FMZ

Elaborazione del linguaggio naturale

Fabio Massimo Zanzotto

FMZ

Part six

Tree Adjoining Grammars

FMZ

Our Aim

Lines of development

Grammatical Representation Power: Build a formalism/model able to give the possibility of reducing the unnecessary interpretations

Grammar Use: Build a formalism (and an associated algorithm) able to represent partial analysis

FMZ

Our Aim

Lines of development

Grammatical Representation Power:

• CFG (context free grammars) DCG

• Feature Structures

Grammar Use:

• CYK

• Chart and Early Algorithm

FMZ

Lesson learnt

• Lexicon (i.e. words) is a very important piece of the Language and of the language model

• Words carry meaning and govern the syntactic structure of sentences

FMZ

What we observed

Toy Examples:

... La vecchia porta la sbarra ...

... Il vecchio porta la sbarra ...

... Flying planes can be dangerous ...

... Flying planes is dangerous ...

FMZ

Continuing the observation of the languages

Some more toy examples:... Il ragazzo mangia la mela con il coltello ...

... L’uomo guarda il monitor con gli occhi stralunati ...

... Le azioni della acme inc aumentano in tre settimane da 2 euro a 3 euro ...

How many interpretations are possible for these sentences?

FMZ

Subcategorisation frames

Necessary subcategorisation frames:... Il ragazzo mangia la mela con il coltello ...

((NP) mangiare (NP) (PP(con)))

... L’uomo opera il paziente di appendicite ...((NP) operare (NP) (PP(di)))

... Le azioni della acme inc aumentano in tre settimane da 2 euri a 3 euro ...

((NP) aumentare (PP(da)) (PP(a)))

FMZ

Modelling Subcat Frames in CFGs

Target Frame: ((NP) mangiare (NP) (PP(con))) S NP VP | NP VP(mangiare)

NP NP SBAR

VP VerbX NP | VerbX NP PP

VerbX Verb | Modal Verb

VP(mangiare) VerbX(mangiare) NP | VerbX (mangiare) NP PP(con)VerbX(mangiare) Verb(mangiare) | Modal Verb(mangiare)

NP Art Noun | Art Adj Noun | Noun | Verb Noun | NP PP

PP Prep NP

FMZ

Observations

Il ragazzo mangia la mela a mezzogiorno con il coltello

How do we modify those(?):VP(mangiare) VerbX(mangiare) NP | VerbX

(mangiare) NP PP(con)VerbX(mangiare) Verb(mangiare) | Modal

Verb(mangiare)

FMZ

Summing up

• We understood that subcategorisation can indicate preferred sentence readings

• We want to build lexicalised rules, that is, rules governed by lexical elements (words)

• We want to empower the grammar

FMZ

Idea!!!

• Lexicalised rules may be partial tree!((NP) aumentare (PP(da)) (PP(a)))

aumentare

V

VP

S

NP

PP PP

IN IN

da a

NPNP

FMZ

Defining better our aim

• We want a lexicalised grammar– each rule (partial tree) has to at least a lexical item

• We want a grammar equivalent to the a given grammar– weak equivalence: equivalence in the language

recognised

– strong equivalence: equivalence in generated trees with respect to input sentences... remember that the structure define the “meaning”

FMZ

Operations in CFG

in the derivation, no terminal symbols are substituted with rewriting rules headed by the same symbol

may be understood as tree substitution

no terminal symbols are substituted with trees headed by the same symbol

is it sufficient to obtain the strong equivalence?

FMZ

Investigating strong equivalence

Given the grammar

and the sequence aaaa, one of the interpretations is:

FMZ

Let’s build the lexicalised grammar

Given the tree collection

the interpretation cannot be obtained!

FMZ

Another example

Given the grammar

it can be lexicalised as follows:

strange rule!!!

FMZ

Another example

The same grammar may be lexicalised also

however, what about this

FMZ

Tree Adjoining Grammars

FMZ

What do we need?

• A new operation!!!

the Tree Adjoining operation

FMZ

Tree Adjoining Example

FMZ

Again the substitution

• The well know operation

FMZ

Substitution example

FMZ

Tree Adjoining again

Does it solve the problem of obtaining the strong equivalence?

This is the solution to the example problem!!!

FMZ

Tree Adjoining again

successive adjoining of (4)

FMZ

More examples

may give the interpretation:

FMZ

What is a grammar now?

It is a collection of:

• initial trees, represent the lexicon, e.g.,

• auxiliary trees, represent grammatical rules, e.g.,

FMZ

Do you remember?

copy-language structures:

Pino, Gino e Rino sono rispettivamente fratello, zio e babbo di Nino

may be read as:

a1a2a3b1b2b3

Exercise: Find a model in TAG for this problem

FMZ

What we have done?

• we have worked on the representation power of the grammar

• we introduced:– lexicalised rules

– the adjoining operation

• where do we pay?– on the parsing algorithm?

FMZ

Question

Have we resolved the problem of selecting between different readings (sentence interpretations)?