My question (also copied below) was closed because "This question already has answers here". The linked answer says that negative polarity items only appear in negative contexts and positive polarity items only appear in positive ones." But, I am not sure if 'at least' is a positive polarity item. I consulted both The Cambridge Grammar of English Language and A Comprehensive Grammar of the English Language, but didn't find 'at least' mentioned as a PPI in their chapters discussing polarity items. And there are sentences which seems to have 'at least' in negative contexts such as
All had also not responded to at least one course of a high-dose oral steroid (1 mg/kg/day) for 2 weeks.
the two health clinics did not notify at least 185 women about abnormal Pap smears.
Hunter, was pulled from duty while internal affairs investigates him for not submitting at least 187 rape kits in 2014, 2015 and 2016 for testing.
So, my question is "Is 'at least' really a positive polarity item?"
My previous question is
I have a question about the following problem.
Fill the gap with appropriate words from the following options.
It won’t take ( ) 15 minutes to walk there, so put your shoes on and let’s go.
(1) at least, (2) at most, (3) less than, (4) more than.
The answer is (4). What I can’t understand is why (1) is not another answer. ‘at least 15’ means ‘the minimum is 15’, which means ‘more than 15’. Yet, ‘more than’ is correct and ‘at least’ is not. Why?