Representing prepositions in lambda calculus/logic notation

How would I represent 'for' in "Are you here for a conference?"

1. conference could be represented as `lam x.conference(x)`.
2. a conference could be represented as `lam Q x.(conference(x) & Q(x))`

I assume that I know the meaning of `for` in this context. (Prepositions are polysemous)

• "Are" is not a preposition: it is a verb. Most prepositions have their own semantics, and would need to be represented by their own operations in any logical form. Some are merely syntactic sugar (some uses of of, for example). – Colin Fine Dec 19 '15 at 17:42
• I'd use "P" for preposition. (But I doubt the question you ask is really meaningful.) – Greg Lee Dec 19 '15 at 18:21
• "For the conference" is a preposition phrase @ColinFine. I provided a complete sentence as an example. – mac389 Dec 19 '15 at 18:22
• @GregLee I do not think you understood my question. Perhaps my edited version is clearer. – mac389 Dec 19 '15 at 18:30
• Lambdas provide a way to express functional abstraction. What does this have to do your question about representing "for"? I just don't see any connection. – Greg Lee Dec 19 '15 at 18:38

Just from this example it would seem that the type of for is `((e,t),t), ((e,t),(e,t))` -- because it combines with a DP to make up an adjunct to the VP. Thus, it could have a semantics like the following (I'm just making it up)
• @GregLee: Nothing particular, just was trying to interpret 'for'. Sure, I've changed it to `for`. – Ivan Kapitonov Dec 20 '15 at 1:48