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Grammar Implementation with Lexicalized Tree Adjoining Grammars and Frame Semantics

Frame semantics Laura Kallmeyer, Timm Lichte, Rainer Osswald & Simon Petitjean

University of Düsseldorf

DGfS CL Fall School, September 14, 2017

SFB 991

The overall story

Reminder

(1) Adam ate an apple.

S VP[I=e] NP[I=y] V ‘ate’ NP[I=x] e         eating actor x theme y        

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 2 2

The overall story

Reminder

(1) Adam ate an apple.

NP[I=u] ‘Adam’ u person name ‘Adam’

• S

VP[I=e] NP[I=y] V ‘ate’ NP[I=x] e         eating actor x theme y         NP[I=v] ‘an apple’ v

• apple
• x u

y v

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 3 2

The overall story

Reminder

(1) Adam ate an apple.

NP[I=u] ‘Adam’ u person name ‘Adam’

• S

VP[I=e] NP[I=y] V ‘ate’ NP[I=x] e         eating actor x theme y         NP[I=v] ‘an apple’ v

• apple
• x u

y v S VP[I=e] NP[I=y] ‘an apple’ V ‘ate’ NP[I=x] ‘Adam’ e            eating actor x person name ‘Adam’

• theme y
• apple
• 

          e eating x person ‘Adam’ y apple actor name theme

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 4 2

Outline of today’s course

1

Introduction to frame semantics Frames in the sense of Fillmore and Barsalou Frames according to this course

2

Formalization of frames Atribute-value descriptions and formulas Formal definition of frames Frames as models Subsumption and unification Atribute-value constraints

3

Further topics Frames versus feature structures Type constraints versus type hierarchy

4

Frame semantics: extensions

5

Summary and outlook

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 5 3

Outline of today’s course

1

Introduction to frame semantics Frames in the sense of Fillmore and Barsalou Frames according to this course

2

Formalization of frames Atribute-value descriptions and formulas Formal definition of frames Frames as models Subsumption and unification Atribute-value constraints

3

Further topics Frames versus feature structures Type constraints versus type hierarchy

4

Frame semantics: extensions

5

Summary and outlook

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 6 4

Introduction to frame semantics

Frames according to Fillmore/FrameNet

[framenet.icsi.berkeley.edu]

The ‘Cuting’ frame, annotated:

• Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf)

7 5

Introduction to frame semantics

Frames according to Fillmore/FrameNet

[framenet.icsi.berkeley.edu]

The ‘Cuting’ frame, annotated:

• The FrameNet database:

> 1200 frames > 13000 lexical units (= word senses)

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 8 5

Introduction to frame semantics

Frames according to Fillmore/FrameNet

[framenet.icsi.berkeley.edu]

Cuting frame Definition: An [Agent] cuts an [Item] into [Pieces] using an [Instrument] (which may or may not be expressed). Core frame elements: Agent The [Agent] is the person cuting the [Item] into [Pieces]. Item The item which is being cut into [Pieces]. Pieces The [Pieces] are the parts of the original [Item] which are the result of the slicing. Non-core frame elements: Instrument The [Instrument] with which the [Item] is being cut into [Pieces]. Manner [Manner] in which the [Item] is being cut into [Pieces]. Result The [Result] of the [Item] being sliced into [Pieces]. (extrathematic) In addition: Means, Purpose, Place, Time Lexical units: carve, chop, cube, cut, dice, fillet, mince, pare, slice

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 9 6

Introduction to frame semantics

Frames according to Fillmore/FrameNet

[framenet.icsi.berkeley.edu]

Frame-to-frame relations in FrameNet Generalization relations: ‘inherits from’, ‘is perspective on’, ‘uses’ Event structure relations: ‘is subframe of’, ‘precedes’ Systematic relations: ‘is causative of’, ‘is inchoative of’ Examples

     Geting Recipient

1

Theme

2

Source

3

          Commerce buy Buyer

1

Goods

2

Seller

3

        Intentionally affect Agent

1

Patient

2

        Cuting Agent

1

Item

2

Pieces

3

        Motion Theme

2

Goal

3

        Bringing Agent

1

Theme

2

Goal

3

    

• Expansion

Item

2

• 

  Cause expansion Cause

1

Item

2

  

inherits from uses is causative of

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 10 7

Introduction to frame semantics

Frames according to Barsalou

[Barsalou 1992:30]

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 11 8

Introduction to frame semantics

Frames according to Barsalou

[Gamerschlag et al. 2014:6]

Bird Beak Foot round pointed webbed clawed

aspect aspect type type type type

Water-bird Beak Foot

aspect aspect

Land-bird Beak Foot

aspect aspect type type type type type type

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 12 9

Introduction to frame semantics

Frames according to this course [Kallmeyer/Osswald 2013; Osswald/Van Valin 2014] A representation format for rich lexical and constructional content. Can nicely capture semantic composition and decomposition. Can be formalized as generalized feature structures with types, relations and node labels.

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 13 10

Introduction to frame semantics

Frames according to this course [Kallmeyer/Osswald 2013; Osswald/Van Valin 2014] A representation format for rich lexical and constructional content. Can nicely capture semantic composition and decomposition. Can be formalized as generalized feature structures with types, relations and node labels. Basic assumptions Atributes (features, functional roles/relations) play a central role in the organization of semantic and conceptual knowledge and representation.

