Full Idea
Basic Monotony: something stays proved if further premises are added. Cautious Monotony: the addition of something which has been proved makes no difference. Rational Monotony: it stays proved as long as the addition's negation hasn't been proved.
Gist of Idea
Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved
Source
G. Aldo Antonelli (Non-Monotonic Logic [2014], 1)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.3
A Reaction
[A compressed and non-symbolic summary]