Semantics Why does a sentence mean what it means?

Semantics

• Why does a sentence mean what it means?

• What are the meanings of words and how do they come together to make larger meanings (i.e. phrases, sentences)?

• Perhaps the only level of linguistic description actually needed for there to be language…?

Overview

• Machine Translation

• Quantifier Scope Ambiguity

• Negative Polarity Items

• Object Language vs Meta Language

• Compositionality

• Idioms

• Presupposition

• Formal Semantics (Propositional Logic, etc.)

• …….

Machine Translation

• Can we make a computer program to translate text between languages automatically?

MT: Morphological Analysis

• Direct word-to-word mapping

• Billy eats the cake quickly.

• Billy come la torta rápidamente.

• (Spanish)

MT: Morphological Analysis

• Word-to-word mapping doesn’t work well.

• Billy ate the cake quickly.

• Billy keki çabukça yedi.

• (Turkish (I hope))

MT: Morphological Analysis

• Word-to-word mapping doesn’t work well.

• What did Billy eat quickly?

• Billy neyi çabukça yedi?

• (Turkish (I hope))

MT: Morphological Analysis

• Word-to-word mapping doesn’t work well.

• Wawirri kapi-rna panti-rni yalumpu.

• “Kangaroo will-I spear that.” .

• I will spear that kangaroo.

• (Warlpiri, from Hale (1983) via Legate (2002)).

MT: Syntactic Analysis

• Tree-to-tree mapping:

MT: The Pyramid

MT: Syntactic Analysis

• Even syntactic MT runs into trouble.

• Let’s take a brief trip into quantifier scope ambiguity…

Quantifier Scope Ambiguity

• Two students met with every teacher.

• (Syntactically unambiguous.)

• Semantically ambiguous.

• Two particular students each met all of the teachers.
• Each teacher was visited by two students, but possibly different students meeting with each.

Quantifier Scope Ambiguity

• 1 2

Quantifier Scope & MT

• Unfortunately, not all languages have the same quantifier scope ambiguities.

• Proper translation requires recognition (& maybe resolution) of ambiguity, and then selection of appropriate form in the target language.

Quantifier Scope & MT

• English: Everyone loves someone.

• Ambiguous.

• Japanese: Daremo-ga dareka-o aisite-iru.

• everyone-NOM someone-ACC love
• Unambiguous. “Everyone loves someone or other.”
• Using this translation would be wrong unless the computer has resolved the ambiguity, i.e. if it knows what the speaker intended.

• Japanese: Dareka-o daremo-ga aisite-iru.

• Ambiguous.
• Close to English “Someone, everyone loves.”
• A (potentially) awkward translation if the other one would work.
• (source: Kuno, Takami, and Wu 1999)

MT: Semantic Analysis

• The holy grail of MT.

• Obviously a computer cannot truly understand anything, but it has to have a symbolic representation of the meaning.

• Translate the input sentence into the ‘interlingua’ which represents the full original meaning.
• Translate ‘interlingua’ into the target language.

Other Practical Applications

• Question-Answering

• Automated Summarization

• Existing solutions don’t use any sophisticated syntax or semantics.

• Because when they try…

Negative Polarity Items

• NPIs are words that seem to only be allowed in negative contexts.

• I did not see anything/any books at the store.
• I didn’t get paid a red cent for my trouble.
• I have not ever been to Mexico.
• I don’t give a damn about the homework.
• * I saw any book at the store.
• * I got paid a red cent for my trouble.
• * I have ever been to Mexico.
• * I give a damn about the homework.

Negative Polarity Items

• What constituents a negative context?

• I didn’t see anyone at the store.
• I never see anyone at the store.
• I rarely see anyone at the store.
• * I saw anyone at the store.
• * I always see anyone at the store.
• * I sometimes see anyone at the store.

Negative Polarity Items

• But there are other licensing contexts too:

• If I see anyone at the store after hours . . .
• Students who bought anything from the bookstore . . .

• What do these have in common?

• Negation
• The antecedent of a conditional
• Relative clauses

Negative Polarity Items

• This is an upward-entailing context:

• I saw something in the fishbowl.

