The object language of this second ACG is defined as follows: Then, a lexicon from Σ 1 to Σ 3 is defined: This allows the ACG G 13 to be defined as The abstract language shared by G 12 and G 13 contains the two following terms: The syntactic lexicon L 12 applied to each of these terms yields the same image.
it β-reduces to the following object term: the semantic lexicon L 13 yields the de re reading when applied to (2): and it yields the de dicto reading when applied to (3): Our handling of the two possible readings of (1) differs from the type-logical account of Morrill (1994) and Carpenter (1996).