That is a good general understanding of one use of the definite article, but I warrant it does not hold universally true. For instance, the speaker may expect that the listener is familiar with the noun, or it may be the only one in existence, or it may be idiomatic, as in your first example, where 'signs of tiredness' (no article) would probably be used in either case.
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Mister Micawberit may be idiomatic, as in your first example, where 'signs of tiredness' (no article) would probably be used in either case.Did you mean that even though both the speaker and the listener know the signs of tiredness (maybe because they both saw the signs together), but since "sign of tiredness" is a natural expression without "the" to a