• I saw a fish in the fishbowl.

• I saw a goldfish in the fishbowl.

Negative Polarity Items

• This is a downward-entailing context:

• I didn’t see a thing in the fishbowl.

• I didn’t see a fish in the fishbowl.

• I didn’t see a goldfish in the fishbowl.

Negative Polarity Items

• If I find a fish in the fishbowl, I will feed it.

• Is fish in an upward-entailing or downward-entailing context?

Negative Polarity Items

• If I find a fish in the fishbowl, I will feed it.

• Situation Feed it?

• I found a worm (an animal). NO

• I found a goldfish. YES

• So the conditional above entails:

• If I find a goldfish in the fishbowl, I will feed it

• Goldfish is more specific.

• It is downward entailing.

Negative Polarity Items

• Students who bought a book will get a rebate.

• Situation Rebate?

• I bought merchandise. NO

• I bought a textbook. YES

• This is also downward-entailing.

Negative Polarity Items

• If Clinton wins in ’08, some politicians will be happy.

• Clinton wins. Let’s see who is happy.

• Group Happy?

• some people YES

• Republicans NO

• This is upward entailing.

• The antecedent of a conditional is downward-entailing, but the consequent is upward-entailing.

Negative Polarity Items

• Licit only in downward-entailing contexts.

• Where replacement with a more specific term yields a sentence entailed by the original.

• NPIs also have a syntactic requirement.

• “c-command” under the standard generative model of sentence structure

• There are also positive-polarity items.

Object vs. Meta Language

• When describing meaning, it doesn’t help to use the words we’re trying to define.

• The quick brown fox jumped.

• What does this mean?
• It doesn’t help to just repeat the sentence.
• We need a controlled vocabulary that we can agree on to describe language.

Object vs. Meta Language

• I will use italics for utterances of English, our object language.

• The quick brown fox jumped.

• I will use CAPITALS for the meta-language, the language to talk about language.

Object vs. Meta Language

• deep blue oceans

• What does this mean? I think it means things that are…

• OCEANS
• AND DEEP
• AND BLUE

• Reduction of meaning into smaller pieces:

• AND , OCEANS , DEEP , BLUE

Object vs. Meta Language

• We can’t possibly list the meaning of every phrase. (Is there a longest phrase?)

• But we can list the meaning of every word.

• “oceans” “deep” “blue”

• And we can add a little bit of glue and some rules for putting the meanings together.

Object vs. Meta Language

• deep blue oceans

• ADJ ADJ …. N

• The meaning 〚…〛 of a noun phrase of the form above is the conjunction of the meaning of its parts.

• 〚ADJ1 ADJ2 ADJ3 . . . N〛 = things that are〚ADJ1〛 AND〚ADJ2〛AND 〚ADJ3〛AND〚N〛

Compositionality

• The meaning of a constituent is determined by

• The meaning of its parts
• The way the parts are put together
• (And nothing else.)

• It seems obvious, but there are some complications.

Compositionality Complications: Idioms

• Idioms

• Phrases that defy compositionality
• Meaning of the whole must be listed lexically

• a red cent (‘nothing’)

• give a damn (‘care’)

• kick the bucket (‘die’)

• sleeping with the fishes (‘killed’)

• the cat has got your tongue (‘speechless’)

Compositionality Complications: Idioms

• Are they just multi-word words?

• Idioms differ in their rigidity...

Compositionality Complications: Idioms

• In most idioms, one cannot replace any words and retain the idiomatic meaning:

• a red cent / *penny / *coin
• *punch/*tap the bucket

• But some have replaceable parts:

• the cat got my/your/the teacher’s tongue

Compositionality Complications: Idioms

• Some but not all idioms can be syntactically shuffled around (here, passivized):

• Keep tabs on Henry. (‘track his whereabouts’)
• Tabs were kept on Henry for three days.
• Don’t spill the beans. (‘don’t give up the secret’)
• The beans were spilled already.
• * The bucket was kicked by the old man.
• * His tongue has been gotten by the cat.

