introduction to language and linguistics 006: syntax & semantics (the interface)

1 Introduction2 A Semantic Model for Language

References

Patterns in Interpretation

Interpretational RulesPSRs

{lm} {mmm}S → NP VPNP → (D) N’N’ → (Adj) NVP → V (NP)

JSK= TRUE iff JNPK ∈ JVPKJNPK = x, x∈JN′K)JN′K = JAdjK ∩ JNK

JVPK = {x: 〈x , JNPK〉∈ JV K}

ELC 231: Introduction to Language and LinguisticsSyntax & Semantics: The Syntax-Semantics Interface

Dr. Meagan Louie

M. Louie ELC 231: Language and Linguistics 1 / 98

References

1.1 REVIEW: Constituency and Phrase Structure Rules1.2 Concatenation VS Compounding1.3 REVIEW: Compositionality, Truth, Reference

Core Subdomains

Linguistics: The study of Language

Phonetics

Phonology

Morphology

Syntax

Semantics

Pragmatics

References

Core Subdomains: Last Week - Morphology and Syntax

Phonetics

Phonology

Morphology

Syntax

Semantics

Pragmatics

References

Core Subdomains: This Week - Syntax-Semantics

Phonetics

Phonology

Morphology

Syntax

Semantics

Pragmatics

References

Core Subdomains: Syntax

• Syntax: The study of phrase- and sentence-formation in language

1 The key notion of Constituency and Structure

2 Phrase Structure Rules (PSRs)

3 Productivity as a Design Feature

References

Core Subdomains: Semantics

• Semantics: The study of MEANING in language

1 Review: Meaning as Truth and reference

2 REVIEW: Compositionality

3 A Semantic Interpretation System for Language

(i) The Model/Ontology(ii) Lexical Entries(iii) Compositional Rules (i.e., how to semantically interpret PSRs)

References

Basic Syntactic Theory: Phrase Structure Rules

Q: How are sentences made?

H1: Sentences are made up of constituents

mailmen

dangerous

Constituents are formed from words withPhrase-Structure Rules (PSRs)

PSRs restrict word order

eg., English PSRsS → NP VPNP → (D) (Adj) NVP → V (NP)

References

mailmen

dangerous

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mailmen

dangerous

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About Phrase Structure Rules (PSRs)

Idea: Each language, X, has a set of PSRs:

Any sentence generated by the PSRs isgrammatical in X

Only the sentences generated by thePSRs are grammatical in X

{mm}English PSRs

S → NP (Vaux) VPNP → (D) (Adj) N

VP → V (NP)

. “The big dog has eaten the raw steak”

. D Adj N Vaux Vptc D Adj N

Q: Can the English PSRs generate a tree structure for this sentence?

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{mm}English PSRs

S → NP (Vaux) VPNP → (D) (Adj) N

VP → V (NP)

. “Le gros chien a mangé le steak cru”

. D Adj N Vaux Vptc D N Adj

Q: Can the English PSRs generate a tree structure for this sentence?

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{mmm}French PSRs

S → NP (Vaux) VPNP → (D) (Adjsize) N (Adj)

VP → V (NP)

. “Le gros chien a mangé le steak cru”

. D Adj N Vaux Vptc D N Adj

Q: Can these PSRs generate a tree structure for this sentence?

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{mmm}French PSRs

S → NP (Vaux) VPNP → (D) (Adjsize) N (Adj)

VP → V (NP)

. /ookina inu-ga sute:ki-o tabemashita/

. Adj Nnom Nacc V

Q: Can the French PSRs generate a tree structure for this sentence?

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{mm}Japanese PSRs

S → NP VPNP → (Adj) NVP → (NP) V

. /ookina inu-ga sute:ki-o tabemashita/

. Adj Nnom Nacc V

Q: Can these PSRs generate a tree structure for the sentence?

References

mailmen

dangerous

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H2: Sentences are strings of words with a flat structure

dangerousAdj

bitesV

mailmenN

Strings are formed from words withSentence-String Rules

These rules restrict word order

eg., English Sentence-String RuleS → (D) (Adj) N V (D) (Adj) (N)

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dangerousAdj

bitesV

mailmenN

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dangerousAdj

bitesV

mailmenN

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Q: Is there any INDEPENDENT evidencefor CONSTITUENTS?

H1: Hierarchically-Ordered Constituents H2: Linearly-Ordered Words

mailmen

dangerous

dangerousAdj

bitesV

slowAdj

mailmenN

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Basic Syntactic Theory: Constituents

Q: Is there independent evidence for constituents?

Q: How do you form Y/N Questions in English?

(1) English Y/N Questions 1

a. Clifford will jump over the house

b. Will Clifford will jump over the house?

H1: A rewrite rule based on linear-order1 2 3 4 5 ... → 2 1 3 4 5 ... (1) X

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a. The big red dog will jump over the house

b. *Big the big red dog will jump over the house?

H1: A rewrite rule based on linear-order1 2 3 4 5 ... → 2 1 3 4 5 ... (2) ×

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b. Will the big red dog will jump over the house?

H2: A rewrite rule based on linear-order, sensitive to lexical categoryX Y Aux1 Z W ... → Aux1 X Y Z W... (2) X

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a. The dog that Beth might1 buy will2 jump over the house

b. might1 the dog that Beth might buy will2 jump over the house?

H2: A rewrite rule based on linear-order, sensitive to lexical categoryX Y Aux1 Z W ... → Aux1 X Y Z W... (3) ×

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Independent Evidence for Constituents

(1) English Y/N Questions 1: H1 X, H2 X

(2) English Y/N Questions 2: H1 ×, H2 X

(3) English Y/N Questions 3: H1 ×, H2 ×

a. The dog that Beth might buy will jump over the house

b. Will1 the dog that Bethmight buy will jump over the house?

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Observation: The Vaux that moves appears after the first NP

(1) English Y/N Questions 1: H1 X, H2 X

a. [Clifford]NP will jump over the house

(2) English Y/N Questions 2: H1 ×, H2 X

a. [The big red dog]NP will jump over the house

(3) English Y/N Questions 3: H1 ×, H2 ×

a. [The dog that Beth might buy]NP will jump over the house

b. Will1 the dog that Bethmight buy will jump over the house?

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H3: Rewrite rule based on constituents, sensitive to lexical category[X Y ...]NP Aux1 Z W ... → Aux1 [X Y ...]NP Z W...

(3) English Y/N Questions 3: H1 ×, H2 ×, H3 X

b. Will1 the dog that Beth might buy will jump over the house?

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(2) English Y/N Questions 2: H1 ×, H2 X, H3 X

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(2) English Y/N Questions 2: H1 ×, H2 X, H3 X

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(1) English Y/N Questions 1: H1 X, H2 X, H3 X

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(1) English Y/N Questions 1: H1 X, H2 X, H3 X

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Data (1) Data (2) Data (3)H1 X × ×H2 X X ×H3 X X X

Observation: Only the hypothesis that makes reference to aconstituent (H3) can account for all of the Y/N question data

→ Y/N Q-formation provides independent evidence for constituents

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→ Y/N Q-formation provides independent evidence for constituents

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→ Passive-formation also requires a constituent-sensitive rule

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→ Using “and” and “or” also provide evidence for constituents

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Q: What strings of words can be conjoined with “and”?

(4) a. Elizabeth bought a puppy.

b. . [Elizabeth and her mother] bought a puppy.

c. Elizabeth [bought a puppy and read a book]

d. *Elizabeth [bought a and hugged the] puppy

Idea: Only matching constituents can be conjoined with “and”

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Q: What strings of words can be conjoined with “or”?

b. . [Elizabeth or her mother] bought a puppy.

c. Elizabeth [bought a puppy or read a book]

d. *Elizabeth [bought a or hugged the] puppy

Idea: Only matching constituents can be conjoined with “or”

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Hypothesis: Only matching constituents can be conjoined

→ Conjunction (use of “and/or”) isindependent evidence for constituents

We can also use conjunction as a diagnosticfor whether a string of words is a constituent

i.e., if a string of lexical categories A B C can be conjoined with“and/or,” that provides evidence that A B C is a constituent

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Constituency Tests: Conjunction Test

Assumption: Only matching constituents can be conjoined

(6) a. Hermione bought the orange cat

b. Hermione bought the [orange cat and expensive book]

c. Hermione bought the [orange cat or expensive book]

Our current PSR NP → (D) (Adj) N doesn’t account for this data!

Should we propose a new type of constituent [Adj N]N’?

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Revised PSRs: Evidence for N’

b. Hermione bought the [orange cat and/or expensive book]

orange

expensive

orange

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b. Hermione bought the [orange cat and/or expensive book]

orange

expensive

orange

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1 NP → (D) N’

2 N’ → (Adj) N

3 X → X conj X (Conjunction Rule)

orange

expensive

orange

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There independent evidence for constituents

→ There are also systematic patterns in meaning/interpretation...

→ These patterns only be described with rulesthat make reference to constituents

(i.e., there is semantic, as well as syntacticevidence for constituents)

References

Review: Types of Word-Formation

1 ConcatenationCombining morphemes together to form new words

- eg., un-believe-abil-ity (predictable/compositional meaning)

2 Neologism/CoinageCombining phonemes together to form new morphemes

- eg., bikini (French coinage) (arbitrary meaning)3 Compounding

Combining entire words together to form new words- eg., binge-watch (non-arbitrary but unpredictable meaning)

4 BlendingCombining parts of words together to form new words

- eg., mansplain (non-arbitrary but unpredictable meaning)5 etc....

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- eg., un-believe-abil-ity (predictable/compositional meaning)2 Neologism/Coinage

Combining phonemes together to form new morphemes- eg., bikini (French coinage) (arbitrary meaning)

3 CompoundingCombining entire words together to form new words

- eg., binge-watch (non-arbitrary but unpredictable meaning)4 Blending

Combining parts of words together to form new words- eg., mansplain (non-arbitrary but unpredictable meaning)

5 etc....

References

- eg., un-believe-abil-ity (predictable/compositional meaning)2 Neologism/Coinage

Combining phonemes together to form new morphemes- eg., bikini (French coinage) (arbitrary meaning)

3 CompoundingCombining entire words together to form new words

- eg., binge-watch (non-arbitrary but unpredictable meaning)4 Blending

Combining parts of words together to form new words- eg., mansplain (non-arbitrary but unpredictable meaning)

5 etc....M. Louie ELC 231: Language and Linguistics 38 / 98

References

Patterns in Interpretation: Systematic VS Non-Systematic

ConcatenationCombining morphemes together to form new words

CompoundingCombining entire words together to form new words

- eg., binge-watch (non-arbitrary but unpredictable meaning)

Q: What’s the difference?

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Q: What’s the difference?

References

The difference is systematicity

un-believe-abil-ity (predictable/compositional meaning)

binge-watch (non-arbitrary but unpredictable meaning)

The meaning of a word formed by concatenation is systematic

A systematic rule can describe how the meaning of the partscombine to form a new meaning

i.e., even if you’ve never heard the word before, as long as you knowwhat the PARTS mean, you’ll know what the new word means

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The systematicity of concatenation

[N-ish]Adj Concatenation

(8) clown clownish “Having properties of a clown”snob snobbish “Having properties of a snob”freak freakish “Having properties of a freak”nightmare nightmarish “Having properties of a nightmare”hawk hawkish “Having properties of a hawk”wolf wolfish ?

Systematic Semantic Rule:[N-ish]Adj means “having properties of a N”

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The systematicity of concatenation

[N-ish]Adj Concatenation

(8) clown clownish “Having properties of a clown”snob snobbish “Having properties of a snob”freak freakish “Having properties of a freak”nightmare nightmarish “Having properties of a nightmare”hawk hawkish “Having properties of a hawk”wolf wolfish ?

Systematic Semantic Rule:[N-ish]Adj means “having properties of a N”

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The meaning of a word formed by compounding is not systematic

We can’t use a systematic rule to explain how the meaning of theword is derived from its parts

i.e., If you’ve never heard the word before, you might guess wrongabout what it means

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The non-systematicity of compounding

[N+N]N Compounds

(9) street streetcar “A car that runs on tracks on in the streets”clown clowncar “A car that contains lots of clowns”soapbox soapbox car “A small car made out of a soapbox”bait bait car “A car used by police as bait for car thieves”cable cable car “A car suspended by cables”

NO Systematic Semantic Rule:[N-car]N means “A car that is located on N”[N-car]N means “A car that contains a lot of N”[N-car]N means “A car that is made out of N”[N-car]N means “A car that is used as N”...

