Taaltheorie en Taalverwerking Samenvatting 2
Lecture 5a
Computational Semantics:
Two important questions for computational semantics:
o Semantic representations: how can we represent the meaning of linguistic expressions
in a computational way? How can we establish a link to the world? With Predicate
Logic.
o Semantic construction (or semantic analysis): how can we systematically associate
semantic representations to linguistic expressions?
Semantic Representations:
To be able to use semantic information computationally, we need a formal and precise way of
representing what linguistic expressions mean. Two main approaches:
o Symbolic approaches: we can represent meaning (knowledge) using logic and reason
with the meaning representations using inference procedures.
o Statistical approaches: we can represent meaning (knowledge) using frequencies or
probabilities derived from observations.
PL as Semantic Representation Formalism:
We will use Predicate Logic (PL or FOL) as our semantic representation formalism. We make a
distinction between syntax and semantics:
o The syntax of PL tells us what are well-formed formulas: we have logical connectives,
quantifiers, predicates, variables, constants …
o The semantics of PL specifies when a formula is true in a formal model. Formal models
are abstract representations of situations in the real world.
PL acts as an intermediate representation level that allows us to connect language to the
world
o We use PL formulas as meaning representations for sentences
o We use PL models to represent world situations
o We know how to check if a PL formula is true in a model
o Therefore, we connect language to the world
We want to be able to establish a systematic (non-arbitrary) relation between sentences and
formulas
,Semantic Construction:
Principle of Compositionality: the meaning of a sentence is a function of the meaning of its
parts
How do we put the meaning of the parts together?
o We may be able to associate a representation with each word in a sentence, but how
is this information combined?
o The meaning of a sentence is not only based on the words that make it up, but also on
the ordering, grouping and structural relations among such words its syntactic
structure
Syntax tells us how to hierarchically decompose a sentence into sub-parts
o If we associate a semantic representation with each lexical item and …
o Describe how the semantic representation of a syntactic constituent is to be built up
from the representation of its sub-parts, then …
o We have at our disposal a compositional semantics: a systematic way of constructing
semantic representations for sentences.
Now we have a plausible strategy for finding a way to systematically associate PL formulas
with sentences. We need to:
o Specify a reasonable syntax by means of a formal grammar such as CFG for the
fragment of natural language of interest
o Specify semantic representations for the lexical items
o Specify how the semantic representation of a syntactic constituent is constructed in
terms of the representations of its sub-parts
We will use a notational extension of PL to do this: lambda calculus
Lambda Abstraction:
We shall view the lambda calculus as a notational extension of PL that allows us to bind
variables with a new operator λ:
o The prefix λx binds the occurrence of x in Sleep(x)
o We often say the prefix λx abstracts over x, and call expressions with such prefixes
lambda expressions or lambda abstractions
o We can use on lambda expression as the body of another one:
We can think of the lambda calculus as a toll dedicated to gluing together the items needed to
build semantic representations
o The purpose of abstracting over variables is to mark the slots where we want
substitutions to be made
o Lambda abstractions can be seen as functors that can be applied to arguments (we
will use the symbol @ for functional application)
o A compound expression of this sort refers to the application of the functor λx.Sleep(x)
to the argument b
Β-conversion (or λ-reduction)
o Compound expressions F@A can be seen as instructions to
Throw away the λx prefix of the functor F, and
Replace any occurrence of x bound by the λ-operator with the argument A
, o This replacement or substitution processes is called Β-conversion:
Lambda abstraction, functional application and Β-conversion are the main ingredients we
need to deal with semantic construction:
o Once we have devised lambda abstractions to represent lexical items, we only need to
use functional application and Β-conversion to combine semantic representations
compositionally
Given a syntactic constituent R with subparts Ra and Rb, we need to specify
which subpart is to be thought as the functor F and which as the argument A
We then construct the semantic representation of R by functional application
F@A
λ -abstractions for Lexical Items
Representing different basic categories
o Intransitive verbs (verbs with no object) and nouns are 1-place relations which are
missing their argument:
o What about determiners such as ‘a’ and ‘every’ in NPs like ‘a boxer’?
For instance, we’d like to represent the meaning of ‘a boxer walks’ as:
What does each word contribute to this formula? And what is the
contribution of the determiner?
If ‘boxer’ contributes Boxer(x) and ‘walks’ contributes Walk(x) to the formula,
then the determiner ‘a’ must contribute something like Ǝx …
Two bits are missing:
The contribution of the NP (the restriction)
The contribution of the VP (the scope)
We can use lambda abstraction to mark the missing arguments that will be
filled in during semantic construction
This is the representation for existential determiners:
Lecture 5a
Computational Semantics:
Two important questions for computational semantics:
o Semantic representations: how can we represent the meaning of linguistic expressions
in a computational way? How can we establish a link to the world? With Predicate
Logic.
o Semantic construction (or semantic analysis): how can we systematically associate
semantic representations to linguistic expressions?
