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The phrase "following logically" is correct and usable in written English.
It can be used to indicate that something is a logical consequence or is in logical sequence to something else. Example sentence: The main argument presented in the first chapter was followed logically by the supporting evidence in the subsequent chapters.
Exact(7)
And, like McCarthy's, it requires appeal to a notion that does not seem any clearer than the notion of a logical constant: the notion of following (logically?) from the meaning of the connective.
Dr. Hamilton, who died in 2000, saw his theory as following logically from what biologists already knew about natural selection.
Such combinations of tonalities may be reviewed as 20th-century extensions of diatonic harmonic practices, following logically from post-Wagnerian chromaticism.
In the Phaedo the statement "The soul is immortal" is presented as following logically from various premises Socrates and his interlocutors consider acceptable (cf. 106b 107a).
This means that risk perception, following logically, must then be related specifically to the particular threat, and restricts our ability to place one 'risk' in relation to broader concerns of individuals and communities.
The Hasidic master R. Neftali Tzvi of Ropshitz notes the following: Logically, a person who is a descendant of distinguished ancestors should be modest and humble.
Similar(53)
The city where the show had the biggest following was, logically enough, its home market of Los Angeles where it hit a 51.5 rating.
"We did a great job at Gleneagles in 2005 – raising the importance of aid and development, so what is the next stage in this vital work?" Cameron's line is that this is the next stage, following on logically from Gleneagles: "The more I have looked into it, the more I see unless you take up tax and transparency agenda you will not get the sort of development and change you want to see.
And your mind is in a strange state just before you fall asleep: a free-associative state in which, rather than following from another logically, one thought "suggests" the next.
All patients were required to meet the following criteria: (a) histo-logically confirmed ESCC; (b) preoperatively staged with locally advanced (cT3, cN0/+, cM0) disease; (c) preoperative radiotherapy and surgery were the only treatment procedures; (d) Eastern Cooperative Oncology Group (ECOG) performance status 0 2; and (e) no other severe medical disease.
Logically, they are following the trends of new smartphone growth areas.
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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