Compositionality Complications: Idioms

• This suggests idioms have internal syntactic structure, but perhaps no internal semantic structure.

Compositionality Complications: Idioms

• This suggests idioms have internal syntactic structure, but perhaps no internal semantic structure.

Compositionality Complications: Non-Intersective Adjectives

• We previously saw ‘intersective’ adjectives:

• A hungry alligator is something that is both hungry and an alligator.
• Something that is a hungry alligator comes from the intersection of the set of hungry things and the set of alligators.
• 〚ADJ N〛= 〚ADJ〛∩ 〚N〛

Compositionality Complications: Non-Intersective Adjectives

• There are also non-intersective adjectives:

• a good plumber is not someone who is both good (in general) and a plumber. He only has to be good at plumbing.
• a proud father is not necessarily a proud person
• 〚ADJ N〛= 〚ADJ〛∩ 〚N〛
• At least a good plumber is a plumber and a proud father is a father. These are called ‘subsective’ because it still finds a subset.
• 〚ADJ N〛⊆ 〚N〛

Compositionality Complications: Non-Intersective Adjectives

• Then there are non-intersective, non-subsective adjectives:

• a former student is not even a student (let alone ‘former’, cf. ‘blue’)
• The whale is blue.
• *John is former.
• an alleged criminal is not (by necessity) a criminal.
• counterfeit money is not money (arguably, but certainly not the way we usually use money).

Compositionality Complications: Non-Intersective Adjectives

• How to reconcile non-intersective adjectives with compositionality?

• If 〚former student〛≠ 〚former〛∩ 〚student〛 then we have to give up either:

• Compositionality
• Intersection ∩

Brief Interlude: Functions

Brief Interlude: Functions

Brief Interlude: Functions

• Notation:

• SQRT(100) = 10
• FORMER(〚student〛) = 〚former student〛 =〚former〛(〚student〛)

Compositionality Complications: Non-Intersective Adjectives

• By treating the meaning of former as a function from one notion to another, we can have a compositional account of former X.

• For non-intersective adjectives:

• 〚ADJ N〛= 〚ADJ〛(〚N〛)
• Treat the meaning of ADJ as a function and apply it to the meaning of N.

Compositionality

• Meanings can be compositional in two ways:

• By conjunction/intersection: 〚X Y〛= things that are both〚X〛and〚Y〛 〚X Y〛= 〚X〛∩〚Y〛
• By function-application: 〚X Y〛= 〚X〛(〚Y〛)

Presupposition

• A man sat in the witness chair awaiting the next question from the attorney….

• When did you stop beating your wife?

• The jury gasps, but the man is simply confused. He responds:

• But I never beat my wife!

Presupposition

• The King of France is bald.

• Huh?

• It’s not false, per se. It’s just weird.

Presupposition

• Compare:

• I don’t think that the Earth is flat.

• (a true statement)

• I don’t know that the Earth is flat.

• (presupposition failure)

Presupposition

• If an utterance has a presupposition π, then π must be true in order for the utterance to be ‘OK’.

• Further, π must be established as common ground in the discourse.

• (Unless the presupposition is ‘accommodated’.)

Presupposition

• The hallmark of presupposition is that it remains despite negation.

• Thus we can separate an utterance into two parts:

• the assertion, which is affected by negation
• the presupposition, which is not

Presuppositions Under Negation

• I think the Earth is flat.

• Assertion: I believe the Earth is flat.
• Presupposition: None
• Sentence is false (i.e. a lie), but otherwise OK.

• I know the Earth is flat.

• Assertion: I believe the Earth is flat.
• Presupposition: The Earth is flat.
• Presupposition is not true, therefore sentence is weird.

Presuppositions Under Negation

• I didn’t think the Earth is flat.

• Assertion: I didn’t believe the Earth is flat.
• Presupposition: None
• Sentence is true.

• I didn’t know the Earth is flat.

• Assertion: I didn’t believe the Earth is flat.
• Presupposition: The Earth is flat.
• Presupposition is still not true, therefore sentence is still weird.