Semantic Representations:
To be able to use semantic information computationally, we need a formal and precise way of
representing what linguistic expressions mean. Two main approaches:
o Symbolic approaches: we can represent meaning (knowledge) using logic and reason
with the meaning representations using inference procedures.
o Statistical approaches: we can represent meaning (knowledge) using frequencies or
probabilities derived from observations.
PL as Semantic Representation Formalism:
We will use Predicate Logic (PL or FOL) as our semantic representation formalism. We make a
distinction between syntax and semantics:
o The syntax of PL tells us what are well-formed formulas: we have logical connectives,
quantifiers, predicates, variables, constants …
o The semantics of PL specifies when a formula is true in a formal model. Formal models
are abstract representations of situations in the real world.
PL acts as an intermediate representation level that allows us to connect language to the
world
o We use PL formulas as meaning representations for sentences
o We use PL models to represent world situations
o We know how to check if a PL formula is true in a model
o Therefore, we connect language to the world
We want to be able to establish a systematic (non-arbitrary) relation between sentences and
formulas
,Semantic Construction:
Principle of Compositionality: the meaning of a sentence is a function of the meaning of its
parts
How do we put the meaning of the parts together?
o We may be able to associate a representation with each word in a sentence, but how
is this information combined?
o The meaning of a sentence is not only based on the words that make it up, but also on
the ordering, grouping and structural relations among such words its syntactic
structure
Syntax tells us how to hierarchically decompose a sentence into sub-parts
o If we associate a semantic representation with each lexical item and …
o Describe how the semantic representation of a syntactic constituent is to be built up
from the representation of its sub-parts, then …
o We have at our disposal a compositional semantics: a systematic way of constructing
semantic representations for sentences.
Now we have a plausible strategy for finding a way to systematically associate PL formulas
with sentences. We need to:
o Specify a reasonable syntax by means of a formal grammar such as CFG for the
fragment of natural language of interest
o Specify semantic representations for the lexical items
o Specify how the semantic representation of a syntactic constituent is constructed in
terms of the representations of its sub-parts
We will use a notational extension of PL to do this: lambda calculus
Lambda Abstraction:
We shall view the lambda calculus as a notational extension of PL that allows us to bind
variables with a new operator λ:
o The prefix λx binds the occurrence of x in Sleep(x)
o We often say the prefix λx abstracts over x, and call expressions with such prefixes
lambda expressions or lambda abstractions
o We can use on lambda expression as the body of another one:
We can think of the lambda calculus as a toll dedicated to gluing together the items needed to
build semantic representations
o The purpose of abstracting over variables is to mark the slots where we want
substitutions to be made
o Lambda abstractions can be seen as functors that can be applied to arguments (we
will use the symbol @ for functional application)
o A compound expression of this sort refers to the application of the functor λx.Sleep(x)
to the argument b
Β-conversion (or λ-reduction)
o Compound expressions F@A can be seen as instructions to
Throw away the λx prefix of the functor F, and
Replace any occurrence of x bound by the λ-operator with the argument A
, o This replacement or substitution processes is called Β-conversion:
Lambda abstraction, functional application and Β-conversion are the main ingredients we
need to deal with semantic construction:
o Once we have devised lambda abstractions to represent lexical items, we only need to
use functional application and Β-conversion to combine semantic representations
compositionally
Given a syntactic constituent R with subparts Ra and Rb, we need to specify
which subpart is to be thought as the functor F and which as the argument A
We then construct the semantic representation of R by functional application
F@A
λ -abstractions for Lexical Items
Representing different basic categories
o Intransitive verbs (verbs with no object) and nouns are 1-place relations which are
missing their argument:
o What about determiners such as ‘a’ and ‘every’ in NPs like ‘a boxer’?
For instance, we’d like to represent the meaning of ‘a boxer walks’ as:
What does each word contribute to this formula? And what is the
contribution of the determiner?
If ‘boxer’ contributes Boxer(x) and ‘walks’ contributes Walk(x) to the formula,
then the determiner ‘a’ must contribute something like Ǝx …
Two bits are missing:
The contribution of the NP (the restriction)
The contribution of the VP (the scope)
We can use lambda abstraction to mark the missing arguments that will be
filled in during semantic construction
This is the representation for existential determiners:
