Representing Meaning

Representing Meaning

Lecture 1812 Sep 2007

Transition

First we did words (morphology) Then simple sequences of words Then we looked at true syntax Now we’re moving on to meaning. Where some would

say we should have started to begin with.

Meaning

Language is useful and amazing because it allows us to encode/decode… Descriptions of the world What we’re thinking What we think about what other people think

Don’t be fooled by how natural and easy it is… In particular, you never really… Utter word strings that match the world Say what you’re thinking Say what you think about what other people think

Meaning

You’re simply uttering linear sequences of words such that when other people read/hear and understand them they come to know what you think of the world.

Meaning Representations

We’re going to take the same basic approach to meaning that we took to syntax and morphology

We’re going to create representations of linguistic inputs that capture the meanings of those inputs.

But unlike parse trees and the like these representations aren’t primarily descriptions of the structure of the inputs…

In most cases, meaning representations are simultaneously descriptions of the meanings of utterances and of some potential state of affairs in some world.

Introduction

Meaning representation languages: capturing the meaning of linguistic utterances using formal notation so that they make semantic processing possible

Example: deciding what to order at a restaurant by reading a menu, giving advice about where to go for dinner Requires knowledge about food, its preparation, what people

like to eat and what restaurants are like Example: answering a question on an exam

Requires background knowledge about the topic of the question

Example: Learning to use a software by reading a manual Requires knowledge about current computers, the specific

software, similar software applications, knowledge about users in general.

Semantic Analysis

Semantic analysis: mapping between language and real life I have a car:1. First Order Logic∃ x,y: Having(x) ^ Haver(speaker,x) ^ HadThing(y,x) ^ Car(y)

2. Semantic Network

Speaker

Car

Having

Haver Had-thing

Speaker Car

3. ConceptualDependency

Diagram

POSS-BY

4. Frame BasedRepresentation

Having Haver: Speaker HadThing: Car

Semantic analysis

A meaning representation consists of structures composed from a set of symbols, or representational vocabulary.

Why meaning representations are needed? What they should do for us?

Example: Giving advice about restaurants to tourists.A computer system that accepts spoken language queries from tourists

and constructs appropriate responses by using a knowledge base of relevant domain knowledge.

Representations that Permit us to reason about their truth (relationship to some world) Permit us to answer questions based on their content Permit us to perform inference (answer questions and determine

the truth of things we don’t actually know)

Semantic Processing

Touchstone application is often question answering Can a machine answer questions involving the

meaning of some text or discourse? What kind of representations do we need to

mechanize that process?

Verifiability

Verifiability: Ability to compare the state of affairs described by a representation to the state of affairs in some world modeled in a knowledge base.

Example: Does Anarkali serve vegetarian food?

Knowledge base (KB) Sample entry in KB: Serves(Anarkali,Vegetarian Food) Convert question to logical form and verify its truth value

against the knowledge base

Unambiguousness

Example:I want to eat someplace near Chowringhee.(multiple interpretations)

Interpretation is important Preferred interpretations Regardless of ambiguity in the input, it is critical that a

meaning representation language support representations that have a single unambiguous interpretation.

Vagueness

Vagueness: I want to eat Italian food.- what particular food?

Meaning representation language must support some vagueness

Canonical form

Inputs that have the same meaning should have the same meaning representation.

Distinct sentences having the same meaning Does Anarkali have vegetarian dishes? Do they have vegetarian food at Anarkali? Are vegetarian dishes served at Anarkali? Does Anarkali serve vegetarian fare?

Words have different senses, multiple words may have the same sense Having vs. serving Food vs. fare vs. dishes (each is ambiguous but one sense of each

matches the others) Alternative syntactic analyses have related meaning (Ex: active vs

passive)

Inference and variables; expressiveness

Inference and variables: Can vegetarians eat at Anarkali? I’d like to find a restaurant that serves vegetarian food. Serves (x,VegetarianFood) System’s ability to draw valid conclusions based on the meaning

representations of inputs and its store of background knowledge. Expressiveness:

system must be able to handle a wide range of subject matter

Semantic Processing

We’re going to discuss 2 ways to attack this problem (just as we did with parsing) There’s the theoretically motivated correct and

complete approach… Computational/Compositional Semantics

And there are practical approaches that have some hope of being useful and successful.

