Reading Chap 14 Jurafsky amp Martin Slide set adapted from Vasile Rus U Memphis Instructor Rada Mihalcea Problem Description There is need for Knowledge Bases Eg Question Answering 1 ID: 615085
Download Presentation The PPT/PDF document "Logic Form Representations" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Logic Form Representations
Reading: Chap 14, Jurafsky & Martin
Slide set adapted from Vasile Rus, U. Memphis
Instructor: Rada MihalceaSlide2
Problem Description
There is need for Knowledge Bases
E.g.: Question Answering
1.
find the
answer
to
Q471: What year did Hitler die?
in a collection of documents
A:
“
Hitler committed suicide in 1945
”
2
.
how would one
justify
that it is the right answer: using
world knowledge
suicide
– {
kill yourself}
kill – {cause to die
}
Create intelligent interfaces to databases:
E.g.: Where can I eat Italian food?
Or: I'd like some pizza for dinner. Where can I go? Slide3
How to Build Knowledge Bases?
Manually
- building common sense knowledge bases
- see Cyc, Open Mind Common Sense
Automatically
- from open text
- from dictionaries like WordNetSlide4
Logic Form Representation
What representation to use?
Logic Form (LF)
is a knowledge representation introduced by Jerry
Hobbs (1983)
Logic form is a
first-order representation
based on natural languageSlide5
First Order Representations
Fulfil the five main desiderata for representing meaning:
1.
Verifiability
:
Does Maharani serve vegetarian food?
Serves(Maharani, vegetarian food)
A representation that can be used to match a proposition against a knowledge base
2.
Unambiguous representations:
I would like to eat someplace close to UNT.
= eat in a place near UNT
= eat a place
Get rid of ambiguity by assigning a sense to words, or by adding additional information that rules out ambiguity.
A representation should be free of ambiguity.Slide6
First Order Representations
3.
Canonical Form
Does Maharani serve vegetarian food?
Are vegetarian dishes served at Maharani?
Do they have vegetarian food at Maharani?
Texts that have the same meaning should have the same representation.
4.
Inference and Variables
The ability to draw inferences from the representations
Serves(x, Vegetarian Food) --> EatAt(Vegetarians, x)
5.
Expresiveness
Representations should be expressive enough to handle a wide range of subjects.Slide7
Induction, Abduction
Use FOP for automatic reasoningHow? InductionAbductionSlide8
Logic Form Transformations
First order representations
- have the characteristics of FOP
Add some extra information (e.g. POS, word sense)
Derived automatically from text, starting with parse trees
Used for automatic construction of knowledge bases:
- e.g. Starting with WordNetSlide9
WordNet as a Source of World Knowledge
[review]
WordNet, developed at Princeton by Prof. Miller, is an electronic semantic network whose main element is the synset
synset
– a set of synonym words that define a concept
E.g.: {cocoa, chocolate, hot chocolate}
a word may belong to more than one synset
WordNet contains synsets for four parts of speech: noun, verb, adjective and adverb
synsets are related to each other via a set of relations: hypernymy (ISA), hyponymy(reverseISA), cause, entailment, meronymy(PART-OF) and others.
hypernymy
is the most important relation which organizes concepts in a hierarchy (see next slide)
adjectives and adverbs are organized in clusters based on similarity and antonymy relationsSlide10
WordNet glosses
Each synset includes a small textual definition and one or more examples that form a
gloss
.
