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The phrase "a strict notion" is correct and usable in written English
It can be used when discussing a concept or idea that is defined in a precise and rigid manner. Example: "In legal contexts, a strict notion of liability often leads to harsher penalties for offenders."
Exact(2)
To facilitate the following discussion, we will adopt a strict notion of accommodation, and take the naive view that what is accommodated is the presupposition as triggered by, e.g., a definite NP or factive verb.
Islamic texts emphasize a strict notion of monotheism (tawhid) and forbid the association of partners with God, which would be idolatry.
Similar(58)
There are some hints in Dretske's writings of a willingness to use a less strict notion of indication for he sometimes speaks of the content of a representation as the "maximally indicated state".
It is clearly a rather strict notion of equality between λ-terms.
In a slightly less strict notion, the words in the query appear frequently in the document, in any order ("bag of words").
We argue that upon taking beta diversity patterns into account, the strict notion of complete sequencing of an entire ecosystem (e.g. soil) is a near impossibility.
However, this strict notion of conserved interaction leads to a very small number of potentially conserved interactions.
Marine Le Pen has decided to portray her party as the true champion of laïcité (France's strict notion of the separation of church and state, which forbids any display of religious affiliations in public offices and schools).
But faking unfailingly patient parenting and perfect children is something closer to betrayal — not of some strict notion of "reality," but of other parents, who get through the tortured mess of raising children in New York only by taking comfort in the details of the tortured mess that other parents confide.
Suddenly young, urban Turks with no background in Kurdish politics were speaking breathlessly of Demirtas, engaged by the HDP's inclusive vision of Turkey, one at odds with Erdogan's strict notion of Turkish identity: conservative, Sunni Muslim, and fiercely nationalistic.
An initial reason to distinguish ontological dependence and metaphysical grounding is that the latter is a much stricter notion.
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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