We give a type logical categorial grammar for the syntax and semantics of Montague's seminal fragment, which includes ambiguities of quantification and intensionality and their interactions, and we present the analyses assigned by a parser/theorem prover CatLog to the examples in the first half of Chapter 7 of the classic text Introduction to Montague Semantics of Dowty, Wall and Peters (1981).
Morrill, G. Structural ambiguity in Montague Grammar and categorial grammar. "The linguistic review", Gener 2015, vol. 32, núm. 1, p. 87-113.