Grammar Implementation with Lexicalized Tree Adjoining Grammars and - PowerPoint PPT Presentation

Introduction to frame semantics Frames according to this course Example actor x man house locomotion e z mover manner in-region path endp part-of walking path region region Ingredients Atributes (funct. relations): actor , mover , path , manner , in-region , ... Type symbols: locomotion , man , path , walking , region , ... Proper relations: part-of Node labels (variables): e , x , z Core property Every node is reachable from some labeled “base” node via atributes. Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 20 11

Introduction to frame semantics Example (2) Anna ran Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 21 12

Introduction to frame semantics Example (2) Anna ran ‘Anna’ running actor name e person Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 22 12

Introduction to frame semantics Example (2) Anna ran to the station. ‘Anna’ running actor name e person Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 23 12

Introduction to frame semantics Example (2) Anna ran to the station. bounded-motion ‘Anna’ running actor name e person final theme loc-stage loc station Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 24 12

Introduction to frame semantics Example (2) Anna ran to the station.    running ∧ bounded-motion  bounded-motion ‘Anna’ � person �   running     actor name  actor  1 e   name ‘Anna’   person e         loc-stage final     theme      final theme 1            loc [ station ]     loc-stage loc station Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 25 12

Introduction to frame semantics Example (2) Anna ran to the station.    running ∧ bounded-motion  bounded-motion ‘Anna’ � person �   running     actor name  actor  1 e   name ‘Anna’   person e         loc-stage final     theme      final theme 1            loc [ station ]     loc-stage loc station Atribute-value logic e · ( running ∧ bounded-motion ∧ actor : ( person ∧ name � ‘Anna’ ) actor � final theme ∧ final : ( loc-stage ∧ loc : station )) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 26 12

Introduction to frame semantics Example (2) Anna ran to the station.    running ∧ bounded-motion  bounded-motion ‘Anna’ � person �   running     actor name  actor  1 e   name ‘Anna’   person e         loc-stage final     theme      final theme 1            loc [ station ]     loc-stage loc station Atribute-value logic e · ( running ∧ bounded-motion ∧ actor : ( person ∧ name � ‘Anna’ ) actor � final theme ∧ final : ( loc-stage ∧ loc : station )) Translation into first-order logic ∃ x ∃ s ∃ y ( running ( e ) ∧ bounded-motion ( e ) ∧ actor ( e , x ) ∧ person ( x ) ∧ name ( x , ‘Anna’ ) ∧ final ( e , s ) ∧ loc-stage ( s ) ∧ theme ( s , x ) ∧ loc ( s , y ) ∧ station ( y )) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 27 12

Introduction to frame semantics Example (2) Anna ran to the station.    running ∧ bounded-motion  bounded-motion ‘Anna’ � person �   running     actor name  actor  1 e   name ‘Anna’   person e         loc-stage final     theme      final theme 1            loc [ station ]     loc-stage loc station Atribute-value logic e · ( running ∧ bounded-motion ∧ actor : ( person ∧ name � ‘Anna’ ) actor � final theme ∧ final : ( loc-stage ∧ loc : station )) Constraints (short for ∀ e ( running ( e ) → activity ( e )) ), running ⇛ activity loc-stage ⇛ theme : ⊤ ∧ loc : ⊤ , ... Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 28 12

Introduction to frame semantics Example Lexical decomposition templates [Rappaport Hovav/Levin 1998] (3) [[ x ACT ] CAUSE [ BECOME [ y BROKEN ]]] Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 29 13

Introduction to frame semantics Example Lexical decomposition templates [Rappaport Hovav/Levin 1998] (3) [[ x ACT ] CAUSE [ BECOME [ y BROKEN ]]] causation   CAUSE EFFECT  causation  � activity �   change-of-state <   activity    cause   effector x    FINAL ACTOR        change-of-state  broken-stage   � broke-stage �        effect    x PATIENT     final     patient y     y cause < effect Description in atribute-value logic causation ∧ cause : activity ∧ cause actor � x ∧ effect ( change-of-state ∧ final : ( broken-stage ∧ patient � y )) ∧ cause < effect Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 30 13

Introduction to frame semantics Example Lexical decomposition templates [Rappaport Hovav/Levin 1998] (3) [[ x ACT ] CAUSE [ BECOME [ y BROKEN ]]] causation   CAUSE EFFECT  causation  � activity �   change-of-state <   activity    cause   effector x    FINAL ACTOR        change-of-state  broken-stage   � broke-stage �        effect    x PATIENT     final     patient y     y cause < effect Description in atribute-value logic causation ∧ cause : activity ∧ cause actor � x ∧ effect ( change-of-state ∧ final : ( broken-stage ∧ patient � y )) ∧ cause < effect Translation into first-order logic λ e ∃ e ′ ∃ e ′′ ∃ s ( causation ( e ) ∧ cause ( e , e ′ ) ∧ effect ( e , e ′′ ) ∧ e ′ < e ′′ ∧ activity ( e ′ ) ∧ actor ( e ′ , x ) ∧ change-of-state ( e ′′ ) ∧ final ( e ′′ , s ) ∧ broken-stage ( s ) ∧ patient ( s , y )) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 31 13

