Reasoning with Dependency PowerPoint Presentation, PPT

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Structures . and . Lexicographic. . Definitions. . using. Unit Graphs. Maxime Lefrançois, Fabien . Gandon. [ . maxime.lefrancois. | . fabien.gandon. ] @. inria.fr. Depling’13, August 30. th. ID: 645999

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Slide1

Reasoning with Dependency Structures and Lexicographic Definitions using Unit Graphs

Maxime Lefrançois, Fabien Gandon

[

maxime.lefrancois

| fabien.gandon ] @inria.fr

Depling’13, August 30

2013, Prague

Slide2

Knowledge Representationanswers recurrent needsrepresentmanipulatequeryreasonshare...here: applied to the linguistic domainMeaning-Text Theory

Lefrançois, Gandon, Reasoning with Dependency Structures and

Lex. Definitions using Unit Graphs

Slide3

3Choose Formalism

Populate

Applications

Lefrançois,

Gandon

, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Slide4

4Choose Formalism

Populate

Applications

Choose

Formalism

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide5

5Semantic Actant Slots (SemASlots

)= Participants of the linguistic

situation denoted

by Lthat have a

favoured position in sentences constructed

with L

Linguistic

Predicates

Need

Theory

Semantic

Actants

(

Mel’cuk

, 2004)

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide6

6Semantic Actant Slots (SemASlots

)= Participants of the linguistic

situation denoted

by Lthat have a

favoured position in sentences constructed

with L

Linguistic

Predicates

Need

Theory

Semantic

Actants

(

Mel’cuk

, 2004)

linguistic

criterions

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide7

7Linguistic Predicates

Need

Theory

of Semantic

Actants

(

Mel’cuk, 2004)

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

(

eat

)

(Paul ;

eggs

;

plate

)

optional

logical

predicate

≠

Slide8

8Linguistic Predicates

Need

Theory

of Semantic

Actants

(

Mel’cuk, 2004)

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

(

outil

)

(Paul ;

Untangle

)

(

outil

)

(Paul ; Carpenter)

(

eat

)

(Paul ;

eggs

;

plate

)

split

optional

logical

predicate

≠

Slide9

9Linguistic Predicates

Need

Theory

of Semantic

Actants

(

Mel’cuk, 2004)

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

an actant

may

predicate

(

outil

)

(Paul ;

Untangle

)

(

outil

)

(Paul ; Carpenter)

(

eat

)

(Paul ;

eggs

;

plate

)

split

optional

logical

predicate

≠

Slide10

Existing KR FormalismsSemantic Web FormalismsRDF - oriented labelled graphs OWL - Description Logics

SPARQL - Query, ...

Lefrançois,

Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Slide11

Existing KR FormalismsSemantic Web FormalismsRDF - oriented labelled graphs No SemanticsOWL - Description Logics

Only binary relations

Reify

? -> No Semantics

11Lefrançois,

Gandon, Reasoning with Dependency Structures and Lex

. Definitions using Unit Graphs

Slide12

Existing KR FormalismsConceptual GraphsSowaOriented labelled GraphsSowa drew his inspiration from

TesnièreRules, reasoning, (

Baget, Mugnier, Chein

, ...)Concepts and Relations

definitions, (Sowa, Leclère, ...)

Lefrançois, Gandon

, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Slide13

Existing KR FormalismsConceptual Graphs Alternation Concept – Relation 13

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex. Definitions using Unit Graphs

Slide14

14t

The Unit Graphs

Formalism

a graph-

based formalism

,to represent

linguistic units

Choose Formalism

Populate

Applications

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide15

15t

Draw inspiration from GCandDevelop a RDF syntax

to exchange knowledge

The Unit Graphs

Formalism

Choose Formalism

Populate

Applications

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide16

16t

The Unit Graphs

Formalism

Choose Formalism

Populate

Applications

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Draw inspiration from GC

and

Develop a RDF syntax

to exchange knowledge

Slide17

17t

The Unit Graphs

Formalism

What

reasoning

capabilities ?

Choose Formalism

Populate

Applications

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide18

1. Choose Formalism18Needs, problems

Existing Knowledge Representation FormalismsThe Unit Graphs

formalismUnit GraphsRules

and DefinitionsReasoning with

Unit GraphsLogical SemanticsEntailment problem

Lefrançois,

Gandon

, The Unit Graphs Framework: Linguistic Knowledge Representation

Slide19

19Units

–

Representations

(c.f., Mel’čuk, 2004)

Unit Types – Lexicon

Lefrançois,

Gandon, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide20

20Unit TypesLefrançois, Gandon

, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Specify

How their

units are to be linked

to other

units in Unit Graphs

through

Actantial Structure

Actant Slots (

ASlots

)

Signatures

Slide21

21Unit Graphs

are

defined over a Support

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide22

22Unit Graphs

are

defined over a Support

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Hierarchy of Unit Types

Primitive Unit Types (

PUTs

)

Lexical unit type ANIMAL

Grammatical unit type

Verb

Noun

plur

Surface Semantic unit type

(

animal

)

Conjunctive

Unit Types (

PUTs

)

A Unit may consist of several conjoint PUTs

{

def

plur

, ANIMAL } (

(

the animals

)

Slide23

23Unit Graphs

are

defined over a Support

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Hierarchy of Unit Types

Primitive Unit Types (

PUTs

)