Information extraction

Meaning Structure of Language

The various methods by which human languages convey meaning Form-meaning associations Word-order regularities Tense systems Conjunctions Quantifiers A fundamental predicate-argument structure

Asserts that specific relationships / dependencies hold among the concepts underlying the constituent words and phrases

The underlying structure permits the creation of a single composite meaning representation from the meanings of the various parts.

Predicate-argument structure

Sentences Syntactic argument framesI want Italian food. NP want NPI want to spend less than five dollars. NP want Inf-VPI want it to be close by here. NP want NP Inf-VPThe syntactic frames specify the number, position and syntactic category of the

arguments that are expected to accompany a verb.

Thematic roles: e.g. entity doing the wanting vs. entity that is wanted (linking surface arguments with the semantic=case roles)

Syntactic selection restrictions: I found to fly to Dallas. Semantic selection restrictions: The risotto wanted to spend less than ten

dollars. Make a reservation for this evening for a table for two persons at eight:

Reservation (Hearer,Today,8PM,2)

Any useful meaning representation language must be organized in a way that supports the specification of semantic predicate-argument structures. Variable arity predicate-argument structures The semantic labeling of arguments to predicates The statement of semantic constraints on the fillers of

argument roles

Model-theoretic semantics

Basic notions shared by representation schemesAbility to represent

Objects Properties of objects Relations among objects

A model is a formal construct that stands for the particular state of affairs in the world that we are trying to represent.

Expressions in a meaning representation language will be mapped in a systematic way to the elements of the model.

Vocabulary of a meaning representation language Non-logical vocabulary: open-ended set of names for the

objects, properties and relations (may appear as predicates, nodes, labels on links, labels in slots in frames, etc)

Logical vocabulary: closed set of symbols, operators, quantifiers, links, etc.provide the formal meaning for composing expressions

Each element of non-logical vocabulary must have a denotation in the model. domain of a model: set of objects that are part of the application Capture properties of objects by a set (of domain elements

having the property) Relations denote sets of tuples of elements on the domain

Interpretation: a mapping that maps from the non-logical vocabulary of our meaning representation to the corresponding denotations in the model.

Representational Schemes

We’re going to make use of First Order Predicate Calculus (FOPC) as our representational framework Not because we think it’s perfect All the alternatives turn out to be either too limiting or They turn out to be notational variants

FOPC

Allows for… The analysis of truth conditions

Allows us to answer yes/no questions Supports the use of variables

Allows us to answer questions through the use of variable binding

Supports inference Allows us to answer questions that go beyond what we know

explicitly

FOPC

This choice isn’t completely arbitrary or driven by the needs of practical applications

FOPC reflects the semantics of natural languages because it was designed that way by human beings

In particular…

Example

I only have five dollars and I don’t have a lot of time. Have(Speaker,FiveDollars) ∧ ¬ Have(Speaker,LotOfTime) variables:

Have(x,FiveDollars) ∧ ¬ Have(x,LotOfTime) Note: grammar is recursive

Semantics of FOPC

FOPC sentences can be assigned a value of true or false.

Anarkali is near RC. Near (LocationOf (Anarkali), LocationOf (RC))

Inference

Modus ponens:

⇒

Example:

VegetarianRestaurant(Joe’s) x: VegetarianRestaurant(x) ⇒ Serves(x,VegetarianFood)Serves(Joe’s,VegetarianFood)

Uses of modus ponens

Forward chaining: as individual facts are added to the database, all derived inferences are generated

Backward chaining: starts from queries. Example: the Prolog programming language

father(X, Y) :- parent(X, Y), male(X).parent(john, bill).parent(jane, bill).female(jane).male (john).?- father(M, bill).