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The non-systematicity of compounding

[N+N]N Compounds

(9) street streetcar “A car that runs on tracks on in the streets”clown clowncar “A car that contains lots of clowns”soapbox soapbox car “A small car made out of a soapbox”bait bait car “A car used by police as bait for car thieves”cable cable car “A car suspended by cables”

NO Systematic Semantic Rule:[N-car]N means “A car that is located on N”[N-car]N means “A car that contains a lot of N”[N-car]N means “A car that is made out of N”[N-car]N means “A car that is used as N”...

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Q: Concatenation or compounding?i.e., systematic or non-systematic meaning change?

/ri:anM/ เรียน “study” /nakHri:anM/ นักเรียน “student”/khitH/ คิด “think” /nakHkhitM/ นักคิด “thinker”/s0:pL/ สืบ ”investigate” /nakHs0:pL/ นักสืบ “detective”/binM/ บิน “fly” /nakHbinM/ นักบิน “pilot”/rO:NH/ นักร้อง “sing” /nakHrO:NH/ นักร้อง “singer”

→Can you formulate a systematic rule?

References

Q: Concatenation or compounding?i.e., systematic or non-systematic meaning change?

/laajM/ ลาย “striped” /laajMtaaM/ ลายตา “be dazzling”/klajM/ ไกล ”far” /klaiMtaaM/ ไกลตา “out of sight”/naaR/ หนา “thick” /naaRtaaM/ หนาตา “dense/crammed”/loNR/ หลง ”lost” /loNRtaaM/ หลงตา “overlooked”/titH/ ติด ”stuck” /titLtaaM/ ติดตา “fresh in one’s memory”

→Can you formulate a systematic rule?

References

Q: What about when we combine wordssyntactically (as opposed to morphologically)?

Is the meaning fully compositional?

References

The Principle of Compositionality

Gottlob Frege (1848-1925)

The Principle of Compositionality“...meaning of a complex expression is

a function of the meaning of its parts

and the way those parts are combined.”

The meaning of a complex phrase or sentenceis based on

(i) the meaning of its parts and

(ii) the way that the parts are combined(e.g., which PSRs are used)

References

The Principle of Compositionality

Gottlob Frege (1848-1925)

The Principle of Compositionality“...meaning of a complex expression is

a function of the meaning of its parts

and the way those parts are combined.”

The meaning of a complex phrase or sentenceis derived from

(i) the meaning of its parts and

(ii) the way that the parts are combined(e.g., which PSRs are used)

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Semantic Interpretation Rules for PSRs

→ Before we can talk about interpretation rules for phrases...Q: What are the basic building blocks of MEANING?

i.e., how can we formalize the meaning of words?

REVIEW: What is Meaning?

The meaning of a sentence is its truth-conditions -i.e., what the world would have to look like, in order for it to be true

The meaning of a WORD or PHRASE is its reference -i.e., what it refers to

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Q: What do you KNOW......when you know what something MEANS?

The meaning of a SENTENCE is its truth-conditions - i.e., underwhat conditions the sentence is true

(10) Seriemas are a kind of bird

If I tell you one of these are a Seriema, and you know what (10)means, then you know in which case (10) would be true

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The meaning of a WORD is its reference - i.e., what it refers to

eg., A word like...

[dAg] “dog” refers to the set of objects that we consider dogs

If you know what “dog” means,then you know how to categorize objects as dog VS non-dog

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eg., A word like...

[ôEd] “red” refers to the set of objects that we consider red

If you know what “red” means,then you know how to categorize objects as red VS non-red

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If you know what “endemic” means, then you know how tocategorize 〈object, place〉 pairs as endemic VS non-endemic

A 〈bermuda petrels,Bermuda〉B 〈glacier bears, southeast Alaska〉C 〈elephants,Asia〉

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2.1 The Ontology2.2 Lexical Entries2.3 Compositional Rules

Q: What are the basic building blocks of MEANING?

1 Truth-Values: True (T) and False (F)

2 Things that words/phrases can refer to:(i) Objects/Individuals: a, b, c, d

eg., “Bao-Bao”=a, “Taz”= d, ...

