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Definitions
Let us recall these definitions
 
 

Grammatical categories known to most competent speakers of English:
 

More Definitions:

• Phrases of many different types:
 
 

Grammar formalisms
 

1. Linguistic Naturalness

The notation for the formalism should allow and encourage to encode their linguistic descriptions in a manner that is easy to understand and modify. The notation should have some empathy with the predominant paradigms in syntax analysis.
 

2. Mathematical Power

Notational restrictions on grammar formalisms can seriously limit the class of grammars that can be expressed. Conversely, minor changes in notation may render the formalism more powerful - capable of representing a larger class of grammars.

Phrase Structure Grammar:
 

A Phrase Structure Grammar has four components:
 

Inadequacy of Phrase Structure Grammar
 

Problem Categories
conjunctions, aux. verbs, passives

Meaning and derivation trees
Apparently similar structures have different meanings
Apparently dissimilar structures have same meanings.
 

Generative Grammars

Thesis An utterance is characterized as the surface manifestation of a "deeper" structure representing the "meaning" of the sentence.

Generative Grammar: An adequate theory of a language like English must be a statement of finite length which can
(a)account for the infinite number of possible sentences
(b) assign to each a structural description which captures the underlying knowledge of a an idealized native speaker.
 
 

A formal system of rules is just such a statement - a device for producing the sentences of a language.
A formal statement is a model of abstract knowledge and not a model of human behaviour
 

A Generative Grammar is said to be concerned with competence, as opposed to performance

X-bar Grammars

Consider the following description of the verb phrase:
return her book to the library in the afternoon

X-bar Grammars

A comparison with phrase-structure grammar

• The above structure indicates, perhaps, that it is unique to a verb phrase. A number of linguist argue that the same verb phrase can be represented with the help of a much richer structure: a structure that encompasses at least all four major phrasal categories.

• The top node, VP, whose subordinate nodes are all and only the words that constitute the entire verb phrase.

• In between the top node, VP, the maximal projection , and the head node, V, there are a series of nodes, , v-bar. Each ,connects exactly one noun phrase or prepositional phrase to the main line between the head node and the verb's maximal projection. Thus, the sentence tree is a binary tree in which no node has more than two branches.

X-bar Grammars

Prepositional Phrases

• Most prepositional phrases also exhibit the same structure as the verb phrases: the prepositional phrase's maximal projection acting as the superordinate node and a head node connected to the instance word. The intermediate connector tying in a phrase from the right. Therefore, one can use the same structural pattern as was used above for parsing a verb phrase:
 
 

X-bar Grammars

Noun Phrases

• The case of the noun phrases, at least superficially, appears different to the VP and PP in that many a noun phrases having nothing to their right and are preceded on the left by a determiner or a pronoun: like the or his or her. Words that appear on the right are called specifiers.

Consider the phrase the library in the city:
 
 

X-bar Grammars

Prepositional and Verb Phrases

• However, for the structure of the NP to be similar to that of PP or VP, NP's with branches to the right should exist, and, correspondingly, verb phrases and prepositional phrases with branches to the left to exist. Consider the following prepositional and the verb phrases:
 

PP = precisely at Noon;

and VP = all return their books.

X-bar Grammars

Some theoretical notes

• X-bar grammar has been developed as an alternative to the traditional accounts of phrase-structure and lexical categories.

• The argument here is that the rules of phrase structure grammar need to be more constrained and that phrasal categories need to be recognised. This is particularly relevant to the identification of the so-called intermediate categories that are larger than the noun but smaller than the phrase, like very fast or very fast car in the phrase the very fast car. These categories are easily identified formally in the X-bar syntax by a system of X-bars: Each bar, a superscript on the phrasal categories, identifies a level of phrasal expansion:

For example, the following binary tree shows two levels of phrasal expansion, double-bar, single bar and zero bar

X-bar Grammars

Inflection Phrase
 
 

and Sarah returned her book

X-bar Grammars

Complementizer Phrase
 

Consider the CP, that Sarah will return her book:

X-bar Grammars

The binary tree hypothesis states that a binary tree is the best kind of tree for representing sentence structure at all levels. It can be shown that a number of (English) verb phrases, noun phrases and prepositional phrases, conform to the general pattern:
 
 

• XP stands for the four principal phrases:

• X stands for the four major heads:

• Note that all phrases do not need to exhibit all the properties. However, all phrases are instances of the X-bar schema. Words or phrases brought from the right are called complements and those brought from the left are called specifiers. The superordinate node of an X-bar tree is called the maximal projection and intermediate nodes are denoted with a superscript bar on them. The leaves are instances of the phrasal class.
 