Variables and quantifiers

A restaurant that serves Mexican food near UM. ∃ x: Restaurant(x)

∧ Serves(x,MexicanFood) ∧ Near(LocationOf(x),LocationOf(UM))

All vegetarian restaurants serve vegetarian food. x: VegetarianRestaurant(x)

⇒ Serves (x,VegetarianFood) If this sentence is true, it is also true for any substitution of x.

However, if the condition is false, the sentence is always true.

Meaning Structure of Language

The semantics of human languages… Display a basic predicate-argument structure Make use of variables Make use of quantifiers Use a partially compositional semantics

Predicate-Argument Structure

Events, actions and relationships can be captured with representations that consist of predicates and arguments to those predicates.

Languages display a division of labor where some words and constituents function as predicates and some as arguments.

Predicate-Argument Structure

Predicates Primarily Verbs, VPs, PPs, Sentences Sometimes Nouns and NPs

Arguments Primarily Nouns, Nominals, NPs, PPs But also everything else; as we’ll see it depends on

the context

Example

Mary gave a list to John. Giving(Mary, John, List) More precisely

Gave conveys a three-argument predicate The first arg is the subject The second is the recipient, which is conveyed by the

NP in the PP The third argument is the thing given, conveyed by

the direct object

Not exactly

The statement The first arg is the subject

can’t be right. Subjects can’t be givers. We mean that the meaning underlying the subject

phrase plays the role of the giver.

Better

Turns out this representation isn’t quite as useful as it could be. Giving(Mary, John, List)

Better would be

),()^,(^),()^,()^(,

ListyIsaxJohnGiveexyGivenxMaryGiverxGivingyx

Predicates

The notion of a predicate just got more complicated… In this example, think of the verb/VP providing a template like the

following

The semantics of the NPs and the PPs in the sentence plug into the slots provided in the template

),()^,()^,()^(,,, xzGiveexyGivenxwGiverxzGivingyxw

Compositional Semantics

Compositional Semantics Syntax-driven methods of assigning semantics to

sentences

Semantic Analysis

Semantic analysis is the process of taking in some linguistic input and assigning a meaning representation to it. There a lot of different ways to do this that make more

or less (or no) use of syntax We’re going to start with the idea that syntax does

matter The compositional rule-to-rule approach

Semantic Processing

We’re going to discuss 2 ways to attack this problem (just as we did with parsing) There’s the theoretically motivated correct and

complete approach… Computational/Compositional Semantics

Create a FOL representation that accounts for all the entities, roles and relations present in a sentence.

And there are practical approaches that have some hope of being useful and successful.

Information extractionDo a superficial analysis that pulls out only the entities, relations and roles that are of interest to the consuming application.

Compositional Analysis

Principle of Compositionality The meaning of a whole is derived from the meanings

of the parts What parts?

The constituents of the syntactic parse of the input What could it mean for a part to have a meaning?

Example

AyCaramba serves meat

),()^,()^( MeateServedAyCarambaeServereServinge

Compositional Analysis

Augmented Rules

We’ll accomplish this by attaching semantic formation rules to our syntactic CFG rules

Abstractly

This should be read as the semantics we attach to A can be computed from some function applied to the semantics of A’s parts.

)}.,....({... 11 semsemfA nn

Example

Easy parts… NP -> PropNoun NP -> MassNoun PropNoun -> AyCaramba MassMoun -> meat

Attachments

{PropNoun.sem}{MassNoun.sem}{AyCaramba}{MEAT}

Example

S -> NP VP VP -> Verb NP Verb -> serves

{VP.sem(NP.sem)} {Verb.sem(NP.sem) ???

),()^,()^( xeServedyeServereServingeyx

Lambda Forms

A simple addition to FOPC Take a FOPC sentence

with variables in it that are to be bound.

