The lexicon in syntax - Computational Linguistics and Spoken ...

2008-11-17 

How to write a grammar 

The lexicon in syntax 

Thorsten Trippel 

Fakultät für Linguistik und Literaturwissenschaft 

Universität Bielefeld 

thorsten.trippel@uni-bielefeld.de 

http://www.spectrum.uni-bielefeld.de/~ttrippel/htwg/ 

1 

How to write a grammar WS 2008-2009

Agenda 

● Heads and dependents 

● Adjuncts and complements 

● Some simple classes of grammars 


2 


Heads and dependents 

• 

Phrase ≔ part of a clause continuing a head 

• 

Head ≔ most important word in a phrase 

• 

Wordclass of head determines wordclass of phrase 

• 

Bears crucial semantic information 

• 

Has the same distribution as the entire phrase 

• 

Can (usually) not be omitted 

• 

Sometimes requires (a) complement(s) 

• 

Dependent part of the phrase which are not the 

≔ 

head 


3 


Generalization 

• 

Subject ≔the subject of a cluase is a phrase of 

one word or more which is headed by a noun 

(NP) 

• 

Predicate ≔ normally a VP; the VP can contain 

dependents 

• 

Heads influence 

• 

Determine dependents (which word classes are possible) 

• 

Agreement of dependents (gender, number, …) 

• 

Case determination 


4 


Adjuncts vs. complements 

Adjuncts ≔ optional additions to a head providing 

extra information 

Complements ≔ often obligatory phrases selected 

by the head 


5 


Adjunct or complement? (see Tallerman, p. 104) 

• 

Optional vs. obligatory phrase 

• 

Adjuncts: always optional 

• 

Complements: often obligatory, esp. with prepositiosn, 

verbs; close relation with the head; selected by the head 

• 

Limited vs. unlimited number of dependent phrases 

• 

Possibly unlimited number of adjuncts 

• 

Strictly limited number of complements 

• 

Properties of PP dependents 

• 

Adjuncts: wide range of head prepostions 

• 

Complements: specific head prepositions 

• 

Decision impossible based on POS 


6 


Head initial or head final languages 

• 

Typological distinction 

• 

English: head initial 

• 

In VP: NP complements after the V 

• 

In PP: NP after the P 

• 

How about NPs? 

• 

Head final languages: 

• 

Turkish 

• 

Japanese 

• 

... 


7 


Ways of writing a grammar 

• 

“'ve been waiting for this for ages...” 

• 

“Sure, how do you write a book” 

• 

“Is there more to grammar than 'It is correct to 

never split an infinitive'?” 


8 


What a grammar is supposed to 

provide: 

A full set of items describing all possible correct 

constructs of a language. (completeness) 

All other constructs should be classified as incorrect 

by the grammar. (soundness) 


9 


The simplest possible grammar: lists 

● No formalism 

● Easy to create 

● List all acceptable sentences: 

● 

● 

● 

● 

● 

● 

Language loses lots of interesting structures. 

Language loses lots and lots of interesting structures. 

Language loses lots and lots and lots of interesting structures. 

Some teachers try to get rid of more students. 

Some teachers try to get rid of more and more students. 

Some teachers try to get rid of more and more and more students. 


10 


Imagine.... 

● ... a language of the "teacher" kind 

● ... every other sentence some and teacher are reversed, i.e.: 

● 

● 

● 

● 

● 

Some teachers try to get rid of more students. 

Teachers some try to get rid of more and more students. 

Some teachers try to get rid of more and more and more 

students. 

Teachers some try to get rid of more and more and more 

and more students. 

*Some teachers try to get rid of more and more and more 

and more students. 


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What we know... 

● There are rules 

● Rules are not expressed in the lists (!) 

● Lists do not "capture a linguistically significant 

generalization" 

● ...luckily there is no natural language where the 

structure depends on the number of words 


12 


Regular expressions 

● Let's pretend: 

● 

There are parts of speech/grammatical categories 

● Verbs, nouns, articles ... 

● Proposal: English grammar is 

● 

● 

● 

● 

● 

● 

● 

A list of patterns: 

ARTICLE NOUN VERB 

ARTICLE NOUN VERB ARTICLE NOUN 

A lexicon: 

ARTICLE: a, the 

NOUN: cat, dog 


VERB: attacked, scratched 

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Possible sentences: 

The cat attacked. 

The cat scratched. 

A cat attacked. 

A cat scratched. 

The dog attacked. 

The dog scratched. 

A dog attacked. 

A dog scratched. 

A dog scratched a cat 

A dog scratched the cat. 

