1. Semantics: Representations and Analyses

2. What kinds of meaning do we want to capture?
Categories/entities
IBM, Jane, a black cat, Pres. Bush
Events
running a mile, AS elected governor of CA
Time
Oct 30, next week, in 2 years
Aspect
Jack knows how to run. Jack is running. Jack ran the mile in 5 min.
Beliefs, Desires and Intentions (BDI)

3. What Can Serve as a Meaning Representation?
Anything that allows us to
Answer questions (What is the tallest building in the world?)
Determine truth (Is the blue block on the red block?)
Draw inferences (If the blue block is on the red block and the red block is on the tallest building in the world, then the blue block is on the tallest building in the world)

4. Meaning Representations
All represent ‘linguistic meaning’ of I have a car
and state of affairs in some world
All consist of structures, composed of symbols representing objects and relations among them
FOPC:
Semantic Net:
having
haver had-thing
speaker car

5. Conceptual Dependency Diagram:
Car
 Poss-By
Speaker
Frame
Having
Haver: S
HadThing: Car

6. A Standard Representation: Predicate-Argument Structure
Represents concepts and relationships among them
Nouns as concepts or arguments (red(ball))
Adjectives, adverbs, verbs as predicates (red(ball))
Subcategorization (or, argument) frames specify number, position, and syntactic category of arguments
NP likes NP
NP likes Inf-VP
NP likes NP Inf-VP

7. Semantic (Thematic) Roles
Subcat frames link arguments in surface structure with their semantic roles
Agent: George hit Bill. Bill was hit by George.
Patient: George hit Bill. Bill was hit by George.
Selectional Restrictions: constraints on the types
of arguments verbs take
George assassinated the senator.
*The spider assassinated the fly.
assassinate: intentional (political?) killing

8. First Order Predicate Calculus
Not ideal as a meaning representation and doesn't do everything we want -- but better than many…
Supports the determination of truth
Supports compositionality of meaning
Supports question-answering (via variables)
Supports inference

9. NL Mapping to FOPC Terms: constants, functions, variables
Constants: objects in the world, e.g. Huey
Functions: concepts, e.g. sisterof(Huey)
Variables: x, e.g. sisterof(x)
Predicates: symbols that refer to relations that hold among objects in some domain or properties that hold of some object in a domain
likes(Huey, kibble)
cat(Huey)

10. Logical connectives permit compositionality of meaning
kibble(x)  likes(Huey,x) “Huey likes kibble”
cat(Vera) ^ odd(Vera) “Vera is an odd cat”
sleeping(Huey) v eating(Huey) “Huey either is sleeping or eating”
Sentences in FOPC can be assigned truth values
Atomic formulae are T or F based on their presence or absence in a DB (Closed World Assumption?)
Composed meanings are inferred from DB and meaning of logical connectives

11. Limitations: cat(Huey) sibling(Huey,Vera)
cat(Huey) ^ sibling(Huey,Vera)  cat(Vera)
Limitations:
Do ‘and’ and ‘or’ in natural language really mean ‘^’ and ‘v’?
Mary got married and had a baby. And then…
Your money or your life!
Does ‘’ mean ‘if’?
If you go, I’ll meet you there.
How do we represent other connectives?
She was happy but ignorant.

12. Quantifiers:
Existential quantification: There is a unicorn in my garden. Some unicorn is in my garden.
Universal quantification: The unicorn is a mythical beast. Unicorns are mythical beasts.
Many? A few? Several? A couple?

13. Temporal Representations
How do we represent time and temporal relationships between events?
Last year Martha Stewart was happy but soon she will be in prison.
Where do we get temporal information?
Verb tense
Temporal expressions
Sequence of presentation
Linear representations: Reichenbach ‘47

14. Utterance time (U): when the utterance occurs
Reference time (R): the temporal point-of-view of the utterance
Event time (E): when events described in the utterance occur
George is eating a sandwich.
-- E,R,U 
George had eaten a sandwich (when he realized…)
E – R – U 
George will eat a sandwich.
--U,R – E 
While George was eating a sandwich his mother arrived.

