Do dictionaries make negative claims?

Could a dictionary provide a definition, for example, in the form of: "Not of, or resembling X"?

Sure and it’s trivial to find such definitions in web-based dictionaries with a good search like site:merriam-webster.com "not of" or site:lexico.com "not of".

For example:

• Nonmicrobial: not of, relating to, caused by, or being microbes (MW)

• Marginal: not of central importance (MW)

• Unnoble: Not of noble birth or rank; rare Of or relating to a person who is not of noble birth or rank. (Lexico)

(Many of the words you see in searches like that are words with negative prefixes, like un- and non-, not by coincidence.)

These definitions have no contradictions, but some do. Some words are autoantonyms, with one sense of the word being the opposite of the other. One of the most well known of these words is literally, which MW defines in one sense as “used in an exaggerated way to emphasize a statement or description that is not literally true or possible”.

bitter Having a sharp, pungent taste or smell; not sweet. Lexico

sweet Having the pleasant taste characteristic of sugar or honey; not salty, sour, or bitter. Lexico

Using this definition of bitter, could I say that something that is salty is also bitter just because it isn't sweet?

M-W takes a different approach with bitter, without saying what it's not, but adds:

— compare SALTY entry 1 sense 1b, SOUR entry 1 sense 1, SWEET entry 1, UMAMI entry 2 sense 1

mediocre not very good Cambridge

vs.

mediocre of moderate or low quality, value, ability, or performance : ORDINARY, SO-SO m-w

The "not" approach here leads to a problem because "not very good" can be understood two ways: (1) How was the food? It wasn't very good. = I wouldn't call it good at all; and (2) How is the food at that new place? I'd say it's good, but not very good. Will a student of English know which was meant? You could also make the case that food that isn't very good at a restaurant (I sent it back) is worse than mediocre (I ate it anyway).