# 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 ||