I'm learning lambda calculus, however I'm quite confused about the quantifiers in lambda calculus. As far as I know, quantifiers such as "∃" are concepts of first order logic (FOL), which are not needed by lambda calculus. Moreover, I didn't find anything about quantifiers in any tutorials I have read.
However, I find this paper (Lambda Dependency-Based Compositional Semantics), in the first page of which the author used quantifier in lambda calculus.
So, are quantifiers used in lambda calculus? If so, what do they mean? Is it the same as in FOL?
Precisely, what does "∃" mean in the following lambda calculus?
λx.∃e.PlacesLived(x, e) ∧ Location(e, Seattle)