Final Review - Linguistics

Allophones appear in

complimentary distributions

Complimentary distributions

not appearing in the same environment

Minimal pair

a pair of words that differ in only one sound and have different meanings

How to find a minimal pair

• look for the two allophones being the only sounds that have switched in a word

• If two sounds switch places, that counts as two differences

• Go through the data thoroughly, but if you cant find a minimal pair after a through search, then believe in yourself and just say there’s no minimal pair

If there exists a minimal pair for the two sounds, then

the two sounds are contrastive

• contrastive sounds are defined with respect to (in the context of) a specific language

The non-contrastive sounds in a language are often treated as

special realizations (allophones) of the same phoneme

The allophones are surface realizations of the underlying phoneme, Consider aspiration in English:

Underlying form: /p/

Surface form(s): [p] and [pʰ]

Allophones (phonetic representations) are expressed in []; while the phonemes (phonemic representations) are expressed in //.

Ex:

Allophone: [p] and [pʰ]

Phoneme: /p/

A general strategy for testing whether an inference is an entailment, implicature, or presupposition

• if the inference can be cancelled or reinforced, then that inference is an implicature

• if the inference persists when the sentence is negated, then the inference is a presupposition

• Otherwise the inference is an entailment

Entailment

an inference where something follows from another thing

Presupposition

an inference that persists when a sentence is negated

Implicature

an inference that can be cancelled or reinforced

Scaler implicature

a special type of implicature where

• stronger quantifier/larger number entails the existence of all weaker quantifiers/(small numbers)

Ex: all entails many, half entails some, two entails one, three entails two and one

• weaker quantifiers/smaller number implicates the negation of stronger quantifiers/(larger numbers)

Ex: some implicates not all, not most, and not half, one implicates not two, not three

Reinforcement test: affirms inference

affirm the inference and add it to the original utterance, If the resulting sentence is not redundant, then the inference is an implicature

Ex Reinforcement test: Dina speaks Odia, Hindi, and Telegu, and she speaks only these three languages

Cancellation test: denies inference

deny the inference and adds it to the original utterance. If the resulting sentence is not contradictory, then the inference is an implicature

Ex Cancellation test: Dina speaks Odia, Hindi, and Telegu, but in fact she speaks other languages as well

Implicature

The additional information that is inferred from a speaker’s utterance

presupposition

for two sentences q and p, q presupposes p iff both p and the negation of p entail q

Test for presupposition: Negation test

Negate the utterance. If the negated utterance still has the same inference, then that inference is a presupposition.

Ex: presupposition test

Utterance: John’s daughter left

Inference: John has a daughter

Negation test: The negated utterance ‘John’s daughter didn’t leave’ still has the inference that John has a daughter. therefore, the inference ‘John has a daughter’ is a presupposition

Vacously true

A sentence is vacuously true when it is true under any circumstances. A vacuously true sentence is entailed by any other sentences.

Any other sentence A can be before it- and that sentence A will entail it

Example: John will have breakfast or he will not have breakfast.

• any sentence put before this sentence will entail it

Ex:

The sky is green (Entails)

John will have breakfast or he will not have breakfast.

Entailment

for two sentence p and q, p entails q iff whenever p is true, q must also be true. There is no possible world where p is true but q is false

(cannot make premise sentence true and conclusion sentence false)

Example: entailment

• John ate an egg and a waffle for breakfast

• John ate a waffle for breakfast

Test: If John ate an egg and a waffle for breakfast, it is automatically true that he ate a waffle. There is no possible world where he ate an egg and a waffle and he did not eat a waffle

The extension of a sentence

truth value

(1 for true, 0 for false)

Extension of a Name

a single, specific entity  ⟦⟧- whatever’s in there you are going to name the extension of

ex:  ⟦Bart⟧ = b,  ⟦Lisa⟧ = l, ⟦Maggie⟧ = m

Extension of a common noun

a set of individuals

ex: ⟦student⟧ = {b,l}

Extension of an Adjective

a set of individuals

ex: suppose Bart and Lisa are sleepy, then ⟦sleepy⟧ = {b,l}

extension of a Complex noun phrase

the intersection of the sets denoted by the noun and adjective

ex: suppose Lis and Maggie are happy and Bart and Lisa are students

⟦happy⟧ = {l,m}

⟦student⟧ = {b,l}

Then ⟦happy student⟧ = ⟦happy⟧ Ո ⟦student⟧ = {l,m} Ո {l,b} = {l}

extension of a Verb Phrase

a set of individuals

ex: Suppose Lisa and Maggie cried, then ⟦cried⟧ = {l,m}

Suppose Lisa and Bark go to school, then ⟦go to school⟧ = {l,b}

Semantic composition of Complex Noun Phrase

(adjective + noun)

the intersection of the sets denoted by the noun and the adjective

ex: ex: suppose Lis and Maggie are happy and Bart and Lisa are students

⟦happy⟧ = {l,m}

⟦student⟧ = {b,l}

Then ⟦happy student⟧ = ⟦happy⟧ Ո ⟦student⟧ = {l,m} Ո {l,b} = {l}

Simple sentences (proper name + verb phrase)

The meaning of a simple sentence in the form of ‘NP VP’: ⟦NP VP⟧ = ⟦NP⟧ ∈ ⟦VP⟧

Sentences with quantifiers

⟦A N VP⟧

⟦Every N VP⟧

⟦no N VP⟧

⟦every N VP⟧

⟦NP⟧ ⊆ ⟦VP⟧ 

(np is a subset of vp)

Ex: ⟦Every cat sleeps⟧ =

1 iff ⟦cat⟧ ⊆ ⟦sleep⟧ 

⟦a/some N VP⟧

⟦NP⟧ Ո ⟦VP⟧ ≠ Ø

(the intersection of NP and VP does not equal 0)

Ex: ⟦Some cats sleep⟧  =

1 iff ⟦cat⟧ Ո ⟦sleep⟧ ≠ Ø

⟦no N VP⟧

⟦NP⟧ Ո ⟦VP⟧ = Ø

(the intersection of NP and VP equals 0)

Ex: ⟦No cat sleeps⟧  =

1 iff ⟦cat⟧ Ո ⟦sleep⟧ = Ø

ways to define a set

• venn diagram

• listing all of its members

• Predicate/Abstract notation

Way to define a set - Venn diagrams

In circle - in set

Not in circle - not in set

Way to define a set - Predicate/Abstract notation

by stating a condition that is satisfied by all and only the elements of the set to be defined

• CF {x│x is a cat friend of Chenli}

• E {x│x is an even number greater than 3}

Way to define a set - List notation

by listing all of its members

• Chenli’s cat friends {x│x is a cat friend of Chenli}

Operations we can do on sets

Union

Intersection

Difference

Complement

Union

written as A U B - The union of A and B add the elements in the set to each other

• a union of sets results in a new set

• if members repeat within sets, only put it down once, means same thing

ex:

if

A = {a,b,c}

B = {b,c,d}

AUB: {a, b, c, d}

Intersection

written as A Ո B - Intersection of A and B singles out elements that are only found in both sets (elements they share)

Ex:

if

A = {a,b,c}

B = {b,c,d}

A Ո B: {b,c}

Difference

written as A - B - basically A minus B, elements in first letter minus the elements in second letter. pick out elements that are only in A and not in B

ex:

if

A = {a,b,c}

B = {b,c,d}

A - B: {a}

• order matters (B - A) is diff than (A - B)

Complement

written as A’ - The complement of A is the difference between the set containing everything, and A

(any member thats not in the set where the apostrophe is)

ex:

A = {a, b, c}

A’ - (anything not in A)

the set that contains anything but a, b, and c

Cardianality

││- indicates the numbers of elements in a set

There are two special sets- the empty set, and the universe of discourse

The empty set

set with no numbers

• written as either Ø or {}

The universe of discourse

the set containing everything (under the specific context. All things in that specific domain)

• written as U

• don’t confuse this for the union sign which is also written U

Subset

 ⊆ - A is a subset of B iff every element of A is also an element of B

A  ⊆ B - A is a subset of B

A  ⊈ B - A is not a subset of B

Ex:

A = {a, b, c}

B = {a, b, c, d, e}

Then A ⊆ B

Identity

sets are identical/equal iff they have exactly the same members, written as A = B. If A and B are not identical/Equal we write A ≠ B

Ex:

A = {a, b, c}

B = {a, b, c}

A = B

(order of members in set doesnt matter, as long as they have the same members they’re = to each other)

Membership

∈- if an element is a member of a set (only used to talk about an element’s relation to a set)

a ∈ S - a is a member/element of the set S

a ∉ S - a is not a member/element of the set S

Ex:

S = {a, b, c}

a ∈ S

d ∉ S

Set

an abstract collection of distinct objects

• objects in a set MUST be distinct. two of the same objects in a set counts as one

  ex: {a, a, b} = {a, b}

• sets can also be objects in a set, a set of sets

Subset vs membership

subset- relation between sets

membership- relation between member and set

Names - elements, Nouns - sets

name- may or may not be within a set

Adj extenstion- set of entities that have the property of being adj

noun ex: student

• denotation would be a set of anyone who is a student

Grice’s Maxims

Maxim of Quantity

Maxim of Quality

Maxim of Relevance

Maxim of Manner

Maxim of Quantity

• Make your contribution as informative as it is required

• do not make your contribution more or less informative than is required

Ex:

Q: What Languages does Dina speak?

A: She speaks Odia, Hindi, and Telugu

Flouting: She actually speaks French as a fourth language

Implicature: She only speaks these three languages

Maxim of Quality

• Do not say what you believe to be false

• Do not say what you lack adequate evidence for

Ex:

Q: Was it raining on Tuesday in New Jersey?

A: No, it was sunny.

Flouting: it was actually raining on Tuesday

Maxim of Relevance

Be relevant

ex:

Q: What do you want for dinner?

Flouting: I made the answers for the quiz last night.

Maxim of Manner

Avoid obscurity of expression and ambiguity

• Be clear/consise

• Be brief

• Be orderly

ex:

RJ got a green scarf as a gift and stopped complaining

Flouting: RJ’s complaints weren’t relevant to the gifted green scarf

Implicature: RJ was complaining he didn’t have a green scarf

Phonetics: Important info

1. There are three dimensions used to characterize consonants

2. There are four dimensions used to characterize vowels

3. There are complex consonants (affricated) and complex vowels (diphthongs), which are essentially two consonants or vowels put together, involving transition from one sound to the other

4. Natural class: A group of sounds is a natural class if there’s an articulatory description that picks out those and only those sounds- no more, no less

Natural class: A group of sounds is a natural class if

there’s an articulatory description that picks out those and only those sounds- no more, no less

Complex consonants (affricates) and complex vowels (diphthongs), are essentially

the two consonants or vowels put together, involving transition from one sound to the other

three dimensions used to characterize consonants

Place of articulation: where the obstruction of airflow occurs

Manner of articulation: How the obstruction of airflow occurs

Voicing: whether the vocal folds vibrate

four dimensions used to characterize vowels

Tongue height: high, mid, low

Tongue advancement: [+front, -back], [-front, -back], [-front, +back]

• in other words, front, central or back

Lip rounding: rounded or unrounded

rounded: u, o, ɔ, ʊ

unrounded: everything else

Tenseness: tense or un tensed/lax

tense vowels: i, e, o, u

lax vowels: everything else

Rounded vowels

u, o, ɔ, ʊ

unrounded: everything else

tense vowels

i, e, o, u

lax vowels: everything else