[Barsalou 1992; Löbner 2014]

Semantic components (participants, subevents) can be (recursively) addressed via atributes (from some “base” node).

• inherently structured representations (models);

composition by unification (under constraints)

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 14 10

Introduction to frame semantics

Frames according to this course

Example

e locomotion x man path walking region z house region actor mover path manner endp in-region part-of

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 15 11

Introduction to frame semantics

Frames according to this course

Example

e locomotion x man path walking region z house region actor mover path manner endp in-region part-of

Ingredients Atributes (funct. relations): actor, mover, path, manner, in-region, ...

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 16 11

Introduction to frame semantics

Frames according to this course

Example

e locomotion x man path walking region z house region actor mover path manner endp in-region part-of

Ingredients Atributes (funct. relations): actor, mover, path, manner, in-region, ... Type symbols: locomotion, man, path, walking, region, ...

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 17 11

Introduction to frame semantics

Frames according to this course

Example

e locomotion x man path walking region z house region actor mover path manner endp in-region part-of

Ingredients Atributes (funct. relations): actor, mover, path, manner, in-region, ... Type symbols: locomotion, man, path, walking, region, ... Proper relations: part-of

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 18 11

Introduction to frame semantics

Frames according to this course

Example

e locomotion x man path walking region z house region actor mover path manner endp in-region part-of

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

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 19 11

Introduction to frame semantics

Frames according to this course

Example

e locomotion x man path walking region z house region actor mover path manner endp in-region part-of

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 e running person ‘Anna’ actor name

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 22 12

Introduction to frame semantics

Example

(2) Anna ran to the station. e running person ‘Anna’ actor name

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 23 12

Introduction to frame semantics

Example

(2) Anna ran to the station. e bounded-motion running person ‘Anna’ loc-stage station actor name final theme loc

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 24 12

Introduction to frame semantics

Example

(2) Anna ran to the station. e bounded-motion running person ‘Anna’ loc-stage station actor name final theme loc e                 running ∧ bounded-motion actor

1

person name ‘Anna’

• final

        loc-stage theme

1

loc [station]                        

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 25 12

Introduction to frame semantics

Example

(2) Anna ran to the station. e bounded-motion running person ‘Anna’ loc-stage station actor name final theme loc e                 running ∧ bounded-motion actor

1

person name ‘Anna’

• final

        loc-stage theme

1

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. e bounded-motion running person ‘Anna’ loc-stage station actor name final theme loc e                 running ∧ bounded-motion actor

1

person name ‘Anna’

• final

        loc-stage theme

1

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. e bounded-motion running person ‘Anna’ loc-stage station actor name final theme loc e                 running ∧ bounded-motion actor

1

person name ‘Anna’

• final

        loc-stage theme

1

loc [station]                         Atribute-value logic e · (running ∧ bounded-motion ∧ actor : (person ∧ name ‘Anna’) actor final theme ∧ final : (loc-stage ∧ loc : station)) Constraints running ⇛ activity (short for ∀e(running(e) → activity(e))), 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 activity change-of-state

x

broken-stage

y CAUSE EFFECT ACTOR FINAL PATIENT

<                 causation cause activity effector x

• effect

        change-of-state final broke-stage patient 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 activity change-of-state

x

broken-stage

y CAUSE EFFECT ACTOR FINAL PATIENT

<                 causation cause activity effector x

• effect

        change-of-state final broke-stage patient 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

λe∃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

1

Introduction to frame semantics Frames in the sense of Fillmore and Barsalou Frames according to this course

2

Formalization of frames Atribute-value descriptions and formulas Formal definition of frames Frames as models Subsumption and unification Atribute-value constraints

3

Further topics Frames versus feature structures Type constraints versus type hierarchy

4

Frame semantics: extensions

5

Summary and outlook

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”) Nvar node variables

} Nlabel

node labels

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”) Nvar node variables

} Nlabel

node labels Primitive atribute-value descriptions (pAVDesc) t | p : t | p q | [p1, . . . , pn] : r | p k

(t ∈ Type, r ∈ Rel, p, q, pi ∈ Atr∗, k ∈ Nlabel)

Semantics

P∶t t

P [P [t] ]

P ≐ Q

P Q ⎡ ⎢ ⎢ ⎢ ⎢ ⎣

P

1

Q

1

⎤ ⎥ ⎥ ⎥ ⎥ ⎦

[P, Q]∶r

P Q

r

⎡ ⎢ ⎢ ⎢ ⎢ ⎣

P

1

Q

2

⎤ ⎥ ⎥ ⎥ ⎥ ⎦ r ( 1 , 2 ) P ≜ k

k

P [P k [ ] ]

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 34 15

Atribute-value formulas

Primitive atribute-value formulas (pAVForm) k · p : t | k · p l · q | k1 · p1, . . . , kn · pn : r

(t ∈ Type, r ∈ Rel, p, q, pi ∈ Atr∗, k, l, ki ∈ Nlabel)

Semantics

k ⋅ P∶t

k

t

P k [P [t] ]

k ⋅ P ≜ l ⋅ Q

k l

P Q k [P

1 ]

l [Q

1 ]