Allow those variables to be bound by treating the lambda form as a function with formal arguments

)(xxP

)())((

SallyPSallyxxP

Example

Syntax/Semantics Interface: Two Philosophies

1. Let the syntax do what syntax does well and don’t expect it to know much about meaning

In this approach, the lexical entry’s semantic attachments do all the work

2. Assume the syntax does know something about meaning• Here the grammar gets complicated and the lexicon

simpler (constructional approach)

Example

Mary freebled John the nim.

Where did he get it from?

Who has it?

Why?

Example

Consider the attachments for the VPsVP -> Verb NP NP rule (gave Mary a book)VP -> Verb NP PP (gave a book to Mary)

Assume the meaning representations should be the same for both. Under the lexicon-heavy scheme, the VP attachments are:VP.Sem (NP.Sem, NP.Sem)VP.Sem (NP.Sem, PP.Sem)

Example

Under a syntax-heavy scheme we might want to do something like

VP -> V NP NP V.sem ^ Recip(NP1.sem) ^ Object(NP2.sem) VP -> V NP PP

V.Sem ^ Recip(PP.Sem) ^ Object(NP1.sem) i.e the verb only contributes the predicate, the grammar

“knows” the roles.

Integration

Two basic approaches Integrate semantic analysis into the parser (assign

meaning representations as constituents are completed)

Pipeline… assign meaning representations to complete trees only after they’re completed

Example

From BERP I want to eat someplace near campus

Two parse trees, two meanings

Pros and Cons

If you integrate semantic analysis into the parser as it is running… You can use semantic constraints to cut off parses

that make no sense But you assign meaning representations to

constituents that don’t take part in the correct (most probable) parse

Mismatches

There are unfortunately some annoying mismatches between the syntax of FOPC and the syntax provided by our grammars…

So we’ll accept that we can’t always directly create valid logical forms in a strictly compositional way We’ll get as close as we can and patch things up after

the fact.

Complex Terms

Allow the compositional system to pass around representations like the following as objects with parts:

Complex-Term → <Quantifier var body>

)Restaurant,(xIsax

Example

Our restaurant example winds up looking like

Big improvement…

Meat)Served(e,))RestaurantxxIsaeServereeServing ,(,()(

Conversion

So… complex terms wind up being embedded inside predicates. So pull them out and redistribute the parts in the right way…

P(<quantifier, var, body>)turns intoQuantifier var body connective P(var)

Example

),()Restaurant(

))Restaurant,(,(

xeServerx, Isax

xIsaxeServer

Quantifiers and Connectives

If the quantifier is an existential, then the connective is an ^ (and)

If the quantifier is a universal, then the connective is an -> (implies)

Multiple Complex Terms

Note that the conversion technique pulls the quantifiers out to the front of the logical form…

That leads to ambiguity if there’s more than one complex term in a sentence.

Quantifier Ambiguity

Consider Every restaurant has a menu

That could mean that every restaurant has a menu

Or thatThere’s some uber-menu out there and all restaurants have

that menu

Quantifier Scope Ambiguity

),(),(),()(,)(

MenuyIsayeHadxeHavereyHavingextxRestauran

),(),()(),(),(yeHadxeHavereeHaving

RestaurantxxIsaMenuyyIsa

Ambiguity

This turns out to be a lot like the prepositional phrase attachment problem

The number of possible interpretations goes up exponentially with the number of complex terms in the sentence

The best we can do is to come up with weak methods to prefer one interpretation over another

Non-Compositionality

Unfortunately, there are lots of examples where the meaning (loosely defined) can’t be derived from the meanings of the parts

Idioms, jokes, irony, sarcasm, metaphor, metonymy, indirect requests, etc

English Idioms

Kick the bucket, buy the farm, bite the bullet, run the show, bury the hatchet, etc…

Lots of these… constructions where the meaning of the whole is either Totally unrelated to the meanings of the parts (kick

the bucket) Related in some opaque way (run the show)

The Tip of the Iceberg

Describe this construction1. A fixed phrase with a particular meaning2. A syntactically and lexically flexible phrase with a

particular meaning3. A syntactically and lexically flexible phrase with a

partially compositional meaning4. …

Example

Enron is the tip of the iceberg.NP -> “the tip of the iceberg”

Not so good… attested examples… the tip of Mrs. Ford’s iceberg the tip of a 1000-page iceberg the merest tip of the iceberg

How about That’s just the iceberg’s tip.

