Apologies if this question is answered elsewhere. I didn't know how to refer to the following phenomenon and consequently I didn't know what to search for. I'm happy for more expert users to add/remove tags or suggest other amendments to the question.
Take as an example the following sentence:
(S1) Women are not permitted to become priests.
My understanding, and I am a native English (UK) speaker educated to PhD level in philosophy, is that when someone says this, unless they add further clauses cancelling the implication, they imply the following:
(S2) Men are permitted to become priests.
The implication can be cancelled, if the speaker adds, for example, "But nor are men, the state forbids anyone to become a priest" (Perhaps non-binary-gendered people or robots could still become priests in this case).
Is my understanding here correct? If so, is there a name for this kind of implication? Where could I read more about it or direct someone to, to learn more?