Notes on Ambiguity

There are two types of ambiguity: Genuine ambiguities, where a sentence really can have two different meanings to an intelligent hearer, and "computer" ambiguities, where the meaning is entirely clear to a hearer but a computer detects more than one meaning. Genuine ambiguity is not a serious problem for NLP problems; it's comparatively rare, and you can't expect computers to do better with natural language than people. Computer ambiguity is a very serious problem; it is extremely common, and it is where computers do much much worse than humans.

Types of ambiguity

Lexical ambiguity

Words have multiple meanings.
"I saw a bat."
bat = flying mammal / wooden club?
saw = past tense of "see" / present tense of "saw" (to cut with a saw.)

Syntactic ambiguity.

A sentence has multiple parse trees.
Particularly common sources of ambiguity in English are:

Phrase attachment. "Mary ate a salad with spinach from Califonia for lunch on Tuesday."
"with spinach" can attach to "salad" or "ate"
"from California" can attach to "spinach", "salad", or "ate".
"for lunch" can attach to "California", "spinach", "salad", or "ate"
and "on Tuesday" can attach to "lunch", "California", "spinach", "salad" or "ate".
(Crossovers are not allowed, so you cannot both attach "on Tuesday" to "spinach" and attach "for lunch" to salad. Nonetheless there are 42 possible different parse trees.)`

Conjunction. "Mary ate a salad with spinach from Califonia for lunch on Tuesday and Wednesday."
"Wednesday" can be conjoined with salad, spinach, California, lunch, or Tuesday.

Noun group structure English allows long series of nouns to be strung together using the enormously ambiguous rule NG -> NG NG. E.g. "New York University Martin Luther King Jr. scholarship program projects coordinator Susan Reid". Even taking "New York" "Martin Luther King Jr." and "Susan Reid" to be effectively single elements, this is 8 elements in a row, and has 429 possible parses.

For a while, I was collecting these as an assignment from students; I saved some of the best in Examples of Compound Nouns

Semantic ambiguity.

Even after the syntax and the meanings of the individual words have been resolved, there are two ways of reading the sentence. "Lucy owns a parrot that is larger than a cat", "a parrot" is extenstensionally quantified, "a cat" is either universally quantified or means "typical cats." Other examples:
"The dog is chasing the cat." vs. "The dog has been domesticated for 10,000 years." In the first sentence, "The dog" means to a particular dog; in the second, it means the species "dog".

"John and Mary are married." (To each other? or separately?) Compare "John and Mary got engaged last month. Now, John and Mary are married." vs. "Which of the men at this party are single? John and Jim are married; the rest are all available."

"John kissed his wife, and so did Sam". (Sam kissed John's wife or his own?)

Compare "Amy's car", "Amy's husband", "Amy's greatest fear", "Michaelangelo's David" etc.

The relation of the meaning of a compound noun to its component can be vary wildly. See Compound Nouns for examples.

Anaphoric ambiguity.

A phrase or word refers to something previously mentioned, but there is more than one possibility.

"Margaret invited Susan for a visit, and she gave her a good lunch." (she = Margaret; her = Susan)

"Margaret invited Susan for a visit, but she told her she had to go to work" (she = Susan; her = Margaret.)

"On the train to Boston, George chatted with another passenger. The man turned out to be a professional hockey player." (The man = another passenger).

"Bill told Amy that he had decided to spend a year in Italy to study art."
"That would be his life's work." (That = art)
"After he had done that, he would come back and marry her." (That = spending a year in Italy)
"That was the upshot of his thinking the previous night" (That = deciding)
"That started a four-hour fight." (That = telling Amy)

Son: I watched a guy do 50 pushups. Can you do that, dad?
Father: Sure! Not to brag, but I could probably watch a guy do 100 pushups.

In many cases, there is no explicit antecedent.

"I went to the hospital, and they told me to go home and rest." (They = the hospital staff.)

Non-literal speech.

"The White House announced today that ..." ("White House" = the Presidents's staff) (Mentonymy)

"The price of tomatoes in Des Moines has gone through the roof" (= increased greatly) Metaphor.

Ellipsis

The omission of words that are needed for grammatical completion, and are "understood". This is very common in speech, less so in writing. E.g. "I am allergic to tomatoes. Also fish." Understood as "I am also allergic to fish" rather than "Also, fish are allergic to tomatoes." "Mozart was born in Salzburg and Beethoven, in Bonn". Understood as "Mozart was born in Salzburg and Beethoven was born in Bonn"

Extended example

A perfectly typical, not contrivedly literary, actual example, from "Nice disguise: Alito's frightening geniality" by Andrew M. Siegel (The New Republic 11/14/05).

If you are a fan of the justices who fought throughout the Rehnquist years to pull the Supreme Court to the right, Alito is a home run --- a strong and consistent conservative with the skill to craft opinions that make radical results appear inevitable and the ability to build trusting professional relationships across ideological lines.

Metaphors: "fought", "pull to the right", "home run", "craft", "build", "across ... lines". (Probably "home run" was the only conscious use of a metaphor.)

Lexical ambiguities: "fan", "strong", "consistent", arguably "conservative", "opinions", "results", "inevitable", "professional". (The line between metaphor and lexical ambiguity is very unclear.)