Example

What we seem to need is something like NP ->

An initial NP with tip as its head followed bya subsequent PP with of as its head and that has iceberg as the head of its NP

And that allows modifiers like merest, Mrs. Ford, and 1000-page to modify the relevant semantic forms

Quantified Phrases

Consider A restaurant serves meat.

Assume that A restaurant looks like

If we do the normal lambda thing we get

)RestaurantxIsax ,(

)),(,()( MeatServed(e,))RestaurantxxIsaeServereeServing

Examples from Russell&Norvig (1)

7.2. p.213

Not all students take both History and Biology. Only one student failed History. Only one student failed both History and Biology. The best history in History was better than the best score in Biology. Every person who dislikes all vegetarians is smart. No person likes a smart vegetarian. There is a woman who likes all men who are vegetarian. There is a barber who shaves all men in town who don't shave themselves. No person likes a professor unless a professor is smart. Politicians can fool some people all of the time or all people some of the time but they

cannot fool all people all of the time.

Categories & Events

Categories: VegetarianRestaurant (Joe’s) – categories are relations and not objects MostPopular(Joe’s,VegetarianRestaurant) – not FOPC! ISA (Joe’s,VegetarianRestaurant) – reification (turn all concepts into

objects) AKO (VegetarianRestaurant,Restaurant)

Events: Reservation (Hearer,Joe’s,Today,8PM,2) Problems:

Determining the correct number of roles Representing facts about the roles associated with an event Ensuring that all the correct inferences can be drawn Ensuring that no incorrect inferences can be drawn

MUC-4 Example

INCIDENT: DATE 30 OCT 89 INCIDENT: LOCATION EL SALVADOR INCIDENT: TYPE ATTACK INCIDENT: STAGE OF EXECUTION ACCOMPLISHED INCIDENT: INSTRUMENT ID INCIDENT: INSTRUMENT TYPEPERP: INCIDENT CATEGORY TERRORIST ACT PERP: INDIVIDUAL ID "TERRORIST" PERP: ORGANIZATION ID "THE FMLN" PERP: ORG. CONFIDENCE REPORTED: "THE FMLN" PHYS TGT: ID PHYS TGT: TYPEPHYS TGT: NUMBERPHYS TGT: FOREIGN NATIONPHYS TGT: EFFECT OF INCIDENTPHYS TGT: TOTAL NUMBERHUM TGT: NAMEHUM TGT: DESCRIPTION "1 CIVILIAN"HUM TGT: TYPE CIVILIAN: "1 CIVILIAN"HUM TGT: NUMBER 1: "1 CIVILIAN"HUM TGT: FOREIGN NATIONHUM TGT: EFFECT OF INCIDENT DEATH: "1 CIVILIAN"HUM TGT: TOTAL NUMBER

On October 30, 1989, one civilian was killed in a reported FMLN attack in El Salvador.

Subcategorization frames

1. I ate2. I ate a turkey sandwich3. I ate a turkey sandwich at my desk4. I ate at my desk5. I ate lunch6. I ate a turkey sandwich for lunch7. I ate a turkey sandwich for lunch at my desk

- no fixed “arity” (problem for FOPC)

One possible solution

1. Eating1 (Speaker)2. Eating2 (Speaker, TurkeySandwich)3. Eating3 (Speaker, TurkeySandwich, Desk)4. Eating4 (Speaker, Desk)5. Eating5 (Speaker, Lunch)6. Eating6 (Speaker, TurkeySandwich, Lunch)7. Eating7 (Speaker, TurkeySandwich, Lunch, Desk)Meaning postulates are used to tie semantics of predicates:

w,x,y,z: Eating7(w,x,y,z) ⇒ Eating6(w,x,y)Scalability issues again!