⟨k ⋅ P,l ⋅ Q⟩∶r

k l

P Q

r

k [P

1 ]

l [Q

2 ]

r ( 1 , 2 )

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 35 16

Atribute-value formulas

Primitive atribute-value formulas (pAVForm) k · p : t | k · p l · q | k1 · p1, . . . , kn · pn : r

(t ∈ Type, r ∈ Rel, p, q, pi ∈ Atr∗, k, l, ki ∈ Nlabel)

Semantics

k ⋅ P∶t

k

t

P k [P [t] ]

k ⋅ P ≜ l ⋅ Q

k l

P Q k [P

1 ]

l [Q

1 ]

⟨k ⋅ P,l ⋅ Q⟩∶r

k l

P Q

r

k [P

1 ]

l [Q

2 ]

r ( 1 , 2 )

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 | k1 · p1, . . . , kn · pn : r

(t ∈ Type, r ∈ Rel, p, q, pi ∈ Atr∗, k, l, ki ∈ Nlabel)

Semantics

k ⋅ P∶t

k

t

P k [P [t] ]

k ⋅ P ≜ l ⋅ Q

k l

P Q k [P

1 ]

l [Q

1 ]

⟨k ⋅ P,l ⋅ Q⟩∶r

k l

P Q

r

k [P

1 ]

l [Q

2 ]

r ( 1 , 2 )

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 | k1 · p1, . . . , kn · pn : r

(t ∈ Type, r ∈ Rel, p, q, pi ∈ Atr∗, k, l, ki ∈ Nlabel)

Semantics

k ⋅ P∶t

k

t

P k [P [t] ]

k ⋅ P ≜ l ⋅ Q

k l

P Q k [P

1 ]

l [Q

1 ]

⟨k ⋅ P,l ⋅ Q⟩∶r

k l

P Q

r

k [P

1 ]

l [Q

2 ]

r ( 1 , 2 )

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 | k1 · p1, . . . , kn · pn : r

(t ∈ Type, r ∈ Rel, p, q, pi ∈ Atr∗, k, l, ki ∈ Nlabel)

Semantics

k ⋅ P∶t

k

t

P k [P [t] ]

k ⋅ P ≜ l ⋅ Q

k l

P Q k [P

1 ]

l [Q

1 ]

⟨k ⋅ P,l ⋅ Q⟩∶r

k l

P Q

r

k [P

1 ]

l [Q

2 ]

r ( 1 , 2 )

Formal definitions (fairly standard) Set/universe of “nodes” V Interpretation function I : Atr → [V ⇀ V], Type → ℘(V), Rel →

n ℘(V n),

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 39 16

Atribute-value formulas

Primitive atribute-value formulas (pAVForm) k · p : t | k · p l · q | k1 · p1, . . . , kn · pn : r

(t ∈ Type, r ∈ Rel, p, q, pi ∈ Atr∗, k, l, ki ∈ Nlabel)

Semantics

k ⋅ P∶t

k

t

P k [P [t] ]

k ⋅ P ≜ l ⋅ Q

k l

P Q k [P

1 ]

l [Q

1 ]

⟨k ⋅ P,l ⋅ Q⟩∶r

k l

P Q

r

k [P

1 ]

l [Q

2 ]

r ( 1 , 2 )

Formal definitions (fairly standard) Set/universe of “nodes” V Interpretation function I : Atr → [V ⇀ V], Type → ℘(V), Rel →

n ℘(V n), Nname → V

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 40 16

Atribute-value formulas

Primitive atribute-value formulas (pAVForm) k · p : t | k · p l · q | k1 · p1, . . . , kn · pn : r

(t ∈ Type, r ∈ Rel, p, q, pi ∈ Atr∗, k, l, ki ∈ Nlabel)

Semantics

k ⋅ P∶t

k

t

P k [P [t] ]

k ⋅ P ≜ l ⋅ Q

k l

P Q k [P

1 ]

l [Q

1 ]

⟨k ⋅ P,l ⋅ Q⟩∶r

k l

P Q

r

k [P

1 ]

l [Q

2 ]

r ( 1 , 2 )

Formal definitions (fairly standard) Set/universe of “nodes” V Interpretation function I : Atr → [V ⇀ V], Type → ℘(V), Rel →

n ℘(V n), Nname → V

(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 [p1, . . . , pn] : r iff I(p1)(v), . . . , I(pn)(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 [p1, . . . , pn] : r iff I(p1)(v), . . . , I(pn)(v) ∈ I(r) V, I, g , v p k iff I(p)(v) = I

g(k) (k ∈ Nlabel)

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 [p1, . . . , pn] : r iff I(p1)(v), . . . , I(pn)(v) ∈ I(r) V, I, g , v p k iff I(p)(v) = I

g(k) (k ∈ Nlabel)

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 [p1, . . . , pn] : r iff I(p1)(v), . . . , I(pn)(v) ∈ I(r) V, I, g , v p k iff I(p)(v) = I

g(k) (k ∈ Nlabel)

Satisfaction of primitive formulas V, I, g k · p : t iff I(p)(I

g(k)) ∈ I(t)

