reasoning with dependency structures and lexicographic definitions using unit graphs maxime...
TRANSCRIPT
![Page 1: Reasoning with Dependency Structures and Lexicographic Definitions using Unit Graphs Maxime Lefrançois, Fabien Gandon [ maxime.lefrancois | fabien.gandon](https://reader036.vdocuments.mx/reader036/viewer/2022062713/56649f475503460f94c69454/html5/thumbnails/1.jpg)
Reasoning with Dependency Structures
and Lexicographic Definitions using Unit Graphs
Maxime Lefrançois, Fabien Gandon[ maxime.lefrancois | fabien.gandon ] @inria.fr
Depling’13, August 30th 2013, Prague
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Knowledge Representation
•answers recurrent needs▫represent▫manipulate▫query▫reason▫share▫...
•here: applied to the linguistic domain▫Meaning-Text Theory
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Choose Formalism
Populate
Applications
t
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Choose Formalism
Populate
Applications
t
1. Choose Formalism
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Semantic Actant Slots (SemASlots)= Participants of the linguistic situation denoted by L
that 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
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Semantic Actant Slots (SemASlots)= Participants of the linguistic situation denoted by L
that 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
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Linguistic 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
logicalpredicate≠
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Linguistic 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
logicalpredicate≠
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Linguistic 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
logicalpredicate≠
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Existing KR Formalisms
•Semantic Web Formalisms▫RDF - oriented labelled graphs
▫OWL - Description Logics
▫SPARQL - Query, ...
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Existing KR Formalisms
•Semantic Web Formalisms▫RDF - oriented labelled graphs
No Semantics
▫OWL - Description LogicsOnly binary relationsReify ? -> No Semantics
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Existing KR Formalisms
•Conceptual Graphs▫SowaOriented labelled Graphs▫Sowa drew his inspiration from Tesnière▫Rules, reasoning, (Baget, Mugnier, Chein, ...)
▫Concepts and Relations definitions, (Sowa, Leclère, ...)
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Existing KR Formalisms
•Conceptual Graphs
Alternation Concept – Relation
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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t
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
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t
Draw inspiration from GC
andDevelop 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
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t
The Unit Graphs Formalism
Choose Formalism
Populate
Applications
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Draw inspiration from GC
andDevelop a RDF syntax
to exchange knowledge
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t
The Unit Graphs FormalismWhat reasoning capabilities ?
Choose Formalism
Populate
Applications
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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1. Choose Formalism
•Needs, problems•Existing Knowledge Representation
Formalisms•The Unit Graphs formalism
▫Unit Graphs▫Rules and Definitions
•Reasoning with Unit Graphs▫Logical Semantics▫Entailment problem
Lefrançois, Gandon, The Unit Graphs Framework: Linguistic Knowledge Representation
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Units – Representations
(c.f., Mel’čuk, 2004)
Unit Types – Lexicon
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Unit Types
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Specify How their units are to be linked
to other units in Unit Graphsthrough Actantial Structure:
Actant Slots (ASlots) Signatures
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Unit Graphs
are defined over a Support
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Unit 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 ANIMALGrammatical unit type Verb, Noun, plurSurface Semantic unit type (animal)
▫Conjunctive Unit Types (PUTs)A Unit may consist of several conjoint PUTs
{ def, plur, ANIMAL } ((the animals))
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Unit 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 ANIMALGrammatical unit type Verb, Noun, plurSurface Semantic unit type (animal)
Are pre-orderedplur pluralizable
/animal\ /dog\
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Unit 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
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Unit 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: NumbersDeep Syntax: Roman numerals
▫May be Obligatory, Optional, Prohibited
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Organization of the Unit Types Hierarchy with respect to a unique ASymbol sThe 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
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Unit 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
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As we go down the hierarchy, signatures may only be specialized
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Unit 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
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Unit Graphs
are defined over a Support
Unit Node MarkersArbitrary SymbolsEvery 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
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Unit Graphs
are defined over a Support
Unit nodesUnit nodes labels : a type + a markerActantial triplesCircumstantial triplesDeclared equivalences of unit nodes
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Unit Graphs
are defined over a Support
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Unit Graphs
are defined over a Support
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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1. Choose Formalism
•Needs, problems•Existing Knowledge Representation
Formalisms•The Unit Graphs formalism
▫Unit Graphs▫Rules and Definitions
•Reasoning with Unit Graphs▫Logical Semantics▫Entailment problem
Lefrançois, Gandon, The Unit Graphs Framework: Linguistic Knowledge Representation
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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 Homomorphism▫arcs must be preserved ▫labels may get specialized
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36Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Unit Graphs Homomorphism
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37Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Unit Graphs Rules
•A Hypothesis H•A Conclusion G•A partial mapping from nodes of H to nodes
of C
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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
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39Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
PUT Definitions
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1. Choose Formalism
•Needs, problems•Existing Knowledge Representation
Formalisms•The Unit Graphs formalism
▫Unit Graphs▫Rules and Definitions
•Reasoning with Unit Graphs▫Logical Semantics▫Entailment problem
Lefrançois, Gandon, The Unit Graphs Framework: Linguistic Knowledge Representation
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41Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Reasoning with Unit Graphs
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42Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical Semantics of UGs: Closure
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43Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical Semantics of UGs: Closure
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Logical Semantics of UGs: Closure
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45Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical Semantics of UGs: Closure
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46Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical Semantics of UGs: Closure
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47Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical Semantics of UGs: Closure
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48Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical Semantics of UGs: Closure
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49Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical Semantics of UGs: Closure
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50Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical Semantics of UGs: Closure
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51Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
Logical Semantics of UGs: Closure
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1. Choose Formalism
•Needs, problems•Existing Knowledge Representation
Formalisms•The Unit Graphs formalism
▫Unit Graphs▫Rules and Definitions
•Reasoning with Unit Graphs▫Logical Semantics▫Entailment problem
Lefrançois, Gandon, The Unit Graphs Framework: Linguistic Knowledge Representation
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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)
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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 Types▫on the set of definitions
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Conclusions
•Linguistic Knowledge Representation•The Unit Graphs Formalism
▫Hierarchy of Unit Types▫Hierarchy of Circumstantial Symbols ▫Unit Graphs▫Rules and Definitions
•Reasoning with UGs▫Logical Semantics: Unit Graph Closure▫Entailment equivalent to the homomorphism
problem
Lefrançois, Gandon, Reasoning with Dependency Structures and Lex. Definitions using Unit Graphs
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Reasoning with Dependency Structures
and Lexicographic Definitions using Unit Graphs
Depling’13, August 30th 2013, Prague
Thank you