Logic Form Representations
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Logic Form Representations Reading: Chap 14, Jurafsky & Martin Slide set adapted from Vasile Rus, U. Memphis Instructor: Rada Mihalcea. Problem Description. There is need for Knowledge Bases E.g.: Question Answering 1. find the answer to Q471: What year did Hitler die?

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Logic Form Representations Reading: Chap 14, Jurafsky & Martin

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Logic form representations reading chap 14 jurafsky martin

Logic Form Representations

Reading: Chap 14, Jurafsky & Martin

Slide set adapted from Vasile Rus, U. Memphis

Instructor: Rada Mihalcea


Problem description

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?


How to build knowledge bases

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


Logic form representation

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


First order representations

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.


First order representations1

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.


Induction abduction

Induction, Abduction

  • Use FOP for automatic reasoning

  • How?

  • Induction

  • Abduction


Logic form transformations

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


Wordnet as a source of world knowledge

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


Wordnet glosses

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


Logic form representation1

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 predicates


An example

Categorial Information

Semantic Information

Functional Information

An Example

  • {lawbreaker, violator}: (someone who breaks the law)

  • Someone:n#1(x1) & break:v#6(e1, x1, x2) & law:n#1(x2)

WordNet sense

Part of Speech

Subject

Direct object


Logic form notation cont d

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)


Comparatives

Comparatives

  • {tower}: (structure taller than its diameter)

  • taller/JJR modifies structure or diameter? Both?

  • Solution: introduce a relation between structureand diameter

  • LF:structure(x1)&taller(x1, x2) &diameter(x2)


Postmodifiers

Postmodifiers

  • {achromatic_lens}: (a compound lens system that forms an imagefreefrom 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)


Relative adverbs

Relative Adverbs

  • {airdock}: (a large building at an airportwhereaircraft 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)


Logic form identification

POS Tag

LF

Transformer

Preprocess

(Extract Defs, Tokenize)

Parse

Logic Form Identification

  • Take advantage of the structural information embedded in a parse tree

S

NP VP-PASS

NP VP-ACT

S -> NP VP

VP

NP

Architecture

Direct object

Subject


Example of logic form

NP

NP

VP

DT

NN

VBN

PP

NP

IN

DT

NN

a monastery ruled by an abbot

Example of Logic Form

monastery:n(x1) rule:v(e1, x2, x1) abbot:n(x2)


Logic form derivation

Identification Rules

Grammar Rule

Rule

Phrase

Synset

NP  DT NN

Noun/NN  noun(x)

(NP (a/DT monastery/NP))

{abbey:n#3}

VP  VP PP

Verb(e, -, -)/VP-PASS by/PP(-,x)  verb(e,x, -) & by(e,x)

(VP (ruled/VBN by/PP))

{abbey:n#3}

NP

VP

DT

NN

VP

PP

Logic Form Derivation

  • Take advantage of the syntactic information from the parser

  • For each grammar rule derive one or more LF identification rules


Building logic forms from wordnet

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)


Building a knowledge base from wordnet

Part of speech

Rules

Noun

5,392

Verb

1,837

Adjectives

1,958

Adverbs

639

Total

9,826

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


Coverage issue

Phrase on the LHS

of Grammar Rule

Occurrences

Unique Rules

Coverage of top ten

Base NP

33,643

857

69%

NP

11,408

244

95%

VP

19,415

450

70%

PP

12,315

40

99%

S

14,740

35

99%

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?


Coverage issue cont d

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


Reduce the number of candidate grammar rules 1

NP

NP

NP

CC

NP

DT

NN

CC

NN

DT

NN

NN

a ruler or institution

a ruler or institution

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


Reduce the number of candidate grammar rules 2

Base NP rule

NP  DT JJ NN|NNS|NNP|NNPS

NP  DT VBG NN|NNS|NNP|NNPS

NP  DT VBN NN| NNS | NNP|NNPS

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)


Map grammar rules into lf rules

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 passive

      • The type of preposition: by or non-by


Logic form derivation results

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


Question answering application

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


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