A quote from the MW Dictionary of Synonyms (without examples here):
"Severe is applicable to persons and their looks, acts, thoughts, and utterances or to things (as laws, penalties, judgments, and styles) for which persons are responsible. In all these applications it implies rigorous standards of what is just, right, ethical, beautiful, or acceptable and unsparing or exacting adherence to them; it not only excludes every hint of laxity or indulgence but often suggests a preference for what is hard, plain, or meager (a severe teacher). Very often the word suggests harshness or even cruelty (severe criticism)."
"Harsh suggests a nature that is unfeeling, cruel, and indifferent to the pain it inflicts (a harsh critic) or when applied to things, effectiveness in promoting discomforts or in imposing rigors (a harsh rebuke)."
Compare the following examples (taken from different sources):
The country has come under severe criticism for its human rights record. [strong, neither bad not good]
Many people feel the punishment should have been more severe.
It may seem harsh to punish him, but he has to learn that this kind of behaviour is unacceptable.
He later regretted his harsh words. [negative]
He accused her of being unduly harsh. [negative]
Nothing can justify such harsh treatment of prisoners. [negative]
Best Answer
An assertion is a statement of a fact or belief, while a premise is a statement from which another is inferred. For example, if we use the assumption X to conclude Y, then the premise X has been used to make the assertion Y.