(ii) Sets of Objects/Individuals: {a, b}, {a, b, c}, {a, c} ...eg., “animal” = {a, b, c, d}, “dog”= {b, c}, “caniformia”={a,b,c}

(iii) Pairs of Objects/Individuals: 〈a,b〉, 〈b,a〉, 〈a,c〉...eg., “is the same species as” = {〈b,c〉, 〈c,b〉}

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2 Things that words/phrases can refer to:

(i) Objects/Individuals: a, b, c, deg., “Bao-Bao”=a, “Taz”= d, ...

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Q: What’s the difference between {} and 〈〉?

These things, {}, are set bracketsA set is defined by its members (the elements inside the brackets)the order of elements in a set don’t matteri.e., {a, b, c, d} = {a, c, d, b} = {a, d, c, b} etc.

These things, 〈〉, are angled tuple bracketsAn n-tuple is defined by its members......and the order of the membersi.e., 〈a, b〉 6= 〈b, a〉(A ‘pair’ is the name of an n-tuple where n=2)

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These things, {}, are set brackets

A set is defined by its members (the elements inside the brackets)the order of elements in a set don’t matteri.e., {a, b, c, d} = {a, c, d, b} = {a, d, c, b} etc.

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These things, 〈〉, are angled tuple brackets

An n-tuple is defined by its members......and the order of the membersi.e., 〈a, b〉 6= 〈b, a〉(A ‘pair’ is the name of an n-tuple where n=2)

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The difference between sets and tuples is importanti.e., to describe natural language meaning, we need

something like ordering

Consider a word like “love”

If you know what a word like “love” means,then you know how to categorize〈a,b〉 pairs into(i) pairs where a loves b, and(ii) pairs where a doesn’t love b

It’s important that 〈a,b〉 6= 〈b,a〉!

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If you know what a word like “love” means,then you know how to categorize〈a,b〉 pairs into

(i) pairs where a loves b, and(ii) pairs where a doesn’t love b

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If you know what a word like “love” means,then you know how to categorize〈a,b〉 pairs into(i) pairs where a loves b, and

(ii) pairs where a doesn’t love b

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Describing unrequited love requires ordered pairs

“Echo and Narcissus” (1903) by John William Waterhouse〈e, n〉, 〈n,n〉〈n,e〉, 〈e,e〉

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Describing unrequited love requires ordered pairs

Young Lily Evans, James Potter and Severus Snape from “Harry Potter and the The Deathly Hallows” (Part 2)

〈s,l〉, 〈l,j〉, 〈j,l〉〈s,j〉, 〈j,s〉, 〈l,s〉

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Basic Semantic Elements: The Ontology

The semantic elements are called the ontology

1 Truth-Values: T, F

2 Individuals:a = Harry Potter,b = Hermione Granger,c = Ron Weasley,d = Draco Malfoy,e = Buckbeak the Hippogrifff = Luna Lovegood,...

3 Operations: Set-formation {}, pair/tuple-formation 〈〉

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The LEXICON: The Repository of MORPHEMES

REVIEW: Definition of a MORPHEME

A morpheme is the smallest unit of language that has/containsmeaning - i.e., it is a systematic 〈form,meaning , category〉 mapping

Now that we have established some basic building blocks of meaning(i.e., an ontology)...

... we can formalize the meaning of various kinds of lexicalcategories as referring to elements in the ontology

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The Lexical Entries of Lexical CategoriesSemantic Ontology

2 Individuals:a = Harryb = Hermionec = Rond = Dracoe = Buckbeakf = Lunag = Ginnyh = Hedwigi = Hagridq = quidditch

3 Operations: {}, 〈〉

Lexical Entries for

PROPER NOUNSrefer to individuals

eg., JHarryK = a

These things, JK, aredenotation brackets

JHarryK is basically a shorthand way ofwriting “the meaning of Harry ”

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Lexical Entries for

eg., JHarryK = a

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Lexical Entries for

eg., JHarryK = a

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Lexical Entries for

eg., JHarryK = a

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Lexical Entries for

COMMON NOUNSrefer to sets of individuals

eg., JgirlK = {b, f, g}

BASIC ADJECTIVESrefer to sets of individuals

eg., JtallK = {c, i}

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Lexical Entries for

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Lexical Entries for

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Exercise

(1) What set does wizardN refer to?

