Lambda notation is of importance since lambda reduction, which is the process to apply lambda notation and get new FOL expressions from where the formal parameter variables are bound to specified terms.
$$\lambda x.P(x)(A)\rightarrow P(A)$$
The lambda reduction can apply to one lambda notation multiple times. 
$$
\lambda x.\lambda y.Near(x,y)(Bacaro)\rightarrow \lambda y.Near(Bacaro,y)
\\
\lambda y.Near(Bacaro,y)(Centro)\rightarrow \ Near(Bacaro,Centro)
$$


University of Colorado at Boulder

Lambda Notation can provide a way to abstract from fully specified FOL formulas in a way that will be particularly useful for semantic analysis.
$$\lambda x.P(x)$$


Lambda Notation


An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

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