Lexical unit type ANIMAL

Grammatical unit type

Verb

Noun

plur

Surface Semantic unit type

(

animal

)

Are pre-ordered

plur

pluralizable

animal

\ /

dog

Slide24

24Unit Graphs

are

defined over a Support

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Hierarchy of Unit Types

Unit Types

specify

how

their

units

are to

linked

through

Actantial Structure

Actant Slots (

ASlots

)

Signatures

Slide25

25Unit Graphs

are

defined over a Support

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Hierarchy of Unit Types

Actant Slots

Have

Symbols

Deep Semantics: lexicalized semantic roles

Surface Semantics: Numbers

Deep Syntax: Roman numerals

May

Obligatory

Optional

Prohibited

Slide26

26Organization of the Unit Types Hierarchy

with respect to a unique ASymbol

The complete Unit Types Hierarchy

is an

intricated

superposition of such figures

≃

radix

obligat

prohibet

absurd

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide27

27Unit Graphs

are

defined over a Support

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Hierarchy of Unit Types

Signatures

denote the type of units

that fill an

ASlot

of a unit of a type

Slide28

28As we go down the hierarchy,

signatures may only be specialized

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide29

29Unit Graphs

are

defined over a Support

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Hierarchy of Circumstantial Symbols

Circumstantial Symbols:

Deep and Surface Semantics:

none

Deep Syntax:

ATTR, COORD, APPEND

...

Are organized in hierarchy

ex:

ATTR

deep syntactic

CSymbol

Are signed

Slide30

Unit Graphs

are

defined over a Support

Unit Node Markers

Arbitrary Symbols

Every Element of

identifies a specific unit;

Multiple elements of

may identify the same unit.

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide31

31Unit Graphs

are

defined over a Support

Unit nodes

Unit nodes labels : a type + a marker

Actantial triples

Circumstantial triples

Declared equivalences of unit nodes

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide32

32Unit Graphs

are

defined over a Support

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide33

33Unit Graphs

are

defined over a Support

Lefrançois,

Gandon

, Reasoning with Dependency Structures and

Lex

. Definitions using Unit Graphs

Slide34

1. Choose Formalism34Needs, problems

Existing Knowledge Representation FormalismsThe Unit Graphs

formalismUnit GraphsRules

and DefinitionsReasoning with

Unit GraphsLogical SemanticsEntailment problem

Lefrançois,

Gandon

, The Unit Graphs Framework: Linguistic Knowledge Representation

Slide35

35Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Unit Graphs Homomorphism

« Is UG G

contained in UG H ? »Oriented

Labelled Graphs Homomorphismarcs must be preserved labels

may get specialized

Slide36

36Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Unit Graphs Homomorphism

Slide37

37Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Unit Graphs Rules

A Hypothesis

HA Conclusion GA partial mapping

from nodes of H to nodes of C

Slide38

38Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Unit Graphs Rules

A rule

R is Applicable to G

iif there is a homomorphism H->G

Apply rule R:

add C to G and

merge nodes

Slide39

39Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

PUT Definitions

Slide40

1. Choose Formalism40Needs, problems

Existing Knowledge Representation FormalismsThe Unit Graphs

formalismUnit GraphsRules

and DefinitionsReasoning with

Unit GraphsLogical SemanticsEntailment problem

Lefrançois,

Gandon

, The Unit Graphs Framework: Linguistic Knowledge Representation

Slide41

41Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Reasoning

with

Unit Graphs

Slide42

42Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Logical Semantics of UGs: Closure

Slide43

43Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Logical

Semantics

of UGs

Closure

Slide44

44Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Logical

Semantics

of UGs

Closure

Slide45

45Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Logical

Semantics

of UGs

Closure

Slide46

46Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Logical

Semantics

of UGs

Closure

Slide47

47Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Logical

Semantics

of UGs

Closure

Slide48

48Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Logical

Semantics

of UGs

Closure

Slide49

49Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Logical

Semantics

of UGs

Closure

Slide50

50Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Logical

Semantics of

UGs:

Closure

Slide51

51Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Logical

Semantics of

UGs:

Closure

Slide52

1. Choose Formalism52Needs, problems

Existing Knowledge Representation FormalismsThe Unit Graphs

formalismUnit GraphsRules

and DefinitionsReasoning with

Unit GraphsLogical SemanticsEntailment problem

Lefrançois,

Gandon

, The Unit Graphs Framework: Linguistic Knowledge Representation

Slide53

53Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Reasoning

with Unit Graphs

entails H if and only if

there is a homomorphism from H to

cl(G)

Slide54

54Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs

Future

Work

Problem

: risk of

infinite closure

need to find conditions :on the

hierarchy of Unit Typeson the set of definitions

Slide55

Conclusions55Linguistic Knowledge RepresentationThe Unit Graphs Formalism

Hierarchy of Unit TypesHierarchy of Circumstantial Symbols

Unit GraphsRules and Definitions

Reasoning with UGs

Logical Semantics: Unit Graph ClosureEntailment equivalent to the homomorphism

problem

Lefrançois, Gandon, Reasoning with Dependency Structures and

Lex. Definitions using Unit Graphs

Slide56

Reasoning with Dependency Structures and Lexicographic Definitions using Unit Graphs

Depling’13, August 30

2013, Prague

Thank you

Slide57

Slide58