logic form representations reading: chap 14, jurafsky & martin

Logic Form Representations

Reading: Chap 14, Jurafsky & MartinSlide 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?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?

Manually- building common sense knowledge bases- see Cyc, Open Mind Common Sense

Automatically - from open text - from dictionaries like WordNet

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

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 Representations

3. Canonical FormDoes 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 VariablesThe ability to draw inferences from the representationsServes(x, Vegetarian Food) --> EatAt(Vegetarians, x)

5. ExpresivenessRepresentations should be expressive enough to handle a

wide range of subjects.

Induction, Abduction

Use FOP for automatic reasoning

How?

• Induction• Abduction

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

• [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

• 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 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

• {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

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

• {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)

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)

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)

Logic Form Identification

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

NP VP

S -> NP VP NP VP-PASSNP VP-ACT

Direct object Subject

S

Preprocess(Extract Defs, Tokenize) POS Tag Parse LF

Transformer

Architecture

Example of Logic Form

NP

NP VPDT NN VBN PP

IN NP

DT NN

a monastery ruled by an abbot monastery:n(x1) rule:v(e1, x2, x1) abbot:n(x2)

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

SynsetPhraseRuleGrammar Rule

Identification Rules

NP

DT NN

VP

VP PP

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

• 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

9,826Total639Adverbs

1,958Adjectives1,837Verb5,392NounRulesPart of speech

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%4012,315PP99%3514,740S

70%45019,415VP

95%24411,408NP

69%85733,643Base NP

Coverage of top tenUnique RulesOccurrencesPhrase on the LHSof Grammar Rule

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)

• 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 NNNP CC NP

DT NN NN

a ruler or institution

a ruler or institution

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|NNPSNP DT JJ NN|NNS|NNP|NNPSBase NP rule

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• 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

• 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

logic form representations reading: chap 14, jurafsky & martin

Documents