Outline of today’s course Introduction to frame semantics 1 Frames in the sense of Fillmore and Barsalou Frames according to this course Formalization of frames 2 Atribute-value descriptions and formulas Formal definition of frames Frames as models Subsumption and unification Atribute-value constraints Further topics 3 Frames versus feature structures Type constraints versus type hierarchy Frame semantics: extensions 4 Summary and outlook 5 Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 32 14

Atribute-value descriptions Vocabulary / Signature Atr atributes ( = dyadic functional relation symbols) Rel (proper) relation symbols Type type symbols ( = monadic predicates) Nname node names (“nominals”) } Nlabel node labels Nvar node variables Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 33 15

Atribute-value descriptions Vocabulary / Signature Atr atributes ( = dyadic functional relation symbols) Rel (proper) relation symbols Type type symbols ( = monadic predicates) Nname node names (“nominals”) } Nlabel node labels Nvar node variables Primitive atribute-value descriptions (pAVDesc) t | p : t | p � q | [ p 1 , . . . , p n ] : r | p � k ( t ∈ Type, r ∈ Rel, p , q , p i ∈ Atr ∗ , k ∈ Nlabel) Semantics ⎡ ⎤ ⎢ ⎥ P [ P [ t ] ] P ∶ t P ⎢ ⎥ P 1 t [ P , Q ]∶ r ⎢ ⎥ ⎢ ⎥ r ⎣ Q 2 ⎦ r ( 1 , 2 ) Q P ⎡ ⎤ ⎢ ⎥ P ≐ Q ⎢ ⎥ 1 P ⎢ ⎥ ⎢ ⎥ P [ P k [ ] ] ⎣ 1 ⎦ P ≜ k Q Q k Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 34 15

Atribute-value formulas Primitive atribute-value formulas (pAVForm) k · p : t | k · p � l · q | � k 1 · p 1 , . . . , k n · p n � : r ( t ∈ Type, r ∈ Rel, p , q , p i ∈ Atr ∗ , k , l , k i ∈ Nlabel) Semantics P P k [ P [ t ] ] 1 ] k ⋅ P ∶ t k [ P t ⟨ k ⋅ P , l ⋅ Q ⟩∶ r k k r 2 ] l [ Q l r ( 1 , 2 ) 1 ] k [ P Q k ⋅ P ≜ l ⋅ Q P k 1 ] l [ Q Q l Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 35 16

Atribute-value formulas Primitive atribute-value formulas (pAVForm) k · p : t | k · p � l · q | � k 1 · p 1 , . . . , k n · p n � : r ( t ∈ Type, r ∈ Rel, p , q , p i ∈ Atr ∗ , k , l , k i ∈ Nlabel) Semantics P P k [ P [ t ] ] 1 ] k ⋅ P ∶ t k [ P t ⟨ k ⋅ P , l ⋅ Q ⟩∶ r k k r 2 ] l [ Q l r ( 1 , 2 ) 1 ] k [ P Q k ⋅ P ≜ l ⋅ Q P k 1 ] l [ Q Q l Formal definitions (fairly standard) Set / universe of “nodes” V Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 36 16

Atribute-value formulas Primitive atribute-value formulas (pAVForm) k · p : t | k · p � l · q | � k 1 · p 1 , . . . , k n · p n � : r ( t ∈ Type, r ∈ Rel, p , q , p i ∈ Atr ∗ , k , l , k i ∈ Nlabel) Semantics P P k [ P [ t ] ] 1 ] k ⋅ P ∶ t k [ P t ⟨ k ⋅ P , l ⋅ Q ⟩∶ r k k r 2 ] l [ Q l r ( 1 , 2 ) 1 ] k [ P Q k ⋅ P ≜ l ⋅ Q P k 1 ] l [ Q Q l Formal definitions (fairly standard) Set / universe of “nodes” V Interpretation function I : Atr → [ V ⇀ V ] , Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 37 16

Atribute-value formulas Primitive atribute-value formulas (pAVForm) k · p : t | k · p � l · q | � k 1 · p 1 , . . . , k n · p n � : r ( t ∈ Type, r ∈ Rel, p , q , p i ∈ Atr ∗ , k , l , k i ∈ Nlabel) Semantics P P k [ P [ t ] ] 1 ] k ⋅ P ∶ t k [ P t ⟨ k ⋅ P , l ⋅ Q ⟩∶ r k k r 2 ] l [ Q l r ( 1 , 2 ) 1 ] k [ P Q k ⋅ P ≜ l ⋅ Q P k 1 ] l [ Q Q l Formal definitions (fairly standard) Set / universe of “nodes” V Interpretation function I : Atr → [ V ⇀ V ] , Type → ℘ ( V ) , Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 38 16

Atribute-value formulas Primitive atribute-value formulas (pAVForm) k · p : t | k · p � l · q | � k 1 · p 1 , . . . , k n · p n � : r ( t ∈ Type, r ∈ Rel, p , q , p i ∈ Atr ∗ , k , l , k i ∈ Nlabel) Semantics P P k [ P [ t ] ] 1 ] k ⋅ P ∶ t k [ P t ⟨ k ⋅ P , l ⋅ Q ⟩∶ r k k r 2 ] l [ Q l r ( 1 , 2 ) 1 ] k [ P Q k ⋅ P ≜ l ⋅ Q P k 1 ] l [ Q Q l Formal definitions (fairly standard) Set / universe of “nodes” V Interpretation function I : Atr → [ V ⇀ V ] , Type → ℘ ( V ) , n ℘ ( V n ) , Rel → � Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 39 16

