# Logic Form Representations

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## Logic Form Representations

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Slide1

Logic Form Representations

Reading: Chap 14, Jurafsky & Martin

Slide set adapted from Vasile Rus, U. Memphis

Slide2

Problem Description

There is need for Knowledge Bases

1.

find the

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 WordNet

Slide4

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 language

Slide5

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 reasoning

How?

Induction

Abduction

Slide8

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 WordNet

Slide9

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 relations

Slide10

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 representation

Slide11

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)

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 predicates

Slide12

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 Information

Slide13

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

{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

Architecture

Slide18

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 parserFor 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

PP

Slide20

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)

: they borrow a virtual argument representing the head they modify

E.g.: american:a#1(x1)

of(x1, x2) & United_States_Of_America(x2)

: 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 treesThe grammar is largeIf 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

1,958

1,837

Verb

5,392

Noun

Rules

Part of speech

Slide22

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 Rule

Slide23

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 LF

Slide24

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% coverageBefore 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 institution

Slide25

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 ignoredEverything in a prenominal position plays the role of a modifierVPs:Negation is ignoredTenses 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 rule

Slide26

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)

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 passive

The type of preposition: by or non-by

Slide27

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 subject

Slide28

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