Syntactic ambiguities: Does "who fought ..." attach to "fan" or "justices"? Does "to the right" attach to "Court", "pull", "years", "fought", "justices" or "fan"? Is "and the ability" conjoined to "opinions" or "the skill" or "conservative"? Does "across ideological lines" attach to "relationships" or "build"? (The last is an example of the phenomenon, not at all rare, of an ambiguity that makes no actual difference; the meaning of either reading is the same.)

Anaphoric ambiguity: Who are the implicit subject and object of "trusting"?

Semantic ambiguity: "the skill ... the ability": Do these denote unique ontological entities? If not, what do they denote?

The hardest part is to find the logical structure, which is, I would argue, "Since Alito is a strong and consistent conservative ... therefore if you are a fan ... then your opinion should be that Alito is a home run." Notice that "your opinion should be" is omitted in the sentence; the linguistic practice of deleting elements and leaving them implicit is known as ellipsis. Notice also that though syntactically "home run" and "strong and consistent conservative" are in apposition, logically they are entirely separate. The author is presenting it as fact that Alito is a strong and consistent conservative with the skill etc. but that Alito is a "home run" is not a fact, it is the presumed opinion of the hypothetical "you".

Example 2

Elsie tried to reach her aunt on the phone, but she didn't answer.

Lexical ambiguity: The word "tried" means "attempted" not "held a court proceedings", or "test" (as in "Elsie tried the lemonade"). The word "reach" means "establish communication" not "physically arrive at" (as in "the boat reached the shore").

Syntatic ambiguity: The phrase "on the phone" attaches to "reach" and thus means "using the phone" not to "aunt" which would mean "her aunt who was physically on top of the phone" (compare "her aunt in Seattle").

Anaphoric ambiguity: "she" means the aunt, not Elsie.

Techniques of ambiguity resolution.

Syntactic constraints.

Frequency.

(Particularly for lexical ambiguity.) Prefer the most common meaning of a word. "I saw the table." "saw" = past tense of see is much more common than "saw" = present tense "cut with a saw."

Frequency in context.

In context = dinner, "pitcher" means "container of liquid"
In context = baseball, "pitcher" means "thrower of ball."

Associational frequency

Make a judgement based on how often two words, or particular meanings of word, appear in text.

Examples: "The cheetah caught up with the sheep because it was very fast." "Fast" is more associated with "cheetah" than "sheep" so "it" is more likely to refer to "cheetah".

"I hammer the nail and I saw the board". "Saw" the tool is strongly associated with "hammer" and "nail", so that interpretation would be preferred.

Selectional restrictions. (= semantic constraints)

Concept A can only combine with concept B in mode Z if A or B have specified features.

E.g. "The bat ate its dinner." The subject of "ate" is generally animate. Therefore "bat" means "flying mammal" not "wooden club."

"The sick bat lay on the ground." The adjective "sick" generally modifies animate objects. Hence "bat" = flying mammal.

"The broken bat lay on the ground." The adjective "broken" generally modifies inanimate objects. Hence "bat" is a wooden club.

"The clock is fast." vs "The horse is fast." vs. "The clothes are fast." vs. "The slopes are fast." vs. "The knot is fast."
"fast" meaning "showing a time later than correct." applies only to a time-piece.
"fast" meaning "speedy" applies only to a mobile object.
"fast" meaning "trendy" applies only to an object of conspicuous display..
"fast" meaning "inducing speedy movement" applies only to a context of movement.
"fast" meaning "secure" applies only to a fastening.

"The horse ran up the hill. It was very steep." vs. "It soon got tired."
"Steep" applies to surfaces, hence "it" = hill.
"Tired" applies to animate objects; hence "it" = horse.

"I went to the hospital on 13th street" vs. "on Wednesday"
"on " cannot modify an object. Hence "on Wenesday" is part of the VP.

Recency rule (for anaphora).

85% of the time of so, the referent is the most recently mentioned object of correct gender and number.

Parallel structure.

(Mostly for anaphora) "John met Mike on the street, and he asked him to dinner." (He = John; him = Mike).

World knowledge.

Prefer the most plausible interpretation.
"The city councilmen refused the demonstrators a permit because they advocated violence." vs.
"The city councilmen refused the demonstrators a permit because they feared violence." (Terry Winograd, Understanding Natural Language).

"I went up to the door of the house with the red shutters."

"Margaret invited Susan for a visit, and she gave her a good lunch."

"Margaret invited Susan for a visit, but she told her she had to go to work"

"Harry scratched his head, and so did Mike."

Textual coherence

"President Bush announced yesterday that he is nominating Michael Mukasey for attorney general. He said he is a great American." (Note that it is not inherently more plausible that Bush should say this about Mukasey than vice versa, but the narrative context disambiguates it.)

Speaker intent.

Interpret the text in a way that gives a reason for the speaker to say it. "Pardon me. Do you know what time it is?"
"You promised you would be back by 11:00. Do you know what time it is?"

"Elsie tried to reach her aunt on the phone, but she didn't answer." Disambiguating "she" requires combining world knowledge with speaker intent. First, you need to know how telephone calls work: one person initiates the call, the other person may or may not answer; the communication is successful (the caller reaches the callee) only if the second person does answer. Second, you have to use a rule, called a Gricean rule, that, when people say or write thintgs, they try to give you new information, not old information. In this case, since the sentence already said that Elsie made the call, there is no point in saying that she didn't answer it; the caller is never the person who answers a call. What is useful information is that the aunt didn't answer.

Winograd schemas

For more discussion see Collection of Winograd Schemas