E.g.:
{suicide:n#1} – {
killing yourself
}
{kill:v#1} – {
cause to die
}
{extremity, appendage, member}
–
{
an external body part that projects from the body
“
it is important to keep the extremities warm
”
}
Glosses are a rich source of world knowledge
Can transform glosses into a computational representationSlide11
Logic Form Representation
A
predicate
is a concatenation of the morpheme
’
s base form, part of speech and WordNet semantic sense
morpheme:POS#sense(list_of_arguments)
There are two types of arguments:
x – for entities
e – for events
The position of the arguments is important
verb:v#sense(e, subject, direct_object, indirect_object)
preposition(head, prepositional_object)
A predicate is generated for each noun, verb, adjective and adverb
Complex nominals are represented using the predicate
nn
:
e.g.:
“
goat hair
”
– nn(x1, x2, x3) & goat(x2) & hair(x3)
The logic form of a sentence is the conjunction of individual predicatesSlide12
An Example
{lawbreaker, violator}: (someone who breaks the law)
Someone:n#1(x1) & break:v#6(e1, x1, x2) & law:n#1(x2)
Part of Speech
WordNet sense
Subject
Direct object
Categorial Information
Semantic Information
Functional InformationSlide13
Logic Form Notation (cont
’
d)
Ignores: plurals and sets, verb tenses, auxiliaries, negation, quantifiers, comparatives
Consequence:
Glosses with comparatives can not be fully transformed in logic forms
The original notation does not handle special cases of postmodifiers (modifiers placed after modifee) respectively relative adverbs (where, when, how, why)Slide14
Comparatives
{tower}: (
structure
taller
than its
diameter
)
taller/JJR
modifies
structure
or
diameter
? Both?
Solution: introduce a
relation
between
structure
and
diameter
LF:
structure(x1)
& taller(x1, x2) & diameter(x2)Slide15
Postmodifiers
{achromatic_lens}: (a compound lens system that forms an
image
free
from chromatic_aberration
)
Free
is a modifier of
image ?
What is the prepositional head of
from
?
Solution:
free_from
–
NEW predicate
LF:
image(x1)
&
free_from(x1, x2)
&
chromatic_aberration(x2) Slide16
Relative Adverbs
{airdock}: (
a large building at an airport
where
aircraft can be stored
)
Equivalent to: (aircraft can be stored
in
a large building at an airport)
LF: large(x1) & building(x1) & at(x1, x2) & airport(x2) &
where(x1, e1)
& aircraft(x3) & store(e1, x4, x3) Slide17
Logic Form Identification
Take advantage of the structural information embedded in a parse tree
NP
VP
S -> NP VP
NP VP-PASS
NP VP-ACT
Direct object
Subject
S
Preprocess
(Extract Defs, Tokenize)
POS Tag
Parse
LF
Transformer
ArchitectureSlide18
Example of Logic Form
NP
NP
VP
DT
NN
VBN
PP
IN
NP
DT
NN
a monastery ruled by an abbot
monastery:n(
x
1) rule:v(
e
1,
x
2,
x
1) abbot:n(
x
2)Slide19
Logic Form Derivation
Take advantage of the syntactic information from the parser
For each grammar rule derive one or more LF identification rules
{abbey:n#3}
(VP (ruled/VBN by/PP))
Verb(e, -, -)/VP-PASS by/PP(-,x)
verb(e,x, -) & by(e,x)
VP
VP PP
{abbey:n#3}
(NP (a/DT monastery/NP))
Noun/NN
noun(x)
NP
DT NN
Synset
Phrase
Rule
Grammar Rule
Identification Rules
NP
DT
NN
VP
VP
PPSlide20
Building Logic Forms from WordNet
From definitions to axioms
WordNet glosses transformed into axioms, to enable automated reasoning
Specific rules to derive axioms for each part of speech:
Nouns
: the noun definition consists of a genus and differentia. The generic axiom is: concept(x)
genus(x) & differentia(x).
E.g.: abbey(x1)
monastery(x1) & rule(e1, x2, x1) & abbot(x2)
Verbs
: are more trickier as some syntactic functional changes can occur from the left hand side to the right hand side
E.g.: kill:v#1(e1, x1, x2, x3)
cause(e2, x1, e3, x3) & die(e3, x2)
Adjectives
: they borrow a virtual argument representing the head they modify
E.g.: american:a#1(x1)
of(x1, x2) & United_States_Of_America(x2)
Adverbs
: the argument of an adverb borrows a virtual event argument as they usually modify an event
E.g: fast:r#1(e1)
quickly:r#1(e1)Slide21
Building a Knowledge Base from WordNet
Parse all glosses and extract all grammar rules embedded in the parse trees
The grammar is large
If we consider that a grammar rule can map in more than one LF rules the effort to analyse and implement all of them would be tremendous
9,826
Total
639
Adverbs
1,958
Adjectives
1,837
Verb
5,392
Noun
Rules
Part of speechSlide22
Coverage issue
Group the grammar rules by the non terminal on the Left Hand Side (LHS) and notice that the most frequent rules for some class cover most of the occurrences of rules belonging to that class
The coverage of top 10 most frequent grammar rule for phrases as measured in 10,000 noun glosses.