V, I, g k · p l · q iff I(p)(I

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 [p1, . . . , pn] : r iff I(p1)(v), . . . , I(pn)(v) ∈ I(r) V, I, g , v p k iff I(p)(v) = I

g(k) (k ∈ Nlabel)

Satisfaction of primitive formulas V, I, g k · p : t iff I(p)(I

g(k)) ∈ I(t)

V, I, g k · p l · q iff I(p)(I

g(k)) = I(q)(I g(l))

V, I, g k1 · p1, . . . , kn · pn : r iff I(p1)(I

g(k1)), . . . , I g(pn)(I(kn)) ∈ 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 [p1, . . . , pn] : r iff I(p1)(v), . . . , I(pn)(v) ∈ I(r) V, I, g , v p k iff I(p)(v) = I

g(k) (k ∈ Nlabel)

Satisfaction of primitive formulas V, I, g k · p : t iff I(p)(I

g(k)) ∈ I(t)

V, I, g k · p l · q iff I(p)(I

g(k)) = I(q)(I g(l))

V, I, g k1 · p1, . . . , kn · pn : r iff I(p1)(I

g(k1)), . . . , I g(pn)(I(kn)) ∈ 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 e locomotion x man path walking region z house region actor mover path manner endp in-region part-of

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

F = e locomotion x man path walking region z house region actor mover path manner endp in-region part-of

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

F = e locomotion x man path walking region z house region actor mover path manner endp in-region part-of 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

F = e locomotion x man path walking region z house region actor mover path manner endp in-region part-of 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

F = e locomotion x man path walking region z house region actor mover path manner endp in-region part-of 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

F = e locomotion x man path walking region z house region actor mover path manner endp in-region part-of 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

F = e locomotion x man path walking region z house region actor mover path manner endp in-region part-of 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

F = e locomotion x man path walking region z house region actor mover path manner endp in-region part-of 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

F = e locomotion x man path walking region z house region actor mover path manner endp in-region part-of 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

F = e locomotion x man path walking region z house region actor mover path manner endp in-region part-of 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

F1 = V1, I

1, g1 subsumes F2 = V2, I 2, g2 (F1 ⊑ F2) iff there is

a (necessarily unique) morphism h : F1 → F2, i.e., a function h : V1 → V2 such that (i) I

2(f )(h(v)) = h(I 1(f )(v)), if I 1(f )(v) is defined, f ∈ Atr, v ∈ V1,

(ii) h(I

1(t)) ⊆ I 2(t), for t ∈ Type

(iii) h(I

1(r)) ⊆ I 2(r), for r ∈ Rel

(iv) h(I

1(n)) = I 2(n), for n ∈ Nname

(v) h(g1(x)) = g2(x), for x ∈ Nvar, if g1(x) is defined

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 65 20

Subsumption and unification

Subsumption

F1 = V1, I

1, g1 subsumes F2 = V2, I 2, g2 (F1 ⊑ F2) iff there is

a (necessarily unique) morphism h : F1 → F2, i.e., a function h : V1 → V2 such that (i) I

2(f )(h(v)) = h(I 1(f )(v)), if I 1(f )(v) is defined, f ∈ Atr, v ∈ V1,

(ii) h(I

1(t)) ⊆ I 2(t), for t ∈ Type

(iii) h(I

1(r)) ⊆ I 2(r), for r ∈ Rel

(iv) h(I

1(n)) = I 2(n), for n ∈ Nname

(v) h(g1(x)) = g2(x), for x ∈ Nvar, if g1(x) is defined

Example

e activity locomotion x man path walking actor mover path manner

⊑

e locomotion man actor mover manner

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 66 20

Subsumption and unification

Subsumption

F1 = V1, I

1, g1 subsumes F2 = V2, I 2, g2 (F1 ⊑ F2) iff there is

a (necessarily unique) morphism h : F1 → F2, i.e., a function h : V1 → V2 such that (i) I

2(f )(h(v)) = h(I 1(f )(v)), if I 1(f )(v) is defined, f ∈ Atr, v ∈ V1,

(ii) h(I

1(t)) ⊆ I 2(t), for t ∈ Type

(iii) h(I

1(r)) ⊆ I 2(r), for r ∈ Rel

(iv) h(I

1(n)) = I 2(n), for n ∈ Nname

(v) h(g1(x)) = g2(x), for x ∈ Nvar, if g1(x) is defined

Example

e activity locomotion x man path walking actor mover path manner

⊑

e locomotion man actor mover manner

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 67 20

Subsumption and unification

Subsumption

F1 = V1, I

1, g1 subsumes F2 = V2, I 2, g2 (F1 ⊑ F2) iff there is

a (necessarily unique) morphism h : F1 → F2, i.e., a function h : V1 → V2 such that (i) I

2(f )(h(v)) = h(I 1(f )(v)), if I 1(f )(v) is defined, f ∈ Atr, v ∈ V1,

(ii) h(I

1(t)) ⊆ I 2(t), for t ∈ Type

(iii) h(I

1(r)) ⊆ I 2(r), for r ∈ Rel

(iv) h(I

1(n)) = I 2(n), for n ∈ Nname

(v) h(g1(x)) = g2(x), for x ∈ Nvar, if g1(x) is defined

Intuition F1 subsumes F2 (F1 ⊑ F2) iff F2 is at least as informative as F1.