Atribute-value formulas Primitive atribute-value formulas (pAVForm) k · p : t | k · p � l · q | � k 1 · p 1 , . . . , k n · p n � : r ( t ∈ Type, r ∈ Rel, p , q , p i ∈ Atr ∗ , k , l , k i ∈ Nlabel) Semantics P P k [ P [ t ] ] 1 ] k ⋅ P ∶ t k [ P t ⟨ k ⋅ P , l ⋅ Q ⟩∶ r k k r 2 ] l [ Q l r ( 1 , 2 ) 1 ] k [ P Q k ⋅ P ≜ l ⋅ Q P k 1 ] l [ Q Q l Formal definitions (fairly standard) Set / universe of “nodes” V Interpretation function I : Atr → [ V ⇀ V ] , Type → ℘ ( V ) , n ℘ ( V n ) , Nname → V Rel → � Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 40 16

Atribute-value formulas Primitive atribute-value formulas (pAVForm) k · p : t | k · p � l · q | � k 1 · p 1 , . . . , k n · p n � : r ( t ∈ Type, r ∈ Rel, p , q , p i ∈ Atr ∗ , k , l , k i ∈ Nlabel) Semantics P P k [ P [ t ] ] 1 ] k ⋅ P ∶ t k [ P t ⟨ k ⋅ P , l ⋅ Q ⟩∶ r k k r 2 ] l [ Q l r ( 1 , 2 ) 1 ] k [ P Q k ⋅ P ≜ l ⋅ Q P k 1 ] l [ Q Q l Formal definitions (fairly standard) Set / universe of “nodes” V Interpretation function I : Atr → [ V ⇀ V ] , Type → ℘ ( V ) , n ℘ ( V n ) , Nname → V Rel → � (Partial) variable assignment g : Nvar ⇀ V Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 41 16

Satisfaction of AV descriptions and formulas Formal definitions (cont’d) Abbreviation: I g ( k ) = v for k ∈ Nlabel iff I ( k ) = v if k ∈ Nname and g ( k ) = v if k ∈ Nvar ( g ( k ) defined) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 42 17

Satisfaction of AV descriptions and formulas Formal definitions (cont’d) Abbreviation: I g ( k ) = v for k ∈ Nlabel iff I ( k ) = v if k ∈ Nname and g ( k ) = v if k ∈ Nvar ( g ( k ) defined) Satisfaction of primitive descriptions � V , I , g � , v � t iff v ∈ I ( t ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 43 17

Satisfaction of AV descriptions and formulas Formal definitions (cont’d) Abbreviation: I g ( k ) = v for k ∈ Nlabel iff I ( k ) = v if k ∈ Nname and g ( k ) = v if k ∈ Nvar ( g ( k ) defined) Satisfaction of primitive descriptions � V , I , g � , v � t iff v ∈ I ( t ) � V , I , g � , v � p : t iff I ( p )( v ) ∈ I ( t ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 44 17

Satisfaction of AV descriptions and formulas Formal definitions (cont’d) Abbreviation: I g ( k ) = v for k ∈ Nlabel iff I ( k ) = v if k ∈ Nname and g ( k ) = v if k ∈ Nvar ( g ( k ) defined) Satisfaction of primitive descriptions � V , I , g � , v � t iff v ∈ I ( t ) � V , I , g � , v � p : t iff I ( p )( v ) ∈ I ( t ) � V , I , g � , v � p � q iff I ( p )( v ) = I ( q )( v ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 45 17

Satisfaction of AV descriptions and formulas Formal definitions (cont’d) Abbreviation: I g ( k ) = v for k ∈ Nlabel iff I ( k ) = v if k ∈ Nname and g ( k ) = v if k ∈ Nvar ( g ( k ) defined) Satisfaction of primitive descriptions � V , I , g � , v � t iff v ∈ I ( t ) � V , I , g � , v � p : t iff I ( p )( v ) ∈ I ( t ) � V , I , g � , v � p � q iff I ( p )( v ) = I ( q )( v ) � V , I , g � , v � [ p 1 , . . . , p n ] : r iff �I ( p 1 )( v ) , . . . , I ( p n )( v ) � ∈ I ( r ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 46 17

Satisfaction of AV descriptions and formulas Formal definitions (cont’d) Abbreviation: I g ( k ) = v for k ∈ Nlabel iff I ( k ) = v if k ∈ Nname and g ( k ) = v if k ∈ Nvar ( g ( k ) defined) Satisfaction of primitive descriptions � V , I , g � , v � t iff v ∈ I ( t ) � V , I , g � , v � p : t iff I ( p )( v ) ∈ I ( t ) � V , I , g � , v � p � q iff I ( p )( v ) = I ( q )( v ) � V , I , g � , v � [ p 1 , . . . , p n ] : r iff �I ( p 1 )( v ) , . . . , I ( p n )( v ) � ∈ I ( r ) iff I ( p )( v ) = I g ( k ) ( k ∈ Nlabel) � V , I , g � , v � p � k Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 47 17

