.
Entails: Bush read a report warning of al-Qaida attacks.
Presupposes: Bush tried or should have tried to read the report.
Other strong implicative constructions:
Positive: bother to, happen to, get around to, succeed, take the trouble, deign, dare, …
Negative: forget to, avoid (-ing), neglect to, …

3. Semi-Implicatives
In negative sentences, positive semi-implicatives entail that the embedded proposition is false; in affirmative sentences there is no entailment but there may be a "conversational implication" that the embedded proposition is true.
Kerry wasn't able to convince McCain to run with him.
Entails: Kerry didn't convince McCain to run with him.
Kerry was able to convince McCain to run with him.
Doesn't entail, strictly speaking, that Kerry convinced McCain to run with him. It is not a contradiction to say "Kerry was able to convince McCain to run with him but chose not to do it."
However, in the absence of any contradictory information, the sentence is misleading if McCain was not convinced by Kerry.
Kerry would have been able to convince McCain to run with him.
In the actual world he wasn't able.
More semi-implicative constructions:
She didn’t have a chance / time / money / courage… to follow your advice.
He wasn’t bold / clever / strong … enough to meet the challenge.
yield a negative entailment under negation, a positive conversational implicature in affirmative sentences if there is no counterindication.
I was too scared / timid / stupid / distracted … to do what I promised.
yield a negative entailment in affirmative sentences, a positive conversational implication in negative sentences

4. Verbs of saying Speech act verbs
Statement
Source
Author
Author relates a Source to a Statement
Bush said that Iraq had aided al Qaida.
Bush didn't say that Iraq had aided al Qaida.
Bush denied that Iraq had aided al Qaida.
The choice of the verb indicates
The relationship, or the lack of it, between the source and the statement.
The stance of the author with respect to the veridicity of the statement.

5. Factive and non-factive verbs of saying
Bush acknowledged that there were no WMD in Iraq.
contains a statement: There were no WMD in Iraq.
attributed to a source: Bush
by an author
By using a "factive" verb, acknowledge, the author indicates that Bush and the author are in agreement: the statement is true. It is a "presupposition", not a logical entailment.
Other factives: avow, admit, concede, confess, regret, …
Non-factives: deny, claim, say, announce, report, suggest, …
The spokesman did not acknowledge that Bush had been mistaken.
With factive verbs, the truth of embedded statement is presupposed even if it was not uttered. Presupposition is a stronger notion than entailment.

6. Factive and non-factive cognitive verbs
Verbs of believing
Proposition
Experiencer
Author
As with verbs of saying, the choice of the verb indicates the stance of the author with respect to the veridicity of the proposition.
Bush realized that the US Army had to be transformed to meet new threats.
Bush didn't realize that Afghanistan is land-locked.
With realize, the embedded statement is presupposed.
Other factives: discover, find out, forget, know, learn, recognize, foresee, notice, …
Non-factives: assume, believe, think, suspect, imagine, hope, …

7. Other factive constructions
Verbs:
It doesn't matter that Bush has more money than Kerry.
Other factives: make sense, suffice, bother, amuse, irritate, fascinate, help matters, …
Non-factives: follow, predict, entail, suggest, imply, …
Adjectives:
It’s not surprising that Bush is expected to beat Kerry.
With surprising that, the embedded statement is presupposed.
Other factives: amazing, unfortunate, known, sad, good, great, lucky, important, relevant, irrelevant, enough, …
Non-factives: likely, unlikely, probable, certain, possible…
Nouns:
It’s no secret that Bush would like voters to see him as Reagan’s heir.
Other factives: accident, coincidence, disaster, miracle, blessing…
Non-factives: claim, rumor, belief, suspicion, hypothesis, idea…

8. Trustworthiness
Reuters reports that Congress has passed the use of force resolution.
Statement: Congress has passed the use of force resolution.
Source: Reuters
Author: uncommitted (reports)
Although the author is noncommittal, the reader may choose to take the statement as true if the source is trustworthy.
trustworthy = well-informed and honest
Reuters reports that the UN said on Monday that the Iraqis claim that Iraq has fully cooperated with the inspectors.