LING 3505 Lecture Notes - Lecture 10: Lambda Calculus, Noam Chomsky

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9 Feb 2016
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LING 3505 – February 8
Words and phrases have a type depending on what the expression denotes
e = the set of all entities/individuals
t = the set of truth values – type of propositions
<e,t> means that it’s describing a set of functions “I am the type of
predicate that is looking for an individual” telling you how to apply certain
functions
one-place predicate
Start at the bottom and work your way up
Roxanna is happy – give me an individual (e, Roxanna) and I will give you a
truth value to determine whether she is happy
<e<e,t>>: two-place predicates – see, hire, brother, fond
<e<e<e,t>>>: three-place predicates – give, put
<<e,t>,<e,t>>: adverbs – quickly (attributive adjectives)
<<e,t>, e>: de4ne articles, “the”
1, a – Adela saw Peter <e>
b – Adela saw Peter <e<e,t>>
c – Rupert wore checkered trousers <e,<e,t>>
d – The wall was very high <<e,t>,<e,t>>
e – Henry allowed the hamsters three nuts each <e,<e,<e,t>>>
f- the wall was very high <t>
2, a – Snails don’t like mustard (don’t = not) <t,t>
d- Snails might like brown mustard, but it seems unlikely <t,t> (might is like
not)
The type of a word = the type of the node that immediately dominates it
Linguistics is a branch of psychology according to modern Chomskian theory
Semantics is also seen as mathematics
Lambda calculus
SLEEP (mandy)
SLEEP (x)
lambda is “the property of
“the meaning of” is represented by ||
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