Satisfaction of AV descriptions and formulas Formal definitions (cont’d) Abbreviation: I g ( k ) = v for k ∈ Nlabel iff I ( k ) = v if k ∈ Nname and g ( k ) = v if k ∈ Nvar ( g ( k ) defined) Satisfaction of primitive descriptions � V , I , g � , v � t iff v ∈ I ( t ) � V , I , g � , v � p : t iff I ( p )( v ) ∈ I ( t ) � V , I , g � , v � p � q iff I ( p )( v ) = I ( q )( v ) � V , I , g � , v � [ p 1 , . . . , p n ] : r iff �I ( p 1 )( v ) , . . . , I ( p n )( v ) � ∈ I ( r ) iff I ( p )( v ) = I g ( k ) ( k ∈ Nlabel) � V , I , g � , v � p � k Satisfaction of primitive formulas � V , I , g � � k · p : t iff I ( p )( I g ( k )) ∈ I ( t ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 48 17

Satisfaction of AV descriptions and formulas Formal definitions (cont’d) Abbreviation: I g ( k ) = v for k ∈ Nlabel iff I ( k ) = v if k ∈ Nname and g ( k ) = v if k ∈ Nvar ( g ( k ) defined) Satisfaction of primitive descriptions � V , I , g � , v � t iff v ∈ I ( t ) � V , I , g � , v � p : t iff I ( p )( v ) ∈ I ( t ) � V , I , g � , v � p � q iff I ( p )( v ) = I ( q )( v ) � V , I , g � , v � [ p 1 , . . . , p n ] : r iff �I ( p 1 )( v ) , . . . , I ( p n )( v ) � ∈ I ( r ) iff I ( p )( v ) = I g ( k ) ( k ∈ Nlabel) � V , I , g � , v � p � k Satisfaction of primitive formulas � V , I , g � � k · p : t iff I ( p )( I g ( k )) ∈ I ( t ) iff I ( p )( I � V , I , g � � k · p � l · q g ( k )) = I ( q )( I g ( l )) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 49 17

Satisfaction of AV descriptions and formulas Formal definitions (cont’d) Abbreviation: I g ( k ) = v for k ∈ Nlabel iff I ( k ) = v if k ∈ Nname and g ( k ) = v if k ∈ Nvar ( g ( k ) defined) Satisfaction of primitive descriptions � V , I , g � , v � t iff v ∈ I ( t ) � V , I , g � , v � p : t iff I ( p )( v ) ∈ I ( t ) � V , I , g � , v � p � q iff I ( p )( v ) = I ( q )( v ) � V , I , g � , v � [ p 1 , . . . , p n ] : r iff �I ( p 1 )( v ) , . . . , I ( p n )( v ) � ∈ I ( r ) iff I ( p )( v ) = I g ( k ) ( k ∈ Nlabel) � V , I , g � , v � p � k Satisfaction of primitive formulas � V , I , g � � k · p : t iff I ( p )( I g ( k )) ∈ I ( t ) iff I ( p )( I � V , I , g � � k · p � l · q g ( k )) = I ( q )( I g ( l )) � V , I , g � � � k 1 · p 1 , . . . , k n · p n � : r iff �I ( p 1 )( I g ( k 1 )) , . . . , I g ( p n )( I ( k n )) � ∈ I ( r ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 50 17

Satisfaction of AV descriptions and formulas Formal definitions (cont’d) Abbreviation: I g ( k ) = v for k ∈ Nlabel iff I ( k ) = v if k ∈ Nname and g ( k ) = v if k ∈ Nvar ( g ( k ) defined) Satisfaction of primitive descriptions � V , I , g � , v � t iff v ∈ I ( t ) � V , I , g � , v � p : t iff I ( p )( v ) ∈ I ( t ) � V , I , g � , v � p � q iff I ( p )( v ) = I ( q )( v ) � V , I , g � , v � [ p 1 , . . . , p n ] : r iff �I ( p 1 )( v ) , . . . , I ( p n )( v ) � ∈ I ( r ) iff I ( p )( v ) = I g ( k ) ( k ∈ Nlabel) � V , I , g � , v � p � k Satisfaction of primitive formulas � V , I , g � � k · p : t iff I ( p )( I g ( k )) ∈ I ( t ) iff I ( p )( I � V , I , g � � k · p � l · q g ( k )) = I ( q )( I g ( l )) � V , I , g � � � k 1 · p 1 , . . . , k n · p n � : r iff �I ( p 1 )( I g ( k 1 )) , . . . , I g ( p n )( I ( k n )) � ∈ I ( r ) Satisfaction of Boolean combinations as usual. Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 51 17

Frames defined Frame F over � Atr , Type , Rel , Nname , Nvar � : F = � V , I , g � , with V finite, such that every node v ∈ V is reachable from some labeled node w ∈ V via an atribute path, Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 52 18

Frames defined Frame F over � Atr , Type , Rel , Nname , Nvar � : F = � V , I , g � , with V finite, such that every node v ∈ V is reachable from some labeled node w ∈ V via an atribute path, i.e., (i) w = I g ( k ) for some k ∈ Nlabel ( = Nname ∪ Nvar ) and (ii) v = I ( p )( w ) for some p ∈ Atr ∗ . Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 53 18

