Semantic Modeling with Frames Rainer Osswald & Wiebke Petersen - - PowerPoint PPT Presentation

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Semantic Modeling with Frames Rainer Osswald & Wiebke Petersen Department of Linguistics and Information Science Heinrich-Heine-Universit at D usseldorf ESSLLI 2018 Introductory Course Sofia University 06. 08. 10. 08. 2018 SFB

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SLIDE 1

Semantic Modeling with Frames

Rainer Osswald & Wiebke Petersen

Department of Linguistics and Information Science Heinrich-Heine-Universit¨ at D¨ usseldorf

ESSLLI 2018

Introductory Course

Sofia University

  • 06. 08. – 10. 08. 2018

SFB 991

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SLIDE 2

Part 5 Nominal frames and Shifs

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 1

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frames as atribute-value structures

tree trunk crown bark crown trunk bark

tree-frame          tree crown: crown trunk:

  • trunk

bark : bark

       

Given a set of types T and a set of atributes A. A basic frame over (T, A) is a tuple Q, ¯ q, arg,θ,δ with Q is a finite set of nodes. ¯ q ∈ Q is the central node arg ⊆ Q argument nodes. ind ⊆ Q individual nodes. θ : Q → T is the typing function δ : