Department

LinguisticsCourse Code

LING 165CProfessor

Dylan BumfordLecture

3This

**preview**shows half of the first page. to view the full**3 pages of the document.**1/23/19 Lecture 4

- Notation too complicated

- Meta Language

- Semantics of the formal language

- For every formula, which object in the model does it refer to

- Language consists of

- Simple predicates: all expelled as verbs for convenience (i.e chase’, see’,

...) and each has an associated number specifying number of arguments

called arity

- Terms: will have

- Constants: names like “john”, “pinky”, “fido”

- Formula: a predicate with arity 0

- For any predicate P with arity n, and any term 𝛕: P(𝛕) is a complex predicate of

arity n - 1. (i.e chase’ has arity 2, and chase’(john’) has arity 1, and

chase’(john’)(fido’) has arity 0, which is now called a formula)

- If P has arit n, then [P] is an in-place function into truth values

- If 𝛕 is a constant, then [𝛕] is an entity in the model

- [ p(𝛕) ] = [p]( [𝛕] )

- Example of this meta language

John chases Fido.

We have only two things in the model: John and Fido

Chase is a predicate that takes in two arguments, it has the following denotation.

We read from inside out. Constituent always combine with the object first. So in the

below case, Fido chased John

[chase’ (john’)(fido’)] ⇒ [ chase’(john’) ]([fido’]) = [ [chase’] ([ john’ ]) ] (‘[fido’])

###### You're Reading a Preview

Unlock to view full version