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Semantics 1

June 12, 2012

Gerhard J¨ager

(June 12, 2012) Semantics 1 Gerhard J¨ager 1 / 4

(2)

QR to PP

(1) No student from a foreign country was admitted.

inverse linking reading:

λs.∃x(country’(s, x)∧foreign’(s, x)∧ ¬∃y(student’(s, y)∧ from’(s, y, x)∧admitted’(s, y)))

more plausible reading:

λs.¬∃y(student’(s, y)∧ ∃x(country’(s, y)∧foreign’(s, y)∧ from’(s, y, x))∧admitted’(s, y))

(June 12, 2012) Semantics 1 Gerhard J¨ager 2 / 4

(3)

QR to PP

Quantifier Raising to PP

transformation rule “Quantifier Raising”:

1 replace theN P-nodeαof a generalized quantifier byN Pi 2 replace someP P-nodeβ that dominatesαin S-structure by the

configuration[P P αi β]

(June 12, 2012) Semantics 1 Gerhard J¨ager 3 / 4

(4)

Quantifiers

Quantifier Raising interpretation of LF

If[P P1N Pi P P2]is a configuration that results from Quantifier Raising:

kP P1k=λP λxλs.P(s, x)∧ kN Pik(s, λxiλs.kP Pk(x, λxλs.⊤))

(June 12, 2012) Semantics 1 Gerhard J¨ager 4 / 4

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