Frames defined Frame F over � Atr , Type , Rel , Nname , Nvar � : F = � V , I , g � , with V finite, such that every node v ∈ V is reachable from some labeled node w ∈ V via an atribute path, i.e., (i) w = I g ( k ) for some k ∈ Nlabel ( = Nname ∪ Nvar ) and (ii) v = I ( p )( w ) for some p ∈ Atr ∗ . Example actor x man house locomotion e z mover manner in-region path endp part-of walking path region region Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 54 18

Frames as models of AV formulas A frame F = � V , I , g � is a model of an AV formula ϕ iff F � ϕ . Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 55 19

Frames as models of AV formulas A frame F = � V , I , g � is a model of an AV formula ϕ iff F � ϕ . Example actor x man house locomotion e z mover F = manner in-region path endp part-of walking path region region Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 56 19

Frames as models of AV formulas A frame F = � V , I , g � is a model of an AV formula ϕ iff F � ϕ . Example actor x man house locomotion e z mover F = manner in-region path endp part-of walking path region region F � Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 57 19

Frames as models of AV formulas A frame F = � V , I , g � is a model of an AV formula ϕ iff F � ϕ . Example actor x man house locomotion e z mover F = manner in-region path endp part-of walking path region region F � e · locomotion Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 58 19

Frames as models of AV formulas A frame F = � V , I , g � is a model of an AV formula ϕ iff F � ϕ . Example actor x man house locomotion e z mover F = manner in-region path endp part-of walking path region region F � e · locomotion F � e · ( locomotion ∧ actor : man ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 59 19

Frames as models of AV formulas A frame F = � V , I , g � is a model of an AV formula ϕ iff F � ϕ . Example actor x man house locomotion e z mover F = manner in-region path endp part-of walking path region region F � e · locomotion F � e · ( locomotion ∧ actor : man ) F � e · ( locomotion ∧ actor � x ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 60 19

Frames as models of AV formulas A frame F = � V , I , g � is a model of an AV formula ϕ iff F � ϕ . Example actor x man house locomotion e z mover F = manner in-region path endp part-of walking path region region F � e · locomotion F � e · ( locomotion ∧ actor : man ) F � e · ( locomotion ∧ actor � x ) F � x · man Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 61 19

Frames as models of AV formulas A frame F = � V , I , g � is a model of an AV formula ϕ iff F � ϕ . Example actor x man house locomotion e z mover F = manner in-region path endp part-of walking path region region F � e · locomotion F � e · ( locomotion ∧ actor : man ) F � e · ( locomotion ∧ actor � x ) F � x · man ∧ z · house Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 62 19

Frames as models of AV formulas A frame F = � V , I , g � is a model of an AV formula ϕ iff F � ϕ . Example actor x man house locomotion e z mover F = manner in-region path endp part-of walking path region region F � e · locomotion F � e · ( locomotion ∧ actor : man ) F � e · ( locomotion ∧ actor � x ) F � x · man ∧ z · house F � e · ( actor � mover ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 63 19

Frames as models of AV formulas A frame F = � V , I , g � is a model of an AV formula ϕ iff F � ϕ . Example actor x man house locomotion e z mover F = manner in-region path endp part-of walking path region region F � e · locomotion F � e · ( locomotion ∧ actor : man ) F � e · ( locomotion ∧ actor � x ) F � x · man ∧ z · house F � e · ( actor � mover ) F � � e · path endp , z · in-region � : part-of Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 64 19

Subsumption and unification Subsumption F 1 = � V 1 , I 1 , g 1 � subsumes F 2 = � V 2 , I 2 , g 2 � ( F 1 ⊑ F 2 ) iff there is a (necessarily unique) morphism h : F 1 → F 2 , i.e., a function h : V 1 → V 2 such that (i) I 1 ( f )( v )) , if I 1 ( f )( v ) is defined, f ∈ Atr, v ∈ V 1 , 2 ( f )( h ( v )) = h ( I (ii) h ( I 1 ( t )) ⊆ I 2 ( t ) , for t ∈ Type (iii) h ( I 2 ( r ) , for r ∈ Rel 1 ( r )) ⊆ I (iv) h ( I 1 ( n )) = I 2 ( n ) , for n ∈ Nname (v) h ( g 1 ( x )) = g 2 ( x ) , for x ∈ Nvar, if g 1 ( x ) is defined Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 65 20

Subsumption and unification Subsumption F 1 = � V 1 , I 1 , g 1 � subsumes F 2 = � V 2 , I 2 , g 2 � ( F 1 ⊑ F 2 ) iff there is a (necessarily unique) morphism h : F 1 → F 2 , i.e., a function h : V 1 → V 2 such that (i) I 1 ( f )( v )) , if I 1 ( f )( v ) is defined, f ∈ Atr, v ∈ V 1 , 2 ( f )( h ( v )) = h ( I (ii) h ( I 1 ( t )) ⊆ I 2 ( t ) , for t ∈ Type (iii) h ( I 2 ( r ) , for r ∈ Rel 1 ( r )) ⊆ I (iv) h ( I 1 ( n )) = I 2 ( n ) , for n ∈ Nname (v) h ( g 1 ( x )) = g 2 ( x ) , for x ∈ Nvar, if g 1 ( x ) is defined Example actor man man activity x actor locomotion locomotion e e mover mover ⊑ manner manner path walking path Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 66 20