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 68 20

Subsumption and unification

Subsumption

F1 = V1, I

1, g1 subsumes F2 = V2, I 2, g2 (F1 ⊑ F2) iff there is

a (necessarily unique) morphism h : F1 → F2, i.e., a function h : V1 → V2 such that (i) I

2(f )(h(v)) = h(I 1(f )(v)), if I 1(f )(v) is defined, f ∈ Atr, v ∈ V1,

(ii) h(I

1(t)) ⊆ I 2(t), for t ∈ Type

(iii) h(I

1(r)) ⊆ I 2(r), for r ∈ Rel

(iv) h(I

1(n)) = I 2(n), for n ∈ Nname

(v) h(g1(x)) = g2(x), for x ∈ Nvar, if g1(x) is defined

Unification Least upper bound F1 ⊔ F2 of F1 and F2 w.r.t. subsumption.

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 69 20

Subsumption and unification

Subsumption

F1 = V1, I

1, g1 subsumes F2 = V2, I 2, g2 (F1 ⊑ F2) iff there is

a (necessarily unique) morphism h : F1 → F2, i.e., a function h : V1 → V2 such that (i) I

2(f )(h(v)) = h(I 1(f )(v)), if I 1(f )(v) is defined, f ∈ Atr, v ∈ V1,

(ii) h(I

1(t)) ⊆ I 2(t), for t ∈ Type

(iii) h(I

1(r)) ⊆ I 2(r), for r ∈ Rel

(iv) h(I

1(n)) = I 2(n), for n ∈ Nname

(v) h(g1(x)) = g2(x), for x ∈ Nvar, if g1(x) is defined

Unification Least upper bound F1 ⊔ F2 of F1 and F2 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

e locomotion x man path walking region z house region actor mover path manner endp in-region part-of

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

e locomotion x man path walking region z house region actor mover path manner endp in-region part-of

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: ϕ1 ∧ . . . ∧ ϕn ⇛ ψ

(ϕi ∈ 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: ϕ1 ∧ . . . ∧ ϕn ⇛ ψ

(ϕi ∈ 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: ϕ1 ∧ . . . ∧ ϕn ⇛ ψ

(ϕi ∈ 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: ϕ1 ∧ . . . ∧ ϕn ⇛ ψ

(ϕi ∈ 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: ϕ1 ∧ . . . ∧ ϕn ⇛ ψ

(ϕi ∈ 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: ϕ1 ∧ . . . ∧ ϕn ⇛ ψ

(ϕi ∈ 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 actor ∶ ⊺ motion mover ∶ ⊺ causation cause ∶ ⊺ ∧ effect ∶ ⊺ activity ∧ motion actor ≐ mover translocation path ∶ ⊺

• nset-causation

cause ∶ punctual-event extended- causation locomotion bounded-translocation 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 ⇛ info-carrier

book book, info-carrier

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 86 24

Atribute-value constraints

Further examples

[Babonnaud et al. 2016]

book ⇛ info-carrier

book 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 ⇛ info-carrier

book 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 ⇛ info-carrier

book 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 ⇛ info-carrier

book 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

reading

• reading

perception comprehension

perc-comp ment-comp

• rdered-
• verlap

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: k1 ·ϕ1 ∧ . . . ∧ kn ·ϕn → 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: k1 ·ϕ1 ∧ . . . ∧ kn ·ϕn → l ·ψ)

Example

e        

eating

actor x theme y         ⊔ u      

person

name ‘Adam’      

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: k1 ·ϕ1 ∧ . . . ∧ kn ·ϕn → l ·ψ)

Example

e        

eating

actor x theme y         ⊔ u      

person

name ‘Adam’       ⊔ x u

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: k1 ·ϕ1 ∧ . . . ∧ kn ·ϕn → l ·ψ)

Example

e        

eating

actor x theme y         ⊔ u      

person

name ‘Adam’       ⊔ x u = e           

eating

actor x u      

person

name ‘Adam’       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: k1 ·ϕ1 ∧ . . . ∧ kn ·ϕn → l ·ψ)

Example

e        

eating

actor x theme y         ⊔ u      

person

name ‘Adam’       ⊔ x u = e           

eating

actor x u      

person

name ‘Adam’       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

1

Introduction to frame semantics Frames in the sense of Fillmore and Barsalou Frames according to this course

2

Formalization of frames Atribute-value descriptions and formulas Formal definition of frames Frames as models Subsumption and unification Atribute-value constraints

3

Further topics Frames versus feature structures Type constraints versus type hierarchy

4

Frame semantics: extensions

5

Summary and outlook

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 97 26

Frames versus feature structures

Feature structures have a designated root node from which each

• ther 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

• ther 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

• ther 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

Frames versus feature structures

Feature structures have a designated root node from which each

• ther node is reachable via an atribute path, and they have no
• relations. |Nvar| = 1, Rel = ∅.

Typed feature structures Nname = ∅

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 101 27

Frames versus feature structures

Feature structures have a designated root node from which each

• ther node is reachable via an atribute path, and they have no
• relations. |Nvar| = 1, Rel = ∅.

