Epistemic modality: degrees of commitment

Every statement carries an implicit claim about how sure you are. At C2 you control this scale deliberately: must and will for a confident inference, should for an expectation, may for a real possibility, might and could for a weaker one, reinforced or softened by adverbs such as presumably, arguably or conceivably.

• That will be the courier — nobody else rings at this hour.
• The results should be available by Friday.
• The decline is arguably the most serious in the industry's history.
• There might conceivably be a second explanation.

Apparently reports what you have heard or read, not what is obvious: Apparently the talks have failed = I am told they have failed. For "obviously" use evidently or clearly.

Deduction about the past: modal + have + past participle

To reason about a past event you did not witness, use a modal with the perfect infinitive. The modal carries your degree of certainty; have + past participle places the event in the past. Continuous and passive forms follow the same logic: must have been waiting, may have been altered.

modal + have + past participle | modal + have been + -ing / past participle