chart parsing and augmenting grammars cse-391: artificial intelligence university of pennsylvania...

Chart Parsing and Augmenting Grammars

CSE-391: Artificial IntelligenceUniversity of Pennsylvania

Matt Huenerfauth

March 2005

Homework 6

• Due Friday, April 1, 2005. (Two weeks.)

• You will write/modify some grammar rules.

• You will enact some parsing algorithms by hand.

• You will use the chart-parsing Python code from the textbook (we’ll learn about chart parsing today).

Last time: Our grammar

S NP VP VP VVP V NP

NP pronounNP noun V verbNP det adj noun V aux verbNP det noun

• NON-TERMINAL vs. terminal…

Last time: Two Parsing Approaches

• Top Down Parsing– Start with the top-level rule for S.– Blindly try all possible rules to build the sub

pieces of the original S rule. Recurse.– When you back up, forget structures you built.

• Bottom Up Parsing– Start by considering the part of speech of all

the words. Build all the possible ‘local’ pieces of structure, and slowly build larger pieces.

Last time: Top-down parse[The, old, can, can, hold, the, water]

S → NP VP Consider NP…

NP → pronoun?pronoun? fail

NP → noun?noun? fail

NP → det adj noun?det? the

adj?old noun? Can

Succeed.Succeed.

What about the VP?

Last time: Top-down parse[can, hold, the, water]

Consider VP… V → verb?

verb? failV → aux verb?

aux? canverb? hold

succeedsucceedfail [the, water]

Bottom Up Parsing

• To illustrate bottom-up parsing, we will draw a chart diagram.

• For a sentence with k words, we will start with k+1 nodes in the diagram.

• We put edges between adjacent nodes labeled with input words & part of speech.

the old can can hold the water

det adj noun

auxverbnoun

auxverbnoun

verb noun

det noun verb

Drawing an edge…

• As we apply grammar rules to build a parse, we draw more edges:– An edge has a starting and a stopping point.

This represents what input words it covers. – An edge has a label. In the bottom-up

algorithm, it looks like this: VP V NP– This means we just found a V and a NP, and

we have combined them to build VP.– We’ll see an example of this on the next slide.

Bottom Up Parsing


det adj noun

auxverbnoun

auxverbnoun

verb noun

det noun verb

NP det noun

VP V NP

V aux verb

V aux verb NP det nounNP det adj noun

VP V NP

VP V NP

VP VP NP

S NP VP

NP noun NP noun

V verb

NP noun

V verb

NP noun

V verb

NP noun

V verb

Bottom Up Parsing


det adj noun

auxverbnoun

auxverbnoun

verb noun

det noun verb

V aux verb NP det nounNP det adj noun

VP VP NP

S NP VP

Three Parsing Algorithms

• Top Down Parsing– Tries lots of rules, does a lot of backtracking.– Has to re-build structures that it forgets about.– Feels a lot like uninformed search.

• Bottom Up Parsing– Starts with the small pieces of structure, but it

builds everything it can. Don’t need all of it.– Most of it not used in the final complete parse.

• Top-Down Chart Parsing

(Top Down) Chart Parsing

• Advantages:– Only build those pieces of structure that we

actually need to parse the entire sentence.– Remember pieces of structure that we build in

a chart so that if we have to backtrack, we don’t have to build those sub-structures all over again.

Add one more rule…

• The first thing we do is add one more rule to our grammar. Our goal will be to produce a parse of the whole sentence that produces an S’:

S’ S

• So, this will be the first rule we’ll try to process with the algorithm…

A New Kind of Edge

• Instead of just drawing edges in our chart diagram for complete structures that we find, now we’ll also add edges that represent incomplete structures that we want to find…

• For example, an edge labeled: VP V • NP could be used to represent a point in the algorithm where we really want to build a VP, and we have already found a V but have not yet found a NP to complete it.

• Why would we want such a thing? We’ll see…

the can can falldet aux

verbnoun

auxverbnoun

verbnoun

How to Start

the can can fall

det auxverbnoun

auxverbnoun

verbnoun

S’•S

Our goal is to build an edge covering the whole sentence labeled S’.So, we first add an edge that covers no words at the start of the sentence.Since we haven’t found any S yet in order to fulfill the S’ rule, then we have to put the dot in front of the S.

So, now our mission is to find an S in this sentence so that we can produce an S’. In other words, when we add edges to the chart thatcontain dots, then we know we are looking for the thing to the rightof the dot.

The Algorithm

• When we add an edge to the diagram, we give it a blue label. After we “process” the edge, then the label turns black. We will process edges in the order they are added to the diagram.

• Process edges like a “queue” (breadth-first feel). Could also use “stack” but this is less traditional. We really want all parses, not just one.

• How to we “process” an edge? It depends on where the dot is.– Before a NON-TERMINAL? – Before a terminal?– At the end?

PREDICT future rules…

• If the dot is before a NON-TERMINAL.

• We look up all the rules in the grammar that can produce that NON-TERMINAL. – We add all of these rules to the diagram as

edges which cover no words.– We put a dot in front of the first item after the

arrow.– Remember: All new edges have blue labels.

Dot before NON-TERMINAL:“Predict”

the can can fall

det auxverbnoun

auxverbnoun

verbnoun

S’ • S(1)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun

S’ • SS • NP VP


(1)

(2)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun

S’ • SS • NP VPNP • proNP • nounNP • det nounNP • det adj noun


(1)

(2)

(3)

(4)

(5)

(6)

SCAN input words…

• When the dot is before a terminal…

• Check the next word of input to see if any of its parts of speech matches the terminal symbol.

