Grammars and Parsing Grammars and Sentence Structure What makes a - - PowerPoint PPT Presentation

Ch.3 Grammars and Parsing 1

Grammars and Parsing

• Grammars and Sentence Structure
• What makes a good grammar
• A Top-Down Parser
• A Bottom-Up Parser
• Transition Network Grammars

Ch.3 Grammars and Parsing 2

Grammars and Sentence Structure

• Ex. John ate the cat

Tree Representation (S (NP (NAME John)) VP (V ate) ( NP ( ART the) (N cat))))

Ch.3 Grammars and Parsing 3

Tree Terminology

• Trees are special form of a graph which are

consisting of nodes connected by links

• The node at the top is called the root
• The nodes at the bottom are called leaves
• An ancestor of node N is defined as N’s

parent

Ch.3 Grammars and Parsing 4

A Simple Grammar

• 1. S -> NP VP
• 2. VP -> V NP
• 3. NP -> NAME
• 4. NP -> ART N
• 5. NAME -> John
• 6. V -> ate
• 7. ART -> the
• 8. N -> cat

Ch.3 Grammars and Parsing 5

Context Free Grammar(CFG)

• It consists of:

– Terminal symbols – Non-terminal symbols – Production Rules – Starting Symbol

Ch.3 Grammars and Parsing 6

Derivation

• A grammar is said to derive a sentence if

there is a sequence of rules that allow you to rewrite the start symbol into the sentence.

• Two important processes are based on

derivations: sentence generation and parsing

• There are two basic methods of parsing Top

down and Bottom up

Ch.3 Grammars and Parsing 7

What makes a Good Grammar

• Generality, the range of sentences the

grammar analyzes correctly

• Selectivity, the range of non-sentences it

identifies as problematic

• Understandability, the simplicity of the

grammar itself

Ch.3 Grammars and Parsing 8

Writing a Grammar

• Try to group words to form a constituent
• Try to construct a new sentence that involves that

group of words in a conjunction with another group of words classified as the same type of constituent

e.g NP-NP I ate a hamburger and a hot dog

but if you define NP -> on NP the sentence I ate a hamburger and on the stove does not work and so the definition is wrong

Ch.3 Grammars and Parsing 9

Writing a Grammar (cont.)

• Another test involves inserting the proposed

constituent into other sentences that take the same category of constituent

e.g John’s hitting of Mary is a NP. It can be inserted

in the following two sentences: John’s hitting of Mary alarmed Sue (S->NP VP) I cannot explain John’s hitting of Mary (VP->VNP)

Ch.3 Grammars and Parsing 10

Grammar Generative Capacity

• Regular grammar, S->aS1, S1->bS2, S2->d

This grammar cannot generate ab, aabb, ….

• Context Free Grammar, S->ab, S->aSb

This grammar cannot generate abc, aabbcc, ……

• Context Sensitive Grammar xAy ->x z y

where A is a symbol x, y are ( possibly empty) sequence

• f symbols, and z is a nonempty sequence of symbols
• Type 0 Grammar are more general and allow

arbitrary rewrite rules

Ch.3 Grammars and Parsing 11

Top Down Parsers

• Start with the starting symbol and attempts to rewrite it

into a sequence of terminals

• The state of the parse at any given time can be represented

as a list of symbols

e.g Starting in the state (s) and applying the rule S-> NP VP, the symbol list will be (NP VP)

• The parser could continue until the state consisted entirely
• f terminal symbols and then check the input sentence. A

better idea is to check the input as soon as it can

• Rather than having a separate rule for each word, a

structure called the lexicon is used to store the possible categories for each word e.g. cried:V, dogs:N, the:ART

Ch.3 Grammars and Parsing 12

Top Down Parsers (cont.)

• With the lexicon specified, a grammar need not contain

any lexical rules

• the current position in the sentence is to be included in the

representation of the state of the parse to memorize the number of terminals that have been matched.

E.g 1 The 2 dogs 3 cried 4 A typical parse state would be ((N VP)2)

• A parsing algorithm that is guaranteed to find a parse if

there is one must systematically explore every possible state ( backtracking)

Ch.3 Grammars and Parsing 13

A Simple Top Down Parsing Algorithm (Example)

Grammar

• 1. S -> NP VP
• 2. NP -> ART N
• 3. NP -> ART ADJ N
• 4. VP -> V
• 5. VP -> V NP

Lexicon

cried:V, dogs:N,V, the:ART, old:ADJ,N, man:N,V

Sentences

• 1. The dogs cried
• 2. The old man cried

Ch.3 Grammars and Parsing 14

Parsing as a Search procedure

• You can think of Parsing as a search problem in

AI

• Two strategies for searching Depth First Search

and Breadth First Search

• DFS uses stack for the possibilities list
• BFS uses queue for the possibilities list
• Left recursion causes DFS to enter into an infinite

loop

Ch.3 Grammars and Parsing 15

A Bottom-Up Chart Parser

• Bottom up parser could be built simply by matching a

sequence of symbol against the LHS of a Production Rule.

• This matching process can be formulated as a search

process

• The state would simply consist of a symbol list, starting

with the words in the sentence.

• Successor states could be generated by exploring all

possible ways to

– rewrite a word by its possible lexical categories – replace a sequence of symbols that matches the RHS of a grammar rule by its LHS symbol

Ch.3 Grammars and Parsing 16

A Bottom-Up Chart Parser (cont.)

• Such simple implementation is expensive
• To avoid this problem, a data structure

called chart is introduced that allows the parser to store partial results

• Matches are considered from the point of

view of one constituent, called the key

Ch.3 Grammars and Parsing 17

Example

• 1. S -> NP VP
• 2. NP -> ART ADJ N
• 3. NP -> ART N
• 4. NP -> ADJ N
• 5. VP -> V
• 6. VP -> V NP
• Assume that you are parsing a sentence that start with an
• ART. With this ART as the key rule 2 and 3 are matched

because they start with ART

• To record this for analyzing the next key, you need to record

that rules 2 and 3 could be continued at the point after the

• ART. Thus you record

2’. NP-> ART@ADJ N 3’. NP -> ART @ N

Ch.3 Grammars and Parsing 18

Example (cont.)

• If the next input key is an ADJ, then rule 4 may be started,

and the modified rule 2’ may be extended to give

– 2’’ NP -> ART ADJ @ N

• The chart maintains the constituents derived from the parse

in addition to the rules that have been matched partially. These rules are called active arcs

• The basic operation of a chart-based parser involves

combining an active arc with a completed constituent. The result is either a new completed constituent or a new active arc that is an extension of the original active arc. New completed constituents are maintained on a list called the agenda

Ch.3 Grammars and Parsing 19

A bottom-up charting algorithm

Do until there is no input left:

• 1. If the agenda is empty, look up the interpretations for the

next word in the input and add them to the agenda

• 2. Select a constituent from the agenda( let’s call it constituent

C from position p1 to p2)

• 3. For each rule in the grammar of form X ->C X1….Xn add an

active arc of form X ->@CX1…Xn from position p1 to p2

• 4. Add C to the chart using the arc extension algorithm.

Ch.3 Grammars and Parsing 20

Arc Extension Algorithm

To add a constituent C from position p1 to p2

• 1. Insert C into the chart from position p1 to p2
• 2. For any active arc of the form X ->X1…@C…Xn from

position p0 to p1, add a new active arc X ->X1...C @…Xn from position p0 to p2.

• 3. For any active arc of the form X -> X1 … Xn @C from

position p0 to p1, then add a new constituent of type X from p0 to p2 to the agenda.