Subsumption and unification Subsumption F 1 = � V 1 , I 1 , g 1 � subsumes F 2 = � V 2 , I 2 , g 2 � ( F 1 ⊑ F 2 ) iff there is a (necessarily unique) morphism h : F 1 → F 2 , i.e., a function h : V 1 → V 2 such that (i) I 1 ( f )( v )) , if I 1 ( f )( v ) is defined, f ∈ Atr, v ∈ V 1 , 2 ( f )( h ( v )) = h ( I (ii) h ( I 1 ( t )) ⊆ I 2 ( t ) , for t ∈ Type (iii) h ( I 2 ( r ) , for r ∈ Rel 1 ( r )) ⊆ I (iv) h ( I 1 ( n )) = I 2 ( n ) , for n ∈ Nname (v) h ( g 1 ( x )) = g 2 ( x ) , for x ∈ Nvar, if g 1 ( x ) is defined Example actor man man activity x actor locomotion locomotion e e mover mover ⊑ manner manner path walking path Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 67 20

Subsumption and unification Subsumption F 1 = � V 1 , I 1 , g 1 � subsumes F 2 = � V 2 , I 2 , g 2 � ( F 1 ⊑ F 2 ) iff there is a (necessarily unique) morphism h : F 1 → F 2 , i.e., a function h : V 1 → V 2 such that (i) I 1 ( f )( v )) , if I 1 ( f )( v ) is defined, f ∈ Atr, v ∈ V 1 , 2 ( f )( h ( v )) = h ( I (ii) h ( I 1 ( t )) ⊆ I 2 ( t ) , for t ∈ Type (iii) h ( I 2 ( r ) , for r ∈ Rel 1 ( r )) ⊆ I (iv) h ( I 1 ( n )) = I 2 ( n ) , for n ∈ Nname (v) h ( g 1 ( x )) = g 2 ( x ) , for x ∈ Nvar, if g 1 ( x ) is defined Intuition F 1 subsumes F 2 ( F 1 ⊑ F 2 ) iff F 2 is at least as informative as F 1 . Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 68 20

Subsumption and unification Subsumption F 1 = � V 1 , I 1 , g 1 � subsumes F 2 = � V 2 , I 2 , g 2 � ( F 1 ⊑ F 2 ) iff there is a (necessarily unique) morphism h : F 1 → F 2 , i.e., a function h : V 1 → V 2 such that (i) I 1 ( f )( v )) , if I 1 ( f )( v ) is defined, f ∈ Atr, v ∈ V 1 , 2 ( f )( h ( v )) = h ( I (ii) h ( I 1 ( t )) ⊆ I 2 ( t ) , for t ∈ Type (iii) h ( I 2 ( r ) , for r ∈ Rel 1 ( r )) ⊆ I (iv) h ( I 1 ( n )) = I 2 ( n ) , for n ∈ Nname (v) h ( g 1 ( x )) = g 2 ( x ) , for x ∈ Nvar, if g 1 ( x ) is defined Unification Least upper bound F 1 ⊔ F 2 of F 1 and F 2 w.r.t. subsumption. Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 69 20

Subsumption and unification Subsumption F 1 = � V 1 , I 1 , g 1 � subsumes F 2 = � V 2 , I 2 , g 2 � ( F 1 ⊑ F 2 ) iff there is a (necessarily unique) morphism h : F 1 → F 2 , i.e., a function h : V 1 → V 2 such that (i) I 1 ( f )( v )) , if I 1 ( f )( v ) is defined, f ∈ Atr, v ∈ V 1 , 2 ( f )( h ( v )) = h ( I (ii) h ( I 1 ( t )) ⊆ I 2 ( t ) , for t ∈ Type (iii) h ( I 2 ( r ) , for r ∈ Rel 1 ( r )) ⊆ I (iv) h ( I 1 ( n )) = I 2 ( n ) , for n ∈ Nname (v) h ( g 1 ( x )) = g 2 ( x ) , for x ∈ Nvar, if g 1 ( x ) is defined Unification Least upper bound F 1 ⊔ F 2 of F 1 and F 2 w.r.t. subsumption. Theorem (Frame unification) [ ≈ Hegner 1994] The worst case time-complexity of frame unification is almost linear in the number of nodes. Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 70 20

Frames as minimal models Frames as minimal models of atribute-value formulas (i) Every frame is the minimal model (w.r.t. subsumption) of a finite conjunction of primitive atribute-value formulas. Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 71 21

Frames as minimal models Frames as minimal models of atribute-value formulas (i) Every frame is the minimal model (w.r.t. subsumption) of a finite conjunction of primitive atribute-value formulas. (ii) Every finite conjunction of primitive atribute-value formulas has a minimal frame model. Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 72 21

Frames as minimal models Frames as minimal models of atribute-value formulas (i) Every frame is the minimal model (w.r.t. subsumption) of a finite conjunction of primitive atribute-value formulas. (ii) Every finite conjunction of primitive atribute-value formulas has a minimal frame model. Example actor x man house locomotion e z mover manner in-region path part-of endp walking path region region Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 73 21

Frames as minimal models Frames as minimal models of atribute-value formulas (i) Every frame is the minimal model (w.r.t. subsumption) of a finite conjunction of primitive atribute-value formulas. (ii) Every finite conjunction of primitive atribute-value formulas has a minimal frame model. Example actor x man house locomotion e z mover manner in-region path part-of endp walking path region region e · ( locomotion ∧ manner : walking ∧ actor � x ∧ mover � actor ∧ path : ( path ∧ endp : region )) ∧ � e · path endp , z · in-region � : part-of ∧ x · man Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 74 21