X-bar Grammars

Maximal Projection, Head and a note on the binary tree representation

• Maximal Projection: In the X-bar system the largest syntactic category which is formally related to some lexical category by the relation of projection , represented by the largest available value of the feature bar, and identified with the traditional (full) phrasal category associated with that lexical category.

Head: That element of a constituent which is syntactically central in that it is primarily responsible for the syntactic character of the constituent. Currently almost all constituents are generally regarded as projections of lexical heads.

• A binary X-bar tree is a representation that is a tree, in which there are three general types of nodes: X, , and XP. Each node has, at most, two branches and leaves are words.

• In English, specifiers enter XP nodes from one side; complements enter X nodes from the other. The direction from which specifiers and complements enter is language specific. The kind of phrase that can serve as a specifier for a particular kind of XP or complement for a particular kind of  depends on the occupant of the head position, X.
 

X-bar Grammars

Sentences as complementizer phrases

• Sentences can be viewed as complementizer phrases, but most have empty specifier and head positions:
 
 

X-bar Grammars

Noun Phrases, Noun Cases and Governors

Consider the variation in the use of pronouns with case in English that can relate case to person and number:
 
 

The substitution of one pronoun by another is permissible in the following two sentences in that both are grammatically acceptable:

X-bar Grammars

Noun Phrases, Noun Cases and Governors

Why one substitution is grammatically acceptable whilst the other is not?

The previous table shows that whilst one pronoun can generally be substituted by another pronoun, it is the head of the noun phrase actually determines the case of each pronoun. The case is determined by the governing head and government is a property determined by the structure of the X-bar tree.
 

X-bar Grammars

Noun Phrases, Noun Cases and Governors

A binary X-bar representation.
 

X-bar Grammars

Noun Phrases, Noun Cases and Governors

The case determining constraint in terms of X-bar schemas for determining a pronoun's case assignment.
 
 

X-bar Grammars

Noun Phrases, Noun Cases and Governors

Pronouns

Consider the following sentence:

Grammar as knowledge representation
 
 

Generalised Phrase Structure Grammars
 

• Generalised Phrase Structure Grammar (GPSG) is a theory of grammar developed in the 1980's.

• The class of grammars permitted by GPSG is strongly equivalent to the context-free grammars.

• GPSG attempts at characterising natural languages in terms of context free grammars while at the same time the theory does not make any claims at psychological reality.

• GPSG is characterised by the separation of grammatical statements into a metagrammar and an object grammar. The metagrammar contains metarules and other generalisations about the rules of grammar. The object grammar directly licenses local subtrees.
 
 

Generalised Phrase Structure Grammars: (CF-PSG, Type 2)

Grammars should characterize the order of elements in a string as opposed to attempting to reconstruct some hypothesized underlying order.

Grammars discussed are declarative and generally based on a decomposition of syntactic categories into components known as features.

An RHS element may then be a category or a particular symbols of the language. When a CF-PSG rule specifies that an LHS category can be realised as a particular RHS , this realisation is deemed to be possible regardless of the context in which the LHS category appears. The rule does not make any restriction on the context in which this can happen - hence the term 'context free' (Gazdar and Mellish 1989:106).

Generalised Phrase Structure Grammars

Grammars used in computational linguistics employ the following:

(i) A representation for syntactic categories or ‘parts of speech’

(ii) A Data type for:

                                        a. words [and hence a lexicon, wordlist etc.].
                                        b. syntactic rules
                                        c. syntactic structures

Three data types------->parser-------> Instantiated syntactic structures
[words/lexicon/wordlist] [syntactic rules]
 

Definitions

Category (categorisation, categorical):

Categorisation in the field of grammar refers to the establishment of a set of classificatory units or properties used in the description of language. These units or properties have the same basic distribution and which occur as a structural unit throughout the language.

Category in some approaches refer to the classes themselves e.g.. NOUN, VERB, SUBJECT, PREDICATE, NP, UP, etc. Grammatical categories include N, V, VP, NP Grammatical functions or functional categories include SUBJECT, OBJECT, COMPLEMENT. A categorical rule is a rule which expands a category into other categories.

Feature
A term used in linguistics (and phonetics) to refer to any typical or noticeable property of spoken or written language.

