Information that compels a rational agent to prefer one course of action over another.

Whatever is true.

An argument that convinces people to act in a way desired by the one who makes the argument.

It's undefined. "Evidence" cannot be defined, since it is the most fundamental concept, from which all others are defined and justified.

That which justifies belief.

Observations which favor some hypotheses over others

E is evidence for hypothesis H if the posterior probability P(H|E) differs from the prior P(H).

Anything that changes the posterior probability of a proposition. E is evidence for or against H if P(H|E) differs from the prior P(H). (It's evidence in favor if the posterior is larger than the prior, and evidence against if it's smaller)

[Unexpanded definition] 5 nouns & a verb meaning variously; a reason for updating belief: an existing body of information: a legal term: a symptom: a phenomenological term: & a verb, to make evident (see Expanded Definition in comments)