Typed feature structures Nname = ∅ Untyped feature structures

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 102 27

Frames versus feature structures

Feature structures have a designated root node from which each

• ther node is reachable via an atribute path, and they have no
• relations. |Nvar| = 1, Rel = ∅.

Typed feature structures Nname = ∅ Untyped feature structures Type = ∅; named nodes have no atributes.

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 103 27

Type constraints versus type hierarchy

Type constraints (Horn) constraints consisting only of type symbols (and ⊤ and ⊥)

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 104 28

Type constraints versus type hierarchy

Type constraints (Horn) constraints consisting only of type symbols (and ⊤ and ⊥) Type hierarchy generated by type constraints ≈ single node models which satisfy all constraints, ordered by (inverse) subsumption

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 105 28

Type constraints versus type hierarchy

Type constraints (Horn) constraints consisting only of type symbols (and ⊤ and ⊥) Type hierarchy generated by type constraints ≈ single node models which satisfy all constraints, ordered by (inverse) subsumption Example activity ⇛ event motion ⇛ event locomotion ⇛ activity locomotion ⇛ motion

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 106 28

Type constraints versus type hierarchy

Type constraints (Horn) constraints consisting only of type symbols (and ⊤ and ⊥) Type hierarchy generated by type constraints ≈ single node models which satisfy all constraints, ordered by (inverse) subsumption Example activity ⇛ event motion ⇛ event locomotion ⇛ activity locomotion ⇛ motion

event activity motion locomotion event activity motion event activity event motion event ∅

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 107 28

Outline of today’s course

1

Introduction to frame semantics Frames in the sense of Fillmore and Barsalou Frames according to this course

2

Formalization of frames Atribute-value descriptions and formulas Formal definition of frames Frames as models Subsumption and unification Atribute-value constraints

3

Further topics Frames versus feature structures Type constraints versus type hierarchy

4

Frame semantics: extensions

5

Summary and outlook

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 108 29

Frame semantics: extensions

Issue How to represent quantification, negation, intensionality, etc. within frame semantics?

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 109 30

Frame semantics: extensions

Issue How to represent quantification, negation, intensionality, etc. within frame semantics? (4) a. Every man kissed some woman.

• b. The king of France is not bald.

c. Adam thinks he has understood what frame semantics is about.

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 110 30

Frame semantics: extensions

Issue How to represent quantification, negation, intensionality, etc. within frame semantics? (4) a. Every man kissed some woman.

• b. The king of France is not bald.

c. Adam thinks he has understood what frame semantics is about. Possible approaches

1 Use an atribute-value language with quantifiers and build

formulas instead of models.

[≈ Kallmeyer/Osswald/Pogodalla 2016]

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 111 30

Frame semantics: extensions

Issue How to represent quantification, negation, intensionality, etc. within frame semantics? (4) a. Every man kissed some woman.

• b. The king of France is not bald.

c. Adam thinks he has understood what frame semantics is about. Possible approaches

1 Use an atribute-value language with quantifiers and build

formulas instead of models.

[≈ Kallmeyer/Osswald/Pogodalla 2016]

2 Keep frames as basic semantic representations and evaluate

quantification over the domain of frames.

[≈ Muskens 2013]

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 112 30

Frame semantics: extensions

Issue How to represent quantification, negation, intensionality, etc. within frame semantics? (4) a. Every man kissed some woman.

• b. The king of France is not bald.

c. Adam thinks he has understood what frame semantics is about. Possible approaches

1 Use an atribute-value language with quantifiers and build

formulas instead of models.

[≈ Kallmeyer/Osswald/Pogodalla 2016]

2 Keep frames as basic semantic representations and evaluate

quantification over the domain of frames.

[≈ Muskens 2013]

3 Try to retain the idea of minimal model building and consider

frame types as proper entities of the model/universe.

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 113 30

Frame semantics: extensions

Atribute-value formulas with quantifiers (qAVForm) ∀ϕ, ∃ϕ (ϕ ∈ AVDesc)

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 114 31

Frame semantics: extensions

Atribute-value formulas with quantifiers (qAVForm) ∀ϕ, ∃ϕ (ϕ ∈ AVDesc) V, I, g ∀ϕ iff V, I, g , v ϕ for every v ∈ V

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 115 31

Frame semantics: extensions

Atribute-value formulas with quantifiers (qAVForm) ∀ϕ, ∃ϕ (ϕ ∈ AVDesc) V, I, g ∀ϕ iff V, I, g , v ϕ for every v ∈ V V, I, g ∃ϕ iff V, I, g , v ϕ for some v ∈ V

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 116 31

Frame semantics: extensions

Atribute-value formulas with quantifiers (qAVForm) ∀ϕ, ∃ϕ (ϕ ∈ AVDesc) A x α, E x α (α ∈ AVForm ∪ qAVForm) V, I, g ∀ϕ iff V, I, g , v ϕ for every v ∈ V V, I, g ∃ϕ iff V, I, g , v ϕ for some v ∈ V

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 117 31

Frame semantics: extensions

Atribute-value formulas with quantifiers (qAVForm) ∀ϕ, ∃ϕ (ϕ ∈ AVDesc) A x α, E x α (α ∈ AVForm ∪ qAVForm) V, I, g ∀ϕ iff V, I, g , v ϕ for every v ∈ V V, I, g ∃ϕ iff V, I, g , v ϕ for some v ∈ V For x dom(g) (= set of variables for which g is defined): V, I, g A x α iff V, I, g′ α for every assignment g′ with dom(g′) = dom(g) ∪ {x} and g(v) = g′(v) for all v ∈ dom(g)

