Department

LinguisticsCourse Code

LING 165CProfessor

Dylan BumfordLecture

4This

**preview**shows half of the first page. to view the full**2 pages of the document.**1/28/19 Lecture 5

- Review

- Predicates are functions that take in arguments (i.e pred’(c)(John’),

chase’(Mary’)(John’)

)

- Variable binding operators (∀, ∃), can be used on any sentence. Where we

evaluate the sentence under certain conditions.

- i.e ∃y [ ∀x [ use’(x)(y) ] ]. The whole expression doesn’t need to know

what x or y is.

- Variables & constant → entities; predicates → functions; sentences → truth

conditions

- [P(𝛕)]g = [P]g([𝛕]g) used to find out the denotation of the predicate

- i.e [∀v[φ])]g = 1 iff [φ]g = 1 for every g’ like g except for φ

- Lambda Calculus

- [ λv [φ]]g = F where F(a) = [φ]^(gr→ a).

- (gr→ a) = an assignment just like g except v is mapped to A

- Example: [sing’] is a predicate that denotes a function from entities to truth

values. As with all predicates and functions, we just assume we know what this

predicate sing.

- λv[p’(v)] = p

- i.e λx[chase’(x)(x)] = property that someone is chasing themself

- i.e chase’(x) = property that some x is being chased

- λx[sing’(x)](john) is a new expression combined by a predicate and an entity. This

expression denotes a truth value. The property holds up by λx[sing’(x)] is true if

and only if the entity x, which is john in this case, holds up this predicate. This

whole expression is basically equivalent to [sing’(x)](john). This whole

equivalence is called the beta-conversion.

-Beta-equivalent: λv[p](ε) = p/ v→ ε

- Lambda-calculus just returns a new predicate, waiting for something to fill the

void.

- [λx[λy[x]]]([y]) → gives back what is given second

- The above expression when beta-converted (λy[y]) are different

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