A dog scratched a dog. 

A dog scratched the dog. 

.... 

= 40 combinations 

(2*2*2+2*2*2*2*2=40) 

Not possible to describe: 

Teachers some try to get rid of 

more and more students. 


14 


Solution: Kleene star and plus 

Notation 

Named after Stephen Kleene 

Notation: * or + (superscripts) 

Meaning 

* 

: 0 or arbitrary many (finite) 

+ 

: 1 or arbitrary many (finite) 

Example: 

Some teacher get rid of more [and 

more] * students 

Some teacher get rid of more [and 

more] + students. 

ARTICLE NOUN VERB (ARTICLE 

NOUN)|ADJECTIVE * 

| denotes alternatives "or" 

() means optional 


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A closer look at regular grammars 

patterns making use of 

Kleene star (0 or more) 

Kleene plus (1 or more) 

parenthesis (optionality) 

NOUN (and NOUN) + chase a cat. 

NOUN (and NOUN) + VERB a cat. 

NOUN (and NOUN) + VERB a NOUN 

(and NOUN)*. 

DET ADJ NOUN (KONJ NOUN) 

VERB DET ADJ NOUN ((DET) KONJ 

ADJ NOUN) 

.... 

Problem: 

how do you indicate that DET ADJ 

NOUN is one “unit”? 

These units are called phrases 

or (syntactic) constituents 


16 


Context Free (Phrase Structure) 

Grammar 

● Contains rules: A→φ 

● Include phrases 

● Grammatical categories 

● Grammatical categories = 

● Parts of speech ('lexical 

category') 

● 

● 

● Types of phrase 

('nonlexical category' or 

'phrasal category') 

● 

● Contains a lexicon: 

● Words 

● 

A nonlexical category, 

φ regular expression 

from lexical and/or 

nonlexical category 

“→” means “can consist 

of 

Rules called phrase 

structure rules 


17 


Example grammar 

Rules 

S→ NP VP 

NP → (D) A* N PP* 

VP → V (NP) (PP) 

PP → P NP 

Lexicon 

D: the, some 

A: big, brown, old 

N: birds, fleas, dog, 

hunter 

V: attack, ate, watched 

P: for, beside, with 

What do sentences look 

like? 


18 


CFG as a tree 

S 

NP 

VP 

D A A N PP V NP PP 

P NP D N P NP 

D 

N 

The big brown dog with fleas watched the birds beside the hunter 


19 


Oh wow, we have seen some of that 

before... 

• 

Branching into phrases 

• 

Each phrase has a head 

• 

Some have adjuncts 

• 

Some have complements 

• 

Some have arguments 


20 


Definition of grammar 

● A Grammar G = consists of 

● 

an alphabet Φ of non terminal symbols (or 

variables) 

● an alphabet Σ of terminal symbols, where Φ∩Σ =∅ 

● a set R ⊆ Γ 

* 

‧ Γ * 

of replacement rules (mappings) 

, where Γ is the complete alphabet Φ⋃Σ and 

α ∉ Σ * 

● a start symbol S ∈ Φ 

● Rules are pairs of , usually written α→β 

● Unrestricted http://www.spectrum.uni-bielefeld.de/~ttrippel/htwg/ 

(general) grammar (Type 0 grammar) 21 


Example grammar (rep.) 

Rules 

S→ NP VP 

NP → (D) A* N PP* 

VP → V (NP) (PP) 

PP → P NP 

Lexicon 

D: the, some 

A: big, brown, old 

N: birds, fleas, dog, hunter 

V: attack, ate, watched 

P: for, beside, with 


Terminals: words in the 

lexicon 

Non-terminals: NP, VP, 

PP, D, A, V, P, N... 

Rules 

Start symbol: S 

22 


Definition of language 

● Let G = be a grammar. Then 

● L(G) = {w ∈Σ* | S ⇒* W} is called the language 

generated by G. 

● Two grammars are equivalent if they generate the 

same language 


23 


The Chomsky Hierarchy 

● Type 0: unrestricted grammar (see also deterministic and 

non deterministic Turing machines) 

● Type 1: context sensitive grammars 

● Type 2: context free grammars 

● Type 3: regular language/regular grammars 


24 


Homework 

• 

Take the sentences from your last homework 

• 

Use the simple sentences/main clauses, relative clauses 

only 

• 

List all terminal symbols! 

• 

Determine all phrases! 

• 

Where is your start symbol? 

• 

Can you draw a syntax tree for them? 


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The lexicon in syntax - Computational Linguistics and Spoken ...

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