(2) What set does animalN refer to?

(3) What set does GryffindorAdj refer to?

(4) What set does blondAdj refer to?

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Lexical Entries for

INTRANSITIVE VERBS(verbs that involve a single individual)

refer to sets of individuals

eg., JfliesK = {e, h}

Unless you count flying via broomsticks,magical motorcycles and airplanes, inwhich case

JfliesK = {a, b, c, d, e, f, g, h, i}

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Lexical Entries for

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Lexical Entries for

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Lexical Entries for

TRANSITIVE VERBS(verbs that involve two individuals)

refer to sets of pairs of individuals

eg., JlovesK = {〈a,q〉, 〈a,h〉, 〈a,g〉,〈b, c〉, 〈c, b〉, 〈c, q〉, 〈g,a〉, 〈g,q〉,〈i.e〉, ...}

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Lexical Entries for

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Lexical Entries for

eg., JlovesK = {〈a,q〉, 〈a,h〉, 〈a,g〉,〈b, c〉, 〈c, b〉, 〈c, q〉, vg,a, 〈g,q〉,〈i.e〉, ...}

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Lexical Entries for

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Lexical Entries for

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Exercise

(1) What set does studiesV refer to?

(2) What set does feedsV refer to?

(3) What set does marriesV refer to?

(4) What set does playsV refer to?

References

Semantic Evidence for PhrasesSemantic Ontology

Observation: Particular lexical categoriesare systematic in terms of what they refer to

What about higher constituents?

{a, c, d}

pureblood

{c, d, f, g}

References

{a, c, d}

pureblood

{c, d, f, g}

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Q: If pureblood refers to {c, d, f, g} andboy refers to {a, c, d}...

... what would pureblood boy refer to?

{a, c, d}

pureblood

{c, d, f, g}

References

If pureblood refers to {c, d, f, g} and boyrefers to {a, c, d}...

...N’ pureblood boy refers to {c, d}

{a, c, d}

pureblood

{c, d, f, g}

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Q: If large refers to {e, i} and animal refersto {e, h}...

... what would large animal refer to?

animal

{e, h}

{e, i}

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If large refers to {e, i} and animal refers to{e, h}...

... N’ large animal refers to {e}

animal

{e, h}

{e, i}

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Q: If gryffindor refers to {a, b, c, g} andgirl refers to {b, f, g}...

... what would gryffindor girl refer to?

{b, f, g}

gryffindor

{a, b, c, g}

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Observation: Constituents are systematicin terms of what they refer to

N’, like Adj and N,refers to sets of individuals

→ the set with members that belongto both Adj and N

JN ′K = JAdjK ∩ JNK

References

Observation: Constituents are systematicin terms of what they refer to

N’, like Adj and N,refers to sets of individuals

→ the set with members that belongto both Adj and N

JN ′K = JAdjK ∩ JNK

References

Semantic Composition Rule: JN ′K = JAdjK ∩ JNK

c, g g, b, f

red-haired girl

c g b, f

The set denoted by red-haired girl

JN ′K = JAdjK ∩ JNK is acompositional rule(call it modification)

This rule describes howwe interpret the PSRN’ → (Adj) N

References

N’ {g}

N {g, b, f}

Adj {c, g}

red-haired

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N’ {g}

N {g, b, f}

Adj {c, g}

red-haired

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What about higher constituents?NP ?

N’ {b, g}

N {g, b, f}

Adj {a, b, c, g}

gryffindor

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N’ {d}

slytherin

Adj {d, f}

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N’ {e}

N {e, h}

animal

Adj {e, i}

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Intuition: The NP the red-haired girl refersto the same thing as the name Ginny

- i.e., g

N’ {g}

N {g, b, f}

Adj {c, g}

red-haired

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Intuition: The NP that blond slytherinrefers to the same thing as the name Draco

- i.e., d

N’ {d}

slytherin

Adj {d, f}

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Intuition: The NP the large animal refersto the same thing as the name Buckbeak

- i.e., e

N’ {e}

N {e, h}

animal

Adj {e, i}

References

Q: What’s the systematicinterpretation for NP → D N’ ?