Atribute-value constraints Constraints (general format) ∀ ϕ , ϕ ∈ AVDesc Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 75 22

Atribute-value constraints Constraints (general format) ∀ ϕ , ϕ ∈ AVDesc � V , I , g � � ∀ ϕ iff � V , I , g � , v � ϕ for every v ∈ V Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 76 22

Atribute-value constraints Constraints (general format) ∀ ϕ , ϕ ∈ AVDesc � V , I , g � � ∀ ϕ iff � V , I , g � , v � ϕ for every v ∈ V Notation: ϕ ⇛ ψ for ∀ ( ϕ → ψ ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 77 22

Atribute-value constraints Constraints (general format) ∀ ϕ , ϕ ∈ AVDesc � V , I , g � � ∀ ϕ iff � V , I , g � , v � ϕ for every v ∈ V Notation: ϕ ⇛ ψ for ∀ ( ϕ → ψ ) Horn constraints: ϕ 1 ∧ . . . ∧ ϕ n ⇛ ψ ( ϕ i ∈ pAVDesc ∪ {⊤} , ψ ∈ pAVDesc ∪ {⊥} ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 78 22

Atribute-value constraints Constraints (general format) ∀ ϕ , ϕ ∈ AVDesc � V , I , g � � ∀ ϕ iff � V , I , g � , v � ϕ for every v ∈ V Notation: ϕ ⇛ ψ for ∀ ( ϕ → ψ ) Horn constraints: ϕ 1 ∧ . . . ∧ ϕ n ⇛ ψ ( ϕ i ∈ pAVDesc ∪ {⊤} , ψ ∈ pAVDesc ∪ {⊥} ) Examples activity ⇛ event causation ∧ activity ⇛ ⊥ agent : ⊤ ⇛ agent � actor activity ⇛ actor : ⊤ activity ∧ motion ⇛ actor � mover Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 79 22

Atribute-value constraints Constraints (general format) ∀ ϕ , ϕ ∈ AVDesc � V , I , g � � ∀ ϕ iff � V , I , g � , v � ϕ for every v ∈ V Notation: ϕ ⇛ ψ for ∀ ( ϕ → ψ ) Horn constraints: ϕ 1 ∧ . . . ∧ ϕ n ⇛ ψ ( ϕ i ∈ pAVDesc ∪ {⊤} , ψ ∈ pAVDesc ∪ {⊥} ) Examples activity ⇛ event (every activity is an event) causation ∧ activity ⇛ ⊥ agent : ⊤ ⇛ agent � actor activity ⇛ actor : ⊤ activity ∧ motion ⇛ actor � mover Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 80 22

Atribute-value constraints Constraints (general format) ∀ ϕ , ϕ ∈ AVDesc � V , I , g � � ∀ ϕ iff � V , I , g � , v � ϕ for every v ∈ V Notation: ϕ ⇛ ψ for ∀ ( ϕ → ψ ) Horn constraints: ϕ 1 ∧ . . . ∧ ϕ n ⇛ ψ ( ϕ i ∈ pAVDesc ∪ {⊤} , ψ ∈ pAVDesc ∪ {⊥} ) Examples activity ⇛ event (every activity is an event) causation ∧ activity ⇛ ⊥ (there is nothing which is both a causation and an activity) agent : ⊤ ⇛ agent � actor activity ⇛ actor : ⊤ activity ∧ motion ⇛ actor � mover Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 81 22

Atribute-value constraints Constraints (general format) ∀ ϕ , ϕ ∈ AVDesc � V , I , g � � ∀ ϕ iff � V , I , g � , v � ϕ for every v ∈ V Notation: ϕ ⇛ ψ for ∀ ( ϕ → ψ ) Horn constraints: ϕ 1 ∧ . . . ∧ ϕ n ⇛ ψ ( ϕ i ∈ pAVDesc ∪ {⊤} , ψ ∈ pAVDesc ∪ {⊥} ) Examples activity ⇛ event (every activity is an event) causation ∧ activity ⇛ ⊥ (there is nothing which is both a causation and an activity) agent : ⊤ ⇛ agent � actor (every agent is also an actor) activity ⇛ actor : ⊤ activity ∧ motion ⇛ actor � mover Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 82 22

Atribute-value constraints Constraints (general format) ∀ ϕ , ϕ ∈ AVDesc � V , I , g � � ∀ ϕ iff � V , I , g � , v � ϕ for every v ∈ V Notation: ϕ ⇛ ψ for ∀ ( ϕ → ψ ) Horn constraints: ϕ 1 ∧ . . . ∧ ϕ n ⇛ ψ ( ϕ i ∈ pAVDesc ∪ {⊤} , ψ ∈ pAVDesc ∪ {⊥} ) Examples activity ⇛ event (every activity is an event) causation ∧ activity ⇛ ⊥ (there is nothing which is both a causation and an activity) agent : ⊤ ⇛ agent � actor (every agent is also an actor) activity ⇛ actor : ⊤ (every activity has an actor) ... activity ∧ motion ⇛ actor � mover Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 83 22

