Reasoning with Dependency

Reasoning with Dependency - PPT

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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Reasoning with Dependency

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Presentations text content in Reasoning with Dependency

Reasoning with Dependency Structures and Lexicographic Definitions using Unit Graphs
Maxime Lefrançois, Fabien Gandon
[
maxime.lefrancois
| fabien.gandon ] @inria.fr
Depling’13, August 30
th
2013, Prague
Knowledge Representationanswers recurrent needsrepresentmanipulatequeryreasonshare...here: applied to the linguistic domainMeaning-Text Theory
2
Lefrançois, Gandon, Reasoning with Dependency Structures and
Lex. Definitions using Unit Graphs
3Choose Formalism
Populate
Applications
t
Lefrançois,
Gandon
, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
4Choose Formalism
Populate
Applications
t
1.
Choose
Formalism
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
5Semantic Actant Slots (SemASlots
)= Participants of the linguistic
situation denoted
by Lthat have a
favoured position in sentences constructed
with L
Linguistic
Predicates
Need
1
:
Theory
of
Semantic
Actants
(
Mel’cuk
, 2004)
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
6Semantic Actant Slots (SemASlots
)= Participants of the linguistic
situation denoted
by Lthat have a
favoured position in sentences constructed
with L
Linguistic
Predicates
Need
1:
Theory
of
Semantic
Actants
(
Mel’cuk
, 2004)
+
linguistic
criterions
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
7Linguistic Predicates
Need
1:
Theory
of Semantic
Actants
(
Mel’cuk, 2004)
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
(
to
eat
)
(Paul ;
eggs
;
plate
)
optional
logical
predicate
≠
8Linguistic Predicates
Need
1:
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)
(
to
eat
)
(Paul ;
eggs
;
plate
)
split
optional
logical
predicate
≠
9Linguistic Predicates
Need
1:
Theory
of Semantic
Actants
(
Mel’cuk, 2004)
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
an actant
may
be
a
predicate
(
outil
)
(Paul ;
Untangle
)
(
outil
)
(Paul ; Carpenter)
(
to
eat
)
(Paul ;
eggs
;
plate
)
split
optional
logical
predicate
≠
0
Existing KR FormalismsSemantic Web FormalismsRDF - oriented labelled graphs OWL - Description Logics
SPARQL - Query, ...
10
Lefrançois,
Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
1
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
2
Existing KR FormalismsConceptual GraphsSowaOriented labelled GraphsSowa drew his inspiration from
TesnièreRules, reasoning, (
Baget, Mugnier, Chein
, ...)Concepts and Relations
definitions, (Sowa, Leclère, ...)
12
Lefrançois, Gandon
, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
3
Existing KR FormalismsConceptual Graphs Alternation Concept – Relation 13
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex. Definitions using Unit Graphs
4
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
5
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
6
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
7
17t
The Unit Graphs
Formalism
What
reasoning
capabilities ?
Choose Formalism
Populate
Applications
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
8
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
9
19Units
–
Representations
(c.f., Mel’čuk, 2004)
Unit Types – Lexicon
Lefrançois,
Gandon, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
0
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
1
21Unit Graphs
are
defined over a Support
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
2
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
)
)
3
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
\
4
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
be
linked
through
Actantial Structure
Actant Slots (
ASlots
)
Signatures
5
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
be
Obligatory
,
Optional
,
Prohibited
6
26Organization of the Unit Types Hierarchy
with respect to a unique ASymbol
s
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
7
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
s
of a unit of a type
t
8
28As we go down the hierarchy,
signatures may only be specialized
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
9
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
0
30
Unit Graphs
are
defined over a Support
Unit Node Markers
Arbitrary Symbols
Every Element of
M
identifies a specific unit;
Multiple elements of
M
may identify the same unit.
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
1
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
2
32Unit Graphs
are
defined over a Support
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
3
33Unit Graphs
are
defined over a Support
Lefrançois,
Gandon
, Reasoning with Dependency Structures and
Lex
. Definitions using Unit Graphs
4
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
5
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
6
36Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Unit Graphs Homomorphism
7
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
8
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
9
39Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
PUT Definitions
0
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
1
41Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Reasoning
with
Unit Graphs
2
42Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical Semantics of UGs: Closure
3
43Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical
Semantics
of UGs
:
Closure
4
44Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical
Semantics
of UGs
:
Closure
5
45Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical
Semantics
of UGs
:
Closure
6
46Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical
Semantics
of UGs
:
Closure
7
47Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical
Semantics
of UGs
:
Closure
8
48Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical
Semantics
of UGs
:
Closure
9
49Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical
Semantics
of UGs
:
Closure
0
50Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical
Semantics of
UGs:
Closure
1
51Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical
Semantics of
UGs:
Closure
2
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
3
53Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Reasoning
with Unit Graphs
G
entails H if and only if
there is a homomorphism from H to
cl(G)
4
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
5
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
6
Reasoning with Dependency Structures and Lexicographic Definitions using Unit Graphs
Depling’13, August 30
th
2013, Prague
Thank you
7
8