Another solution

- Say that everything is a special case of Eating7 with some arguments unspecified: ∃w,x,y Eating (Speaker,w,x,y)

- Two problems again:- Too many commitments (e.g., no eating except at meals: lunch, dinner, etc.)- No way to individuate events:

∃w,x Eating (Speaker,w,x,Desk) ∃w,y Eating (Speaker,w,Lunch,y) – cannot combine into ∃w Eating (Speaker,w,Lunch,Desk)

Reification

∃ w: Isa(w,Eating) ∧ Eater(w,Speaker) ∧ Eaten(w,TurkeySandwich) – equivalent to sentence 5.

Reification: No need to specify fixed number of arguments for a given

surface predicate No more roles are postulated than mentioned in the input No need for meaning postulates to specify logical connections

among closely related examples

Representing time

1. I arrived in New York2. I am arriving in New York3. I will arrive in New York

∃ w: Isa(w,Arriving) ∧ Arriver(w,Speaker) ∧ Destination(w,NewYork)

Representing time

∃ i,e,w,t: Isa(w,Arriving) ∧ Arriver(w,Speaker) ∧ Destination(w,NewYork) ∧ IntervalOf(w,i) ∧ EndPoint(I,e) ∧ Precedes (e,Now)

∃ i,e,w,t: Isa(w,Arriving) ∧ Arriver(w,Speaker) ∧ Destination(w,NewYork) ∧ IntervalOf(w,i) ∧ MemberOf(i,Now)

∃ i,e,w,t: Isa(w,Arriving) ∧ Arriver(w,Speaker) ∧ Destination(w,NewYork) ∧ IntervalOf(w,i) ∧ StartPoint(i,s) ∧ Precedes (Now,s)

Representing time

We fly from San Francisco to Boston at 10. Flight 1390 will be at the gate an hour now.

Use of tenses Flight 1902 arrived late. Flight 1902 had arrived late.

“similar” tenses When Mary’s flight departed, I ate lunch When Mary’s flight departed, I had eaten lunch

reference point

Aspect

Stative: I know my departure gate Activity: John is flying

no particular end point Accomplishment: Sally booked her flight

natural end point and result in a particular state Achievement: She found her gate Figuring out statives:

* I am needing the cheapest fare.* I am wanting to go today.* Need the cheapest fare!

Representing beliefs

Want, believe, imagine, know - all introduce hypothetical worlds I believe that Mary ate British food. Reified example:

∃ u,v: Isa(u,Believing) ∧ Isa(v,Eating) ∧ Believer (u,Speaker) ∧ BelievedProp(u,v) ∧ Eater(v,Mary) ∧ Eaten(v,BritishFood)

However this implies also: ∃ u,v: Isa(v,Eating) ∧ Eater(v,Mary) ∧ Eaten(v,BritishFood)

Modal operators: Believing(Speaker,Eating(Mary,BritishFood)) - not FOPC! – predicates

in FOPC hold between objects, not between relations. Believes(Speaker, ∃ v: ISA(v,Eating) ∧ Eater(v,Mary) ∧

Eaten(v,BritishFood))

Modal operators

Beliefs Knowledge Assertions Issues:

If you are interested in baseball, the Red Sox are playing tonight.

Examples from Russell&Norvig (2)

7.3. p.214

One more outburst like that and you'll be in comptempt of court. Annie Hall is on TV tonight if you are interested. Either the Red Sox win or I am out ten dollars. The special this morning is ham and eggs. Maybe I will come to the party and maybe I won't. Well, I like Sandy and I don't like Sandy.

Representing Meaning

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