Presupposition Triggers

• definite descriptions (‘the King of France’)

• π = ‘there is a King of France’

• quantificational NPs (‘every cat I own’)

• π = ‘I own at least one cat’

• factive verbs (‘regret’, ‘know’, ‘discover’)

• π = the proposition regretted/known/discovered

• aspectual verbs/adverbs (‘stop’, ‘still’)

• π = the action was happening previously

• questions (‘who stole the cookies?’)

• π = ‘someone stole the cookies’

Presupposition Projection

• Presuppositions can ‘project’ or percolate up recursively embedded sentences.

• I think [John knows [the Earth is flat.]]

• If [John knows the Earth is flat] then . . .

• Even though ‘think’/‘if’ are not a p-triggers, ‘know’ is, and its presupposition passes through ‘think’/‘if’.

Presupposition Filters

• On the other hand, presuppositions can be blocked.

• If the Earth is flat, then a good scientist probably would know the Earth is flat.

• There is no presupposition here.

• If π, a presupposition of the consequent, is asserted in the antecedent, it is not a presupposition of the whole sentence.

Presupposition Filters

• If France had a King, the King of France would be a very powerful man.

Presupposition Accommodation

• Usually presuppositions have to be established:

• A man off the street walks up to you and says:
• I regret that I didn’t buy the tomato.

• You say: “Oh. You were going to buy a tomato?”

• The presupposition was not a part of the common ground.

Presupposition Accommodation

• But sometimes we accept sentences with presuppositions not already established:

• If the North Korean ambassador turned up, then it is amazing that both the North and South Korean ambassadors are here.

• (Beaver 2002)

• π = the S.K. ambassador is here

• π is ‘accommodated’

Formal Semantics

• Not just what things mean,

• but representing meaning & composition in precise logical terms

• Hashing out the meta language.

Propositional Logic

• Mathematical representation of meaning.

• Symbols like p, q stand in for propositions about what is true in the world. Propositions can be either true or false.

• Let p = ‘It is raining.’

• p is true iif it is raining.

• If p is true, it must be raining.
• If it is raining, p must be true.

Propositional Logic: Connectives

• Propositions can be combined into formulas using special connectives:

• and: ∧
• or: ∨
• not: ￢
• if: → (aka implies, conditional)
• iif: ↔ (aka if and only if, biconditional)

Propositional Logic: Connectives

• Let p = ‘It is raining.’

• Let q = ‘It is snowing.’

• Let r = ‘I will play outside.’

• (p ∨ q) → ￢ r

• ‘If it is raining or snowing, then I will not play outside.’

Predicate Logic

• Predicate logic adds names and predicates on top of propositional logic.

• KNOWS(JOHN, MARY)

• Let KNOWS be the predicate that is true just when the first argument knows the second argument.

Predicate Logic: Examples

• If John meets Mary, then he will know her.

• MEETS(JOHN, MARY) → KNOWS(JOHN, MARY)

Predicate Logic: Examples

• On days without a cloud in the sky,

• whenever my dog Sparky barks, and only when he barks, I take him for a walk.

• ￢CLOUDY → [BARKS(SPARKY) ↔ WALK(ME, SPARKY)]

Predicate Logic & Natl. Language

• 〚John〛= JOHN

• 〚Mary〛= MARY

• 〚knows〛= KNOWS( … , … )

• 〚John knows Mary〛= some combination of 〚John〛〚Mary〛and 〚knows〛with either conjunction/intersection or function application

Predicate Logic & Compositionality

• Formal semantics starts where generative syntax ends.

Predicate Logic & Compositionality

• Syntax Semantics

• S → NP1 V NP2 〚S〛=〚V〛(〚NP1〛,〚NP2〛)

• S → John knows Mary 〚S〛=〚knows〛(〚John〛,〚Mary〛)

• S → John knows Mary 〚S〛= KNOWS(JOHN, MARY)

Predicate Logic & Compositionality

• Syntax Semantics

• CP → if S1 then S2 〚CP〛=〚S1〛 → 〚S2〛

• (roughly)