In this, "to be" is the base verb, conjugated in the first, singular, present tense "am". The verb is then put in a contraction with first, singular, pronoun "I" to create "I'm". This contraction is then made into a phrasal verb by adding either of the adjectives "up" or "down".
I am curious about why, in these cases, adding the prepositional phrase "for that" changes the meaning between the examples (2) and (4) which use "up".
But the change in meaning does not occur between (1) and (3).
(1) I'm down for that
(2) I'm up for that
(1) and (2) both parse as someone stating their own interest/availability for what "that" refers to. As in, for example, Person A asking "Want to go to the movies?" and Person B replying either "(1) I'm down for that" or "(2) I'm up for that".
(3) I'm down
(3) parses as someone stating their own interest/availability. In the same example, Person A asks "Want to go to the movies?" and Person B replies "(3) I'm down". So, saying "(1) I'm down for that" and "(3) I'm down" both have pretty much equivalent meaning in colloquial English.
(4) I'm up
(4) parses as someone stating they "are up" as in...
a) they have physically stood up or,
b) they are now conscious (after being asleep or unconscious).
So in the conversation example, Person A asks "Want to go to the movies?" and if Person B replies "(4) I'm up" -- it would be a strange answer.
Comparing "(2) I'm up for that" and "(4) I'm up" -- these do not have equivalent meaning. Adding the prepositional phrase "for that" changes the focus and meaning of the sentence. In (2) the focus is that the "I" is interested/available. In (4) the focus is on the state of being, not their interests.
Is there any slang etymology about "up" and the verb "to be" being combined as a phrasal verb? Additionally, is the effect of the prepositional phrase "for that" something that has trends, or is is an interesting isolated case in the situation of (2) vs (4)?