• If there is a match, then we:spread the rule to the right and we move the dot to the right as well.

the can can fall

det auxverbnoun

auxverbnoun

verbnoun


Dot before terminal: “Scan”

(1)

(2)

(3)

(4)

(5)

(6)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun



NP det • noun

(1)

(2)

(3)

(4)

(5)

(6)

(7)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun



NP det • nounNP det • adj noun

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun




NP det noun •

(1)

(2)

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(4)

(5)

(6)

(7)

(8)

(9)

Edge Extension

• When the dot is at the end of the label…

• Assume current edge is labeled: X … •– Look at all of the edges that ended where the

current edge began. – If any of these preceding edges have a label

of the form: … … • X … – Then spread this preceding edge across the

width of the current edge, and label it:… … X • … (move the dot to the right)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun


Dot at end: “Edge Extension”


NP det noun •

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun


Dot at end: “Edge Extension”


NP det noun •S NP • VP

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Remember…

• Process one edge at a time in the order they were added to the diagram. (queue)

• If the dot is just before:– a NON-TERMINAL:

Then “predict.” (grab rules from the grammar)– a terminal:

Then “scan.” (compare to POS of next word)– the end of the label:

Then “edge extend.” (check preceding edges)

• Don’t add an edge with same exact label and same exact span as a previous one.

the can can fall

det auxverbnoun

auxverbnoun

verbnoun



(7)

(8)

(9)

(10)


(1)

(2)

(3)

(4)

(5)

(6)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun




(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

VP • VVP • V NP

(11)

(12)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun




(1)

(2)

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(6)

(7)

(8)

(9)

(10)

VP • VVP • V NPV • verbV • aux verb

(11)

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(14)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun




(1)

(2)

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(6)

(7)

(8)

(9)

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V verb • (15)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun




(1)

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V verb •V aux • verb

(15)

(16)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun




(1)

(2)

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(5)

(6)

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V verb •V aux • verbVP V •VP V • NP

(15)

(16)

(17)

(18)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun




(1)

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V aux verb • (19)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun




(1)

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(15)

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V aux verb • (19)

S NP VP • (20)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun




(1)

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(11)

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(15)

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V aux verb • (19)

S NP VP • (20)

NP • proNP • nounNP • det nounNP • det adj noun

(21)

(22)

(23)

(24)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun




(1)

(2)

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(7)

(8)

(9)

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(11)

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(15)

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V aux verb • (19)

S NP VP • (20)


(21)

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VP V • VP V • NP

(25)

(26)

the can can fall

det auxverbnoun

auxverbnoun

verbnoun




(1)

(2)

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(5)

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(7)

(8)

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(11)

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(15)

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V aux verb • (19)

S NP VP • (20)


(21)

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(24)

VP V • VP V • NP

(25)

(26)

We’ll stop here for now, but you would continue until you found a S’ edge that covered all the words.

Hybrid Approach

• This use of dots helps us understand what we are looking for – it gives this parsing algorithm its top-down feel. – In other words, we are guided to look for only those

syntactic structures that will help build a parse for the whole sentence.

• The use of a chart diagram gives this algorithm a bottom-up feel (we used a diagram in the bottom-up algorithm).

Augmenting a Grammar

How Do You Modify a Grammar

• What if we want to extend a grammar to include a new linguistic structure?

S NP VP VP VVP V NP

NP pronounNP noun V verbNP det adj noun V aux verbNP det noun

Adding Adverbs

• How would we augment this grammar to add adverbs and adverb phrases?

• We’d like to allow sentences like:

The can can fall quickly.

The can can fall quickly and quietly.

The can can quickly fall.

Quickly the can can fall.

Modify the lexicon…

• Let’s add the new words we need…– Quickly, quietly, and.

• What part of speech are they?– Adverb: quickly– Adverb: quietly– Conjunction: and

Modify Grammar (1)

• We’d like to allow single adverbs and adverbs combined with ‘and’ to occur in sentences…

– So we add a new kind of NON-TERMINAL to the grammar: an adverb phrase. ADVP

ADVP adv

ADVP adv conj adv

– This defines the internal structure of an adverb phrase.

Modify Grammar (2)

• Now that we have specified the internal structure of an adverb phrase, we should add rules to specify how to position adverb phrases within entire sentences.

• Where do we want to allow adverb phrases to go?– Start of sentence.– End of sentence.– Between aux and verb.

Beginning / End of Sentences

Modify the rules for a sentence…

S NP VPS ADVP NP VPS NP VP ADVP

But how to we position adverb phrases between aux’s and verb’s ?

Between AUX and VERB

• We have to edit a different rule to allow adverbs between Auxiliaries and Verbs.

V verb

V aux verb

V aux ADVP verb

In between aux and verb…

Our New GrammarS NP VP VP V

S ADVP NP VP VP V NP

S NP VP ADVP

V verb

NP pronoun V aux verb

NP noun V aux ADVP verb

NP det adj noun

NP det noun ADVP adv

ADVP adv conj adv

Our New Lexicon

Same entries as before, plus…

adv(quickly)

adv(quietly)

conj(and)

chart parsing and augmenting grammars cse-391: artificial intelligence university of pennsylvania...

Documents

vp v verb

old noun

water s np vp

parsing algorithms

water slide

parsing approaches

terminal slide

original s rule