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These two approaches work well for simple sentences, but they are challenged by more complicated sentences in which the surface order is not a possible reading, or where the different scope readings are logically independent.
For example, formal tools are especially useful to make scope ambiguities explicit, since different scope readings of one and the same natural language sentence can be represented with different formal sentences which themselves have no scope ambiguities.
A recent method is by means of 'lifting rules' (see Sect. 3.3): the meaning of a noun-phrase is 'lifted' to a more abstract level, and different levels yield different scope readings (Hendriks 2001).
In Tree Adjoining Grammars (TAG's) the different scope readings of the sentence about loving a woman differ in the order in which the noun-phrases are substituted in the basic tree.
Similar(56)
Shortly after these scoping readings were taken, system-wide remediation was begun and subsequent measurements no longer reflected the exposures of the study subjects.
Although Whitehead and Russell take the descriptions in these examples to be the expressions which have scope, the above readings in both expanded PM notation and in modern notation suggest why some modern logicians take the difference in readings here to be a matter of the scope of the negation sign.
In this paper, we trace and contrast two very different readings of the scope of their argument.
The deep substantive questions about Wall Street and Goldman are beyond the humble scope of my weekly blog, Reading for Leading.
Certain languages express the two readings via manipulating the scope relation between the modal and the perfect aspect.
His account of their love affair is so morally ambiguous as to allow wildly divergent readings, providing plenty of interpretative scope for directors.
Barthes made a crucial distinction between the "writerly" and the "readerly" text, emphasizing the scope a "readerly" text gives to plural, disruptive readings.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com