Atribute-value constraints Graphical presentation of constraints event activity motion causation actor ∶ ⊺ mover ∶ ⊺ cause ∶ ⊺ ∧ effect ∶ ⊺ activity ∧ motion translocation onset-causation extended- actor ≐ mover path ∶ ⊺ cause ∶ punctual-event causation bounded-translocation locomotion goal ∶ ⊺ bounded-locomotion Caveat : Reading convention required ! Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 84 23

Atribute-value constraints Further examples [Babonnaud et al. 2016] book ⇛ info-carrier Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 85 24

Atribute-value constraints Further examples [Babonnaud et al. 2016] book � book , info-carrier book ⇛ info-carrier Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 86 24

Atribute-value constraints Further examples [Babonnaud et al. 2016] book � book , info-carrier book ⇛ info-carrier info-carrier ⇛ phys-obj ∧ content : information Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 87 24

Atribute-value constraints Further examples [Babonnaud et al. 2016] book � book , info-carrier book ⇛ info-carrier info-carrier ⇛ phys-obj ∧ content : information info-carrier � info-carrier , phys-obj information content Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 88 24

Atribute-value constraints Further examples [Babonnaud et al. 2016] book � book , info-carrier book ⇛ info-carrier info-carrier ⇛ phys-obj ∧ content : information info-carrier � info-carrier , phys-obj information content reading ⇛ perc-comp : perception ∧ ment-comp : comprehension ∧ [ perc-comp , ment-comp ] : ordered-overlap Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 89 24

Atribute-value constraints Further examples [Babonnaud et al. 2016] book � book , info-carrier book ⇛ info-carrier info-carrier ⇛ phys-obj ∧ content : information info-carrier � info-carrier , phys-obj information content reading ⇛ perc-comp : perception ∧ ment-comp : comprehension ∧ [ perc-comp , ment-comp ] : ordered-overlap perception perc-comp ordered- overlap reading reading � ment-comp comprehension Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 90 24

Unification under constraints Theorem (Frame unification under Horn constraints) [ ≈ Hegner 1994] The worst case time-complexity of frame unification under a finite set of labeled Horn constraints is almost linear in the number of nodes. Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 91 25

Unification under constraints Theorem (Frame unification under Horn constraints) [ ≈ Hegner 1994] The worst case time-complexity of frame unification under a finite set of labeled Horn constraints is almost linear in the number of nodes. (Labeled Horn constraint: k 1 · ϕ 1 ∧ . . . ∧ k n · ϕ n → l · ψ ) Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 92 25

Unification under constraints Theorem (Frame unification under Horn constraints) [ ≈ Hegner 1994] The worst case time-complexity of frame unification under a finite set of labeled Horn constraints is almost linear in the number of nodes. (Labeled Horn constraint: k 1 · ϕ 1 ∧ . . . ∧ k n · ϕ n → l · ψ ) Example       eating     person     actor x e   ⊔ u      name ‘Adam’      theme y  

Unification under constraints Theorem (Frame unification under Horn constraints) [ ≈ Hegner 1994] The worst case time-complexity of frame unification under a finite set of labeled Horn constraints is almost linear in the number of nodes. (Labeled Horn constraint: k 1 · ϕ 1 ∧ . . . ∧ k n · ϕ n → l · ψ ) Example       eating     person     actor x e   ⊔ u   ⊔ x � u    name ‘Adam’      theme y  

Unification under constraints Theorem (Frame unification under Horn constraints) [ ≈ Hegner 1994] The worst case time-complexity of frame unification under a finite set of labeled Horn constraints is almost linear in the number of nodes. (Labeled Horn constraint: k 1 · ϕ 1 ∧ . . . ∧ k n · ϕ n → l · ψ ) Example    eating            eating           person person     actor x     actor x e   ⊔ u   ⊔ x � u = e    u     name ‘Adam’   name ‘Adam’          theme y       theme y   Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 95 25

Unification under constraints Theorem (Frame unification under Horn constraints) [ ≈ Hegner 1994] The worst case time-complexity of frame unification under a finite set of labeled Horn constraints is almost linear in the number of nodes. (Labeled Horn constraint: k 1 · ϕ 1 ∧ . . . ∧ k n · ϕ n → l · ψ ) Example    eating            eating           person person     actor x     actor x e   ⊔ u   ⊔ x � u = e    u     name ‘Adam’   name ‘Adam’          theme y       theme y   A general view on semantic processing Semantic processing as the incremental construction of minimal ( frame ) models (by unification under constraints) based on the input, the context, and background knowledge (lexicon, ...). Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 96 25

Outline of today’s course Introduction to frame semantics 1 Frames in the sense of Fillmore and Barsalou Frames according to this course Formalization of frames 2 Atribute-value descriptions and formulas Formal definition of frames Frames as models Subsumption and unification Atribute-value constraints Further topics 3 Frames versus feature structures Type constraints versus type hierarchy Frame semantics: extensions 4 Summary and outlook 5 Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 97 26

Frames versus feature structures Feature structures have a designated root node from which each other node is reachable via an atribute path, and they have no relations. Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 98 27

Frames versus feature structures Feature structures have a designated root node from which each other node is reachable via an atribute path, and they have no relations. � | Nvar | = 1, Rel = ∅ . Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 99 27

Frames versus feature structures Feature structures have a designated root node from which each other node is reachable via an atribute path, and they have no relations. � | Nvar | = 1, Rel = ∅ . Typed feature structures Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 100 27