Semantics

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Semantics
and some syntax, math, and computational
linguistics too
LING 001 - October 16, 2006 Joshua Tauberer
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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?

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Overview

• Machine Translation
• Quantifier Scope Ambiguity
• Negative Polarity Items
• Object Language vs Meta Language
• Compositionality
• Idioms
• Presupposition
• Formal Semantics (Propositional Logic, etc.)
• .

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Machine Translation

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

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MT Morphological Analysis

• Direct word-to-word mapping
• Billy eats the cake quickly.
• Billy come la torta rápidamente.
• (Spanish)

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MT Morphological Analysis

• Word-to-word mapping doesnt work well.
• Billy ate the cake quickly.
• Billy keki çabukça yedi.
• (Turkish (I hope))

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MT Morphological Analysis

• Word-to-word mapping doesnt work well.
• What did Billy eat quickly?
• Billy neyi çabukça yedi?
• (Turkish (I hope))

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MT Morphological Analysis

• Word-to-word mapping doesnt 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)).

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MT Syntactic Analysis

• Tree-to-tree mapping

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MT The Pyramid
Interlingua
tree-to-tree translation
SyntacticStructure
SyntacticStructure
actual MT systems today
word-to-word translation
Morphological Structure
Morphological Structure
Input Language
Output Language
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MT Syntactic Analysis

• Even syntactic MT runs into trouble.
• Lets take a brief trip into quantifier scope
  ambiguity

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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.

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Quantifier Scope Ambiguity

• 1 2

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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.

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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)

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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.

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Other Practical Applications

• Question-Answering
• Automated Summarization
• Existing solutions dont use any sophisticated
  syntax or semantics.
• Because when they try

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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 didnt get paid a red cent for my trouble.
• I have not ever been to Mexico.
• I dont 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.

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Negative Polarity Items

• What constituents a negative context?
• I didnt 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.

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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

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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.

more general more specific
entails
entails
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Negative Polarity Items

• This is a downward-entailing context
• I didnt see a thing in the fishbowl.
• I didnt see a fish in the fishbowl.
• I didnt see a goldfish in the fishbowl.

more general more specific
entails
entails
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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?

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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.

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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.

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Negative Polarity Items

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

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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.

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Object vs. Meta Language

• When describing meaning, it doesnt help to use
  the words were trying to define.
• The quick brown fox jumped.
• What does this mean?
• It doesnt help to just repeat the sentence.
• We need a controlled vocabulary that we can agree
  on to describe language.

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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.

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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

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Object vs. Meta Language

• We cant 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.

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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
  areADJ1 ANDADJ2AND ADJ3ANDN

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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.

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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)

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Compositionality Complications Idioms

• Are they just multi-word words?
• Idioms differ in their rigidity...

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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 teachers tongue

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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.
• Dont spill the beans. (dont 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.

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Compositionality Complications Idioms

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

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Compositionality Complications Idioms

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

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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 ADJn N

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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 ADJn 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

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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).

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Compositionality Complications Non-Intersective
Adjectives

• How to reconcile non-intersective adjectives with
  compositionality?
• If former student? formern student then we
  have to give up either
• Compositionality
• Intersection n

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Brief InterludeFunctions
A FUNCTION FROM GREY- BROWN COGS TO RED/YELLOW
COGS
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Brief InterludeFunctions
FORMER
(the notion of a student)
(the notion of aformer student)
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Brief InterludeFunctions

• Notation
• SQRT(100) 10
• FORMER(student) former studentformer(st
  udent)

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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.

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Compositionality

• Meanings can be compositional in two ways
• By conjunction/intersectionX Y things that
  are bothXandYX Y XnY
• By function-applicationX Y X(Y)

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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!

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Presupposition

• The King of France is bald.
• Huh?
• Its not false, per se. Its just weird.

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Presupposition

• Compare
• I dont think that the Earth is flat.
• (a true statement)
• I dont know that the Earth is flat.
• (presupposition failure)

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Presupposition

• If an utterance has a presupposition p, then p
  must be true in order for the utterance to be
  OK.
• Further, p must be established as common ground
  in the discourse.
• (Unless the presupposition is accommodated.)

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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

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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.

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Presuppositions Under Negation

• I didnt think the Earth is flat.
• Assertion I didnt believe the Earth is flat.
• Presupposition None
• Sentence is true.
• I didnt know the Earth is flat.
• Assertion I didnt believe the Earth is flat.
• Presupposition The Earth is flat.
• Presupposition is still not true, therefore
  sentence is still weird.

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Presupposition Triggers

• definite descriptions (the King of France)
• p there is a King of France
• quantificational NPs (every cat I own)
• p I own at least one cat
• factive verbs (regret, know, discover)
• p the proposition regretted/known/discovered
• aspectual verbs/adverbs (stop, still)
• p the action was happening previously
• questions (who stole the cookies?)
• p someone stole the cookies

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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.

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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 p, a presupposition of the consequent, is
  asserted in the antecedent, it is not a
  presupposition of the whole sentence.

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Presupposition Filters

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

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Presupposition Accommodation

• Usually presuppositions have to be established
• A man off the street walks up to you and says
• I regret that I didnt buy the tomato.
• You say Oh. You were going to buy a tomato?
• The presupposition was not a part of the common
  ground.

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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)
• p the S.K. ambassador is here
• p is accommodated

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Formal Semantics

• Not just what things mean,
• but representing meaning composition in precise
  logical terms
• Hashing out the meta language.

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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.

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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)

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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.

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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.

capitals for themeta language
the predicate the arguments (also names)
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Predicate Logic Examples

• If John meets Mary, then he will know her.
• MEETS(JOHN, MARY) ? KNOWS(JOHN, MARY)

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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)

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Predicate Logic Natl. Language

• John JOHN
• Mary MARY
• knows KNOWS( , )
• John knows Mary some combination
  ofJohnMaryand knowswith either
  conjunction/intersection or function application

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Predicate Logic Compositionality

• Formal semantics starts where generative syntax
  ends.

KNOWS(JOHN, MARY)
JOHN
KNOWS(, )
MARY
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Predicate Logic Compositionality

• Syntax Semantics
• S ? NP1 V NP2 SV(NP1,NP2)
• S ? John knows Mary Sknows(John,Mary)
• S ? John knows Mary S KNOWS(JOHN, MARY)

KNOWS(JOHN, MARY)
JOHN
MARY
KNOWS(, )
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Predicate Logic Compositionality

• Syntax Semantics
• CP ? if S1 then S2 CPS1 ? S2
• (roughly)

MEETS(JOHN, MARY) ? KNOWS(JOHN, MARY)
MET(JOHN, MARY)
KNOWS(JOHN, MARY)