1. Natural Language Processing
Semantics I
What is semantics for?
Role of FOL
Montague Approach
November 2006
Semantics I

2. Semantics Semantics is the study of the meaning of NL expressions
Expressions include sentences, phrases, and sentences.
What is the goal of such study?
Provide a workable definition of meaning.
Explain semantic relations between expressions.
November 2006
Semantics I

3. Examples of Semantic Relations
Synonymy
John killed Mary
John caused Mary to die
Entailment
John fed his cat
John has a cat
Consistency
John is very sick
John is not feeling well
John is very healthy
November 2006
Semantics I

4. Different Kinds of Meaning X means Y
Meaning as definition:
a bachelor means an unmarried man
Meaning as intention:
What did John mean by waving?
Meaning as reference: "Eiffel Tower " means
November 2006
Semantics I

5. Workable Definition of Meaning
Restrict the scope of semantics.
Ignore irony, metaphor etc.
Stick to the literal interpretations of expressions rather than metaphorical ones. (My car drinks petrol).
Assume that meaning is understood in terms of something concrete.
November 2006
Semantics I

6. Concrete Semantics
Procedural semantics: the meaning of a phrase or sentence is a procedure: “Pick up a big red block” (Winograd 1972)
Object–Oriented Semantics: meaning is an instance of a class.
Truth-Conditional Semantics
November 2006
Semantics I

7. Truth Conditional Semantics
Key Claim: the meaning of a sentence is identical to the conditions under which it is true.
Know the meaning of "Ġianni ate fish for tea" = know exactly how to apply it to the real world and decide whether it is true or false.
On this view, one task of semantic theory is to provide a system for identifying the truth conditions of sentences.
November 2006
Semantics I

8. TCS and Semantic Relations
TCS provides a precise account of semantic relations between sentences.
Examples:
S1 is synonymous with S2.
S1 entails S2
S1 is consistent with S2.
S1 is inconsistent with S2.
Just like logic!
Which logic?
November 2006
Semantics I

9. NL Semantics: Two Basic Issues
How can we automate the process of associating semantic representations with expressions of natural language?
How can we use semantic representations of NL expressions to automate the process of drawing inferences?
We will focus mainly on first issue.
November 2006
Semantics I

10. Associating Semantic Representations Automatically
Design a semantic representation language.
Figure out how to compute the semantic representation of sentences
Link this computation to the grammar and lexicon.
November 2006
Semantics I

11. Semantic Representation Language
Logical form (LF) is the name used by logicians (Russell, Carnap etc) to talk about the representation of context-independent meaning.
Semantic representation language has to encode the LF.
One concrete representation for logical form is first order logic (FOL)
November 2006
Semantics I

12. Why is FOL a good thing? Has a precise, model-theoretic semantics.
If we can translate a NL sentence S into a sentence of FOL, then we have a precise grasp on at least part of the meaning of S.
Important inference problems have been studied for FOL. Computational solutions exist for some of them.
Hence the strategy of translating into FOL also gives us a handle on inference.
November 2006
Semantics I

13. Anatomy of FOL Symbols of different types constant symbols: a,b,c
variable symbols: x, y, z
function symbols: f,g,h
predicate symbols: p,q,r
connectives: &, v, 
quantifiers: , 
punctuation: ), (, “,”
November 2006
Semantics I

14. Anatomy of FOL Symbols of different types
constant symbols: csa3180, nlp, mike, alan, rachel, csai
variable symbols: x, y, z
function symbols: lecturerOf, subjectOf
predicate symbols: studies, likes
connectives: &, v, 
quantifiers: , 
punctuation: ), (, “,”
November 2006
Semantics I

15. Anatomy of FOL
With these symbols we can make expressions of different types
Expressions for referring to things
constant: alan, nlp
variable: x
term: subject(csa3180)
Expressions for stating facts
atomic formula: study(alan,csa3180)
complex formula: study(alan,csa3180) & teach(mike, csa3180)
quantified expression:
xy teaches(lecturer(x),x) & studies(y,subject(x)) xy likes(x,subjectOf(y))  studies(x,y)
November 2006
Semantics I

16. Logical Form of Phrases
word
POS
Logic
Representation
csai
proper noun
individual constant
student
common noun
1 place predicate
student(x)
easy
adjective
easy(x)
easy interesting course
adj/noun
easy(x) & interesting(x) & course(x)
snores
intrans verb
snore (x)
studies
trans. verb
2 place predicate
study(x,,y)
gives
ditrans verb
3 place pred
give(x,y,z)

17. Logical Forms of Sentences
John kicks Fido:
kick(john, fido)
Every student wrote a program
xy( stud(x)  prog(y) & write(x,y))
yx(stud(x)  prog(y) & write(x,y))
Semantic ambiguity related to quantifier scope
November 2006
Semantics I

18. Some simple exercises 1."x (bike(x)  $y (car(y) & exp(y,x))
Let van(x) represent ‘x is a van’,
car(x) represent ‘x is a car’,
bike(x) represent ‘x is a bike’,
exp(x,y) ‘x is more expensive y’,
faster(x,y) ‘x is faster than y’.
Translate the following formula into natural language:
1."x (bike(x)  $y (car(y) & exp(y,x))
2."x"y ((van(x) & bike(y))  faster(x,y))
3.$z (car(z) & "x"y((van(x) & bike(y)) 
faster(z,x) & faster(z,y) & exp(z,x) & exp(z,y)
November 2006
Semantics I

19. Building Logical Form Frege’s Principle of Compositionality
The POC states that the LF of a complex phrase can be built out of the LFs of the constituent parts.
An everyday example of compositionality is the way in which the “meaning” of arithmetic expressions is computed (2+3) * (4/2) = (5 * 2) = 10
November 2006
Semantics I

20. Compositionality for NL
The LF of the whole sentence can be computed from the LF of the subphrases, i.e.
Given the syntactic rule X  Y Z.
Suppose [Y], [Z] are the LFs of Y, and Z respectively.
Then [X] = ([Y],[Z]) where  is some function for semantic combination
November 2006
Semantics I

21. Claims of Richard Montague:
Each syntax rule is associated with a semantic rule that describes how the LF of the LHS category is composed from the LF of its subconstituents
1:1 correspondence between syntax and semantics (rule-to-rule hypothesis)
Functional composition proposed for combining semantic forms.
Lambda calculus proposed as the mechanism for describing functions for semantic combination.
November 2006
Semantics I

22. Sentence Rule Syntactic Rule: S  NP VP
Semantic Rule: [S] = [VP]([NP]) i.e. the LF of S is obtained by "applying" the LF of VP to the LF of NP.
For this to be possible [VP] must be a function, and [NP] the argument to the function.
November 2006
Semantics I

23. Parse Tree with Logical Forms
write(bertrand,principia) NP
bertrand VP
y.write(y,principia) V
x.y.write(y,x)
principia
writes
November 2006
Semantics I