Calling this 'non-classical' is interesting—it's definitely non-classical from the point of view of formalisation, but I'm not sure formalisation has been around long enough to have classics ….
As of course you know but non-mathematicians may not, from a non-formalising mathematician's point of view, it's the non-constructive logic that's classical, to the extent that it's actually sometimes called classical logic (https://en.wikipedia.org/wiki/Classical_logic).
Calling this 'non-classical' is interesting—it's definitely non-classical from the point of view of formalisation, but I'm not sure formalisation has been around long enough to have classics ….
As of course you know but non-mathematicians may not, from a non-formalising mathematician's point of view, it's the non-constructive logic that's classical, to the extent that it's actually sometimes called classical logic (https://en.wikipedia.org/wiki/Classical_logic).