What does this remind you of?
99%
40
12,315
PP
99%
35
14,740
S
70%
450
19,415
VP
95%
244
11,408
NP
69%
857
33,643
Base NP
Coverage of top ten
Unique Rules
Occurrences
Phrase on the LHS
of Grammar RuleSlide23
Coverage issue (cont
’
d)
Two phases:
Phase 1: develop LF rules for most frequent rules and ignore the others
Phase 2: select more valuable rules
The accuracy of each LF rule is almost perfect
The performance issue is mainly about how many glosses are entirely transformed into LF
i.e. how many glosses the selected grammar rules fully map into LFSlide24
Reduce the number of candidate grammar rules (1)
Selected grammar rules for baseNPs (non-recursive NPs) have only a coverage of 69%
Selected grammar rules for VPs have only 70% coverage
Before selecting rules for baseNPs we make some transformations to reduce more complex ones to simpler ones
Coordinated base NPs are transformed into coordinated NPs and simple base NPs
NP
NP
DT
NN
CC
NN
NP
CC
NP
DT
NN
NN
a ruler or institution
a ruler or institutionSlide25
Reduce the number of candidate grammar rules (2)
Base Nps:
Determiners are ignored (an increase of 11% in coverage for selected grammar rules for base NPs)
Plurals are ignored
Everything in a prenominal position plays the role of a modifier
VPs:
Negation is ignored
Tenses are ignored (auxiliaries and modals)
NP
DT VBN NN| NNS | NNP|NNPS
NP
DT VBG NN|NNS|NNP|NNPS
NP
DT JJ NN|NNS|NNP|NNPS
Base NP ruleSlide26
Map grammar rules into LF rules
Selected grammar rules map into one or more Logic Form rules
Case 1: grammar rule is mapped into one LF rule
Grammar rule: PP -> IN NP
LFT: prep(_, x)
prep(_, x) & headNP(x)
Case 2: grammar rule is mapped into one or more LF rules:
Grammar rule: VP -> VP PP
LFT 1: verb(e, x1, _)
verb-
PASS
(e,x1, _) & prep-
By
(e, x1)
LFT 2: verb(e, _, x2)
verb-
PASS
(e, _, x2) & prep-
nonBy
(e, x2)
To differentiate among the two cases we use two features:
The mood of the VP: active or passiveThe type of preposition: by or non-bySlide27
Logic Form Derivation Results
Phase 1:
From a corpus of 10,000 noun glosses extract grammar rules, sort them by the nonterminal on the LHS, select the most frequent grammar rules and generate LF rules for them
Manually develop a test corpus of 400 glosses
Test the implemented LF rules on 400 noun glosses
72%
coverage (with almost 100% accuracy)
Phase 2:
Select iteratively more rules that bring an increase in coverage of at least
For glosses
was established at 1%
This resulted in a total number of 70 grammar rules selected
The new coverage achieved is 81%
Open issue: how to fully cover the remaining 19% of glosses which are not fully transformed
using a set of heuristics
E.g.: if the subject argument of a verb is missing use the first previous noun as its subjectSlide28
Question Answering Application
Given a question and an answer the task is to select the answer from a set of candidate answers and to automatically justify that the answer is the right answer
Ideal case: all the keywords from the question together with their syntactic relationship exist in the answer
Question: What year did Hitler die?
Perfect Answer: Hitler died in 1945.
Real case:
Real Answer: Hitler committed suicide in 1945.
Requires extra resources to link suicide to die: use WordNet as a knowledge base