15. Verbs and Event Types: Aspect
Statives: states or properties of objects at a particular point in time
I am hungry.
Activities: events with no clear endpoint
I am eating.
Accomplishments: events with durations and endpoints that result in some change of state
I ate dinner.
Achievements: events that change state but have no particular duration – they occur in an instant
I got the bill.

16. Beliefs, Desires and Intentions
Very hard to represent internal speaker states like believing, knowing, wanting, assuming, imagining
Not well modeled by a simple DB lookup approach so..
Truth in the world vs. truth in some possible world
George imagined that he could dance.
George believed that he could dance.
Augment FOPC with special modal operators that take logical formulae as arguments, e.g. believe, know

17. Mutual belief: I believe you believe I believe….
Believes(George, dance(George))
Knows(Bill,Believes(George,dance(George)))
Mutual belief: I believe you believe I believe….
Practical importance: modeling belief in dialogue
Clark’s grounding

18. Compositional Semantics
The meaning of the whole is made up of the meaning of its parts (predicates and arguments)
George cooks. Dan eats. Dan is sick.
Cook(George) Eat(Dan) Sick(Dan)
If George cooks and Dan eats, Dan will get sick.
(Cook(George) ^ eat(Dan))  Sick(Dan)
Sick(Dan)  Cook(George)
Syntax tells us how to combine the parts

19. Syntax-Driven Semantics
NP VP eat(Dan)
Nom V N
Dan eats
Task: can we link up syntactic structures to a corresponding semantic representation to produce the ‘meaning’ structure of a sentence in the course of parsing it?

20. Rule-to-Rule Hypothesis
We don’t want to have to specify for every possible parse tree what semantic representation it maps to
We want to identify general mappings from parse trees to semantic representations:
Hypothesis: A mapping exists between rules of the grammar and rules of semantic representation

21. Semantic Attachments
Extend each grammar rule with instructions on how to map the components of the rule to a semantic representation
S  NP VP {VP.sem(NP.sem)}
Each semantic function is defined in terms of the semantic representation of choice
Problem: how to define these functions and how to specify their composition so we always get the meaning representation we want from our grammar?

22. A ‘Simple’ Example AyCaramba serves meat.
Associating constants with arguments
ProperNoun  AyCaramba {AyCaramba}
MassNoun  meat {Meat}
Defining functions to produce these from input
NP  ProperNoun {ProperNoun.sem}
NP  MassNoun {MassNoun.sem}
Assumption: meaning reps of children are passed up to parents for non-branching constuents
Verbs here are where the action is

23. How do we combine these pieces?
V  serves {E(e,x,y) Isa(e,Serving) ^ Server(e,x) ^ Served(e,y)}
Will every verb need its own distinct representation?
George served in the army
How do we combine these pieces?
VP  V NP
Goal: E(e,x) Isa(e,Serving) ^ Server(e,x) ^ Served(e,Meat)
VP semantics must tell us
Which vars to be replaced by which args?
How this replacement is done?

24. Non-Compositional Language
What do we do with language whose meaning isn’t derived from the meanings of its parts
Metaphor:
You’re the cream in my coffee.
She’s the cream in George’s coffee.
The break-in was just the tip of the iceberg.
This was only the tip of Shirley’s iceberg.
Idioms:
The old man finally kicked the bucket.
The old man finally kicked the proverbial bucket.

25. Problems with Syntactic-Driven Semantics
Syntactic structures often don’t fit semantic structures very well
Important semantic elements often distributed very differently in trees for sentences that mean ‘the same’
I like soup. Soup is what I like.
Parse trees contain many structural elements not clearly important to making semantic distinctions
Syntax driven semantic representations are sometimes pretty bizarre

26. Sum Many hard problems in full semantic representation:
Temporal relations: tense, aspect
BDI
Current representations impoverished in many respects
Next time: Read Ch 16