(a) When JN ′K = {g}, JNPK = g(b) When JN ′K = {d}, JNPK = d(c) When JN ′K = {e}, JNPK = e

The NP refers to an individual

→ The/an individual member of the setthat N’ refers to1

JNPK = x, x∈JN ′K1An over-simplification, but don’t worry about the details!

References

(a) When JN ′K = {g}, JNPK = g

(b) When JN ′K = {d}, JNPK = d(c) When JN ′K = {e}, JNPK = e

References

(a) When JN ′K = {g}, JNPK = g(b) When JN ′K = {d}, JNPK = d

(c) When JN ′K = {e}, JNPK = e

References

Semantic Composition Rule: JNPK = x, x∈JN ′K

c g b, f

The set denoted by red-haired girl

The individual denoted by the red-haired girl

JNPK = x, x∈JN ′K is acompositional rule(call it selection)

This rule describes howwe interpret the PSRNP → D N

References

Semantic Composition Rules

Semantic Interpretation/Composition Rules

1. Modification:JN ′K = JAdjK∩ JNK N’ → (Adj) NN’ refers to the set with members in both JAdjK and JNK

2. Selection:JNPK = x, x∈JN ′K NP → D N’NP refers to an/the individual in JN ′K

3. Predication:JSK = T iff, JNPK∈ JVPK S → NP VPNP is true if and only if the individual JNPK is in JVPK

References

Compositional Rules: Interpreting PSRsSemantic Ontology

Consider sentences like

Hedwig

studies

Hermione

Are these sentences true?

JfliesK = {e, h}JstudiesK = {b, f}

References

Consider sentences like

Hermione

studies

Hedwig

What about these sentences?

References

True sentences:

Hedwig

studies

Hermione

Observation: h ∈ JfliesK

References

True sentences:

Hedwig

studies

Hermione

Observation: b ∈ JstudiesK

References

False sentences

Hermione

studies

Hedwig

Observation: b /∈ JfliesK

References

False sentences

Hermione

studies

Hedwig

Observation: h /∈ JstudiesK

References

Semantic Composition Rule: JSK=T iff JNPK∈JVPK

a, c, d, g

The set denoted by plays quidditch

The individual denoted by the red-haired girl

g∈{a, c, d, g}

∴ “The red-haired girl plays quidditch” is T

JSK=T iff JNPK∈JVPKis acompositional rule(call it predication)

This rule describes howwe interpret the PSRS → NP VP

References

Semantic Composition Rule: JSK=T iff JNPK∈JVPK

a, c, d, g

The set denoted by plays quidditch

The individual denoted by the curly-haired girl

b/∈{a, c, d, g}

∴ “The curly-haired girl plays quidditch” is F

JSK=T iff JNPK∈JVPKis acompositional rule(call it predication)

This rule describes howwe interpret the PSRS → NP VP

References

Summary:PSRs are systematic rules about combining words to formphrases/sentences

Evidence for PSRs includes(1) Sentence transformation rules

(i.e., Y/N question-formation, passives)(2) Systematic interpretations for PSRs

(i.e., semantic compositional rules)

These interpretation rules can be mathematically formalized in termsof set membership (∈, /∈) or set intersection (∩)

References

Evidence for PSRs includes

(1) Sentence transformation rules(i.e., Y/N question-formation, passives)

(2) Systematic interpretations for PSRs(i.e., semantic compositional rules)

References

(i.e., Y/N question-formation, passives)

(2) Systematic interpretations for PSRs(i.e., semantic compositional rules)

References

Next Time: Semantics and PragmaticsMeaning as TRUTH VS Meaning as USE

1 Homework: A005 - Semantics and Pragmatics

2 Instagram Homework: Semantic Minimal Pair AND/ORFind and post an example (or non-example) of a Design Feature

DiscretenessSemanticityArbitrarinessProductivity

References

References I

Heim, Irene & Angelika Kratzer. 1998. Semantics in generative grammarBlackwell Textbooks in Linguistics. Blackwell Oxford.

Montague, Richard. 1973. The Proper Treatment of Quantification in OrdinaryEnglish. Formal Semantics 17–34.

Partee, Barbara, Alice Ter Meulen & Robert Wall. 1990. MathematicalMethods in Linguistics, vol. 30 Studies in Linguistics and Philosophy. KluwerAcademic Publishers.

introduction to language and linguistics 006: syntax & semantics (the interface)

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