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The word 'rule-governed' is correct and can be used in written English.
It is typically used to describe something that is regulated or controlled by a set of rules. Example: The game of chess is a highly strategic and rule-governed activity, requiring players to follow a set of rules in order to win.
Exact(55)
We are rule-governed creatures because we conceive of ourselves as rule-governed creatures.
Music, too, is rule-governed in a way that should make it easily simulated".
Although this "poverty of the stimulus" argument proved extremely controversial, most philosophers enthusiastically endorsed the idea that natural languages are syntactically rule-governed.
It is, of course, controversial to claim that monkeys have rule-governed propositional social knowledge systems as claimed in (iv) and (v).
Sovereign dictatorship, then, is still necessary to create the substantive equality that grounds the legitimate operation of constituted, rule-governed democratic politics.
Finally, Kochanska, Aksan, and Joy (2007) found that child fearfulness moderated the association between both positive motherchild relationships and later successful socialisation and paternal discipline style and child rule-governed behaviour, with more fearful children being apparently more susceptible to the effect of positive interactions with their mothers and their fathers discipline style.
Gottsched's derivative, rule-governed poetics made him an unlikely candidate for founder of modern German literature.
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African-American English is just as rule governed as Standard English, but the dialect is often ridiculed because of cultural snobbery.
For the first time, Forbes.com has compiled a list of Luxury Wildlife Tours, and a single rule governed our selection criteria: more is more on a wildlife trip.
Ivan Sratsimir and his family were captured and taken to the castle of Humnik in modern Croatia and the region of Vidin was placed under direct Hungarian rule governed through a Ban appointed by the King of Hungary.
No evident rule governed the accession-coverage frequencies of specific ncRS sequences.
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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