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 118 31

Frame semantics: extensions

Atribute-value formulas with quantifiers (qAVForm) ∀ϕ, ∃ϕ (ϕ ∈ AVDesc) A x α, E x α (α ∈ AVForm ∪ qAVForm) V, I, g ∀ϕ iff V, I, g , v ϕ for every v ∈ V V, I, g ∃ϕ iff V, I, g , v ϕ for some v ∈ V For x dom(g) (= set of variables for which g is defined): V, I, g A x α iff V, I, g′ α for every assignment g′ with dom(g′) = dom(g) ∪ {x} and g(v) = g′(v) for all v ∈ dom(g) V, I, g E x α iff V, I, g′ α for some assignment g′ with ...

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 119 31

Frame semantics: extensions

Atribute-value formulas with quantifiers (qAVForm) ∀ϕ, ∃ϕ (ϕ ∈ AVDesc) A x α, E x α (α ∈ AVForm ∪ qAVForm) V, I, g ∀ϕ iff V, I, g , v ϕ for every v ∈ V V, I, g ∃ϕ iff V, I, g , v ϕ for some v ∈ V For x dom(g) (= set of variables for which g is defined): V, I, g A x α iff V, I, g′ α for every assignment g′ with dom(g′) = dom(g) ∪ {x} and g(v) = g′(v) for all v ∈ dom(g) V, I, g E x α iff V, I, g′ α for some assignment g′ with ... Note: ∀ϕ ≡ A x(x ·ϕ), ∃ϕ ≡ E x(x ·ϕ) (with x not occurring in ϕ)

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 120 31

Frame semantics: extensions

Examples

(5) Every dog barked.

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 121 32

Frame semantics: extensions

Examples

(5) Every dog barked. A x(x · dog → ∃(barking ∧ agent x))

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 122 32

Frame semantics: extensions

Examples

(5) Every dog barked. A x(x · dog → ∃(barking ∧ agent x)) corresponding first-order formula: ∀x(dog(x) → ∃e(barking(e) ∧ agent(e, x)))

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 123 32

Frame semantics: extensions

Examples

(5) Every dog barked. A x(x · dog → ∃(barking ∧ agent x)) corresponding first-order formula: ∀x(dog(x) → ∃e(barking(e) ∧ agent(e, x))) (6) Every man kissed some woman.

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 124 32

Frame semantics: extensions

Examples

(5) Every dog barked. A x(x · dog → ∃(barking ∧ agent x)) corresponding first-order formula: ∀x(dog(x) → ∃e(barking(e) ∧ agent(e, x))) (6) Every man kissed some woman. A x(x · man → E y(y · woman ∧ ∃(kissing ∧ agent x ∧ theme y))

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 125 32

Frame semantics: extensions

Examples

(5) Every dog barked. A x(x · dog → ∃(barking ∧ agent x)) corresponding first-order formula: ∀x(dog(x) → ∃e(barking(e) ∧ agent(e, x))) (6) Every man kissed some woman. A x(x · man → E y(y · woman ∧ ∃(kissing ∧ agent x ∧ theme y)) Example model

• Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf)

126 32

Frame semantics: extensions

Examples

(7) Every man walked into some house. A x(x · man → E z(z · house ∧ ∃(locomotion ∧ manner : walking ∧ actor x ∧ mover actor ∧ goal z ∧ path : (path ∧ endp : region) ∧ [path endp, goal in-region] : part-of )))

endp path manner in-region goal a c t

• r

mover name path manner mover a c t

• r

goal name

locomotion path walking house man ‘John’ locomotion path walking man ‘Peter’ part-of part-of

endp

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 127 33

Frame semantics: extensions

Examples

(7) Every man walked into some house. A x(x · man → E z(z · house ∧ ∃(locomotion ∧ manner : walking ∧ actor x ∧ mover actor ∧ goal z ∧ path : (path ∧ endp : region) ∧ [path endp, goal in-region] : part-of ))) Example model

endp path manner in-region goal a c t

• r

mover name path manner mover a c t

• r

goal name

locomotion path walking house man ‘John’ locomotion path walking man ‘Peter’ part-of part-of

endp

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 128 33

Frame semantics: extensions

AV logic with quantifiers + underspecification (“hole semantics”)

(8) Every dog barked. NP[i = x, mins =

3 ]

NP∗

[e =

2 ]

Det ‘every’ A x(x ⋅ 5 →

6 ), 5 ⊲∗ 2 , 6 ⊲∗ 3

NP[e = l2] N ‘dog’ l2 ∶ dog S VP V ‘barked’ NP[i =

4 , mins = l1]

l1 ∶ ∃(barking ∧ agent ≜

4 )

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 129 34

Frame semantics: extensions

AV logic with quantifiers + underspecification (“hole semantics”)

(8) Every dog barked. NP[i = x, mins =

3 ]

NP∗

[e =

2 ]

