"Let's get a steak" doesn't represent "let's"?

When parsing phrases with “let’s” like “Let’s get a steak”, there isn’t a representation of “Let’s” in the MRS that I can see. In this case, there is only one parse:

[ "let's get a steak'"
  TOP: h0
  INDEX: e2 [ e SF: comm TENSE: pres MOOD: indicative PROG: - PERF: - ]
  RELS: < [ pronoun_q<0:5> LBL: h4 ARG0: x5 [ x PERS: 1 NUM: pl PT: zero ] RSTR: h6 BODY: h7 ]
          [ pron<0:5> LBL: h8 ARG0: x5 ]
          [ _get_v_1<6:9> LBL: h1 ARG0: e2 ARG1: x5 ARG2: x9 [ x PERS: 3 NUM: sg IND: + ] ]
          [ _a_q<10:11> LBL: h10 ARG0: x9 RSTR: h11 BODY: h12 ]
          [ _steak_n_1<12:17> LBL: h13 ARG0: x9 ] >
  HCONS: < h0 qeq h1 h6 qeq h8 h11 qeq h13 > ]

For speakers I imagine a difference between “get a steak” and “let’s get a steak”, at least from a “softening” point of view. In my scenario, I’m implementing a restaurant scenario where saying “get a steak” to the waiter would be pretty different (even beyond softening) than “let’s get a steak”.

Is this a case where it is considered a “Pragmatics” and not a “Semantics” issue and so stripped? I wonder if this is related to this question about “what else”?

Edit: I just noticed that there is at least one distinction between the parses for “get a steak” and “let’s get a steak”. Both are parsed as SF: comm, but the “let’s” version sets the implied pronoun to PERS: 1 NUM: pl and the other sets it to PERS: 2.

Further, it can be distinguished from the phrase “we get a steak” because that one is a SF: prop.

So I think that answers my question: it really is represented, just not as a predication.

Yep – let’s is the hortative, i.e. 1st person equivalent of an imperative.

I think I just found my vocabulary term of the week. Thanks @ebender!