• In Generative Grammatical Analysis the term is associated with the way in which words are classified in the lexicon in terms of their grammatical properties, such as

• In Generalised Phrase Structure Grammar grammatical categories are defined in terms of feature specifications - ordered pairs containing a feature and feature value which rules can access.
 

Generalised Phrase Structure Grammars: Exemplar grammars

Grammar:                     Name;
                                    Syntactic Rule-base
                                    Lexical Data-base
 
 

Rule sentence formation
S-->NP, VP

Rule verb
VP-->V, NP

Rule verb
VP-->V

word Ken Clarke:
<cat(egory)>=NP
word StLukes:
<cat>=NP
word clients:
<cat>=NP
word died:
<cat>=V
word employed:
<cat>=V

Generalised Phrase Structure Grammars

Consider the following sentences:

(i). Michael employed miners.

(ii). Michael employed car-workers and car-dealers flourished.

• The following schema introduces the co-ordinate construction and suggests that a given category can consist of two further instances of the same category separated by an item of category 'C', which will turn out to be realized as 'and' or 'or'.
 

An example parser is given below:

Generalised Phrase Structure Grammars

Grammar:         Name
                        Syntactic Rule-base
                        Lexical Data-base

GRAMMAR 2 (CF-PSG)

Rule {simple sentence formation}
S-->NP VP
Rule {intransitive verb}
VP-->V:
    <V arg1> = 0
Rule {single complement verb}
VP-->V:
    <V arg1> = <X cat>
Rule {co-ordination of identical categories}
X0 = X1 C X2:
<X0 cat> = <X1 cat>
<X0 cat> = <X2 cat>
<X0 arg1> = <X1 arg1>
<X0 arg1> = <X2 cat>

word Michael:
    <cat(egory)>=NP
word car-workers:
    <cat>=NP
word miners:
    <cat>=NP
word car-dealers:
    <cat>=NP
word flourished:
    <cat>=V
    <arg1>= 0
word employed:
    <cat>=V
    <arg1> = NP
word and:
    <cat> = C

Generalised Phrase Structure Grammars

Grammar:         Name
                          Syntactic Rule-base
                          Lexical Data-base
 

GRAMMAR 2 (CF-PSG)

The important points to be highlighted here that there are major grammatical categories, like S(entence), NP (Noun Phrase) and V(erbs); that subcategorisation has been used to classify transitive and intransitive verbs (e.g. employed and flourished) not in an ad-hoc manner but through the use of rules; and, that the relationship between categories and features can help in expressing complex co-ordination relationships, like the use of the conjunction and .

Generalised Phrase Structure Grammars

Grammar:         Name
                          Syntactic Rule-base
                          Lexical Data-base
 

GRAMMAR 3 (CF-PSG)

Rule {simple sentence formation}
S-->NP VP
Rule {intransitive verb}
VP-->V:
    <V arg1> = 0
Rule {single complement verb}
VP-->V:
<V arg1> = <X cat>
Rule {prepositional attachment}
PP --> P X:
<P arg1> = <X cat>
Rule {co-ordination of identical categories}
X0 = X1 C X2:
<X0 cat> = <X1 cat>
<X0 cat> = <X2 cat>
<X0 arg1> = <X1 arg1>
<X0 arg1> = <X2 cat>
word Trevor:
<cat(egory)>=NP
word Celia:                                                    word Larry:
<cat>=NP                                                     <cat>=NP
word flourished:                                             word hated:                                     word hated:
<cat>=V                                                       <cat>=V                                         <cat>=V
<arg1>= 0                                                     <arg1>= NP                                   <arg1>= NP
word disapproved:                                         word thought:                                   word looked:
<cat>=V                                                        <cat>=V                                         <cat>=V
<arg1>= PP                                                   <arg1>= S                                      <arg1>= AP
word and:                                                       word handsome
<cat> = C                                                      <cat> = AP

GRAMMAR 3 (CF-PSG)

References

Gazdar, Gerald., and Mellish, Chris. (1989). Natural Language Processing in PROLOG - An Introduction to Computational Linguistics.
Wokingham (England): Addison Wesley Publishing Co.

Introduces computational linguistics and discusses the generalised phrase structure grammars in some considerable detail (Chapter 1 for introduction and Chapters 4 and 5 on grammars)

Winston, Patrick Henry (1992). Artificial Intelligence (Third Edition). Reading (MASS., USA): Addison Wesley Publishing Co.

See chapter on natural language processing, especially on X-bar grammars, entitled 'Expressing Language Constraints' (Chapter 28).