Det ‘every’ A x(x ⋅ 5 →

6 ), 5 ⊲∗ 2 , 6 ⊲∗ 3

NP[e = l2] N ‘dog’ l2 ∶ dog S VP V ‘barked’ NP[i =

4 , mins = l1]

l1 ∶ ∃(barking ∧ agent ≜

4 )

• A

x(x · 5 → 6 ), l2 : dog, l1 : ∃(barking ∧ agent x), 5 ⊳∗ l2, 6 ⊳∗ l1

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 130 34

Frame semantics: extensions

AV logic with quantifiers + underspecification (“hole semantics”)

(8) Every dog barked. NP[i = x, mins =

3 ]

NP∗

[e =

2 ]

Det ‘every’ A x(x ⋅ 5 →

6 ), 5 ⊲∗ 2 , 6 ⊲∗ 3

NP[e = l2] N ‘dog’ l2 ∶ dog S VP V ‘barked’ NP[i =

4 , mins = l1]

l1 ∶ ∃(barking ∧ agent ≜

4 )

• A

x(x · 5 → 6 ), l2 : dog, l1 : ∃(barking ∧ agent x), 5 ⊳∗ l2, 6 ⊳∗ l1

• A

x(x · dog → ∃(barking ∧ agent x))

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 131 34

Outline of today’s course

1

Introduction to frame semantics Frames in the sense of Fillmore and Barsalou Frames according to this course

2

Formalization of frames Atribute-value descriptions and formulas Formal definition of frames Frames as models Subsumption and unification Atribute-value constraints

3

Further topics Frames versus feature structures Type constraints versus type hierarchy

4

Frame semantics: extensions

5

Summary and outlook

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 132 35

Summary & outlook

Summary Motivation and background to frame semantics Atribute-value logic as a tailored logic for specifying frames Frames as minimal models of atribute-value formulas Possible ways to express quantification in frames semantics

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 133 36

Summary & outlook

Summary Motivation and background to frame semantics Atribute-value logic as a tailored logic for specifying frames Frames as minimal models of atribute-value formulas Possible ways to express quantification in frames semantics Tomorrow Combining LTAG with frame semantics Elementary constructions as elementary trees with semantic frames Linguistic applications Looking ahead to the factorization of elementary constructions in the metagrammar.

Kallmeyer, Lichte, Osswald & Petitjean (HHU Düsseldorf) 134 36

References

Babonnaud, William, Laura Kallmeyer & Rainer Osswald. 2016. Polysemy and coercion – a frame-based approach using LTAG and Hybrid Logic. In Maxime Amblard, Philippe de Groote, Sylvain Pogodalla & Christian Retoré (eds.), Logical Aspects of Computational Linguistics, 9th International Conference Lecture Notes in Artificial Intelligence 10054, 18–33. Berlin: Springer. Barsalou, Lawrence W. 1992. Frames, concepts, and conceptual fields. In Adrienne Lehrer & Eva Feder Kitay (eds.), Frames, fields, and contrasts, 21–74. Hillsdale, NJ: Lawrence Erlbaum Associates. Carpenter, Bob. 1992. The logic of typed feature structures Cambridge Tracts in Theoretical Computer Science 32. Cambridge: Cambridge University Press. Hegner, Stephen J. 1994. Properties of Horn clauses in feature-structure logic. In C. J. Rupp, Michael A. Rosner & Rod L. Johnson (eds.), Constraints, language and computation, 111–147. San Diego, CA: Academic Press. Kallmeyer, Laura & Rainer Osswald. 2013. Syntax-driven semantic frame composition in Lexicalized Tree Adjoining Grammars. Journal of Language Modelling 1(2). 267–330. Kallmeyer, Laura, Rainer Osswald & Sylvain Pogodalla. 2016. For-adverbials and aspectual interpretation: An LTAG analysis using hybrid logic and frame semantics. In Christopher Pi˜ nón (ed.), Empirical issues in syntax and semantics EISS, vol. 11, . Muskens, Rheinard. 2013. Data semantics and linguistic semantics. In Maria Aloni, Michael Franke & Floris Roelofsen (eds.), The dynamic, inquisitive, and visionary life of ϕ, ?ϕ, and ⋄ϕ. A festschrif for Jeroen Groenendijk, Martin Stokhof, and Frank Veltman, 175–183. Osswald, Rainer. 1999. Semantics for atribute-value theories. In Paul Dekker (ed.), Proceedings of the twelfh amsterdam colloquium, 199–204. Amsterdam: University of Amsterdam, ILLC.

References (cont.)

Osswald, Rainer & Robert D. Van Valin, Jr. 2014. FrameNet, frame structure, and the syntax-semantics interface. In Thomas Gamerschlag, Doris Gerland, Rainer Osswald & Wiebke Petersen (eds.), Frames and concept types (Studies in Linguistics and Philosophy 94), 125–156. Dordrecht: Springer. Rappaport Hovav, Malka & Beth Levin. 1998. Building verb meanings. In Miriam But & Wilhelm Geuder (eds.), The projection of arguments: Lexical and compositional factors, 97–134. Stanford, CA: CSLI Publications. Rounds, William C. 1997. Feature logics. In Johan van Benthem & Alice ter Meulen (eds.), Handbook of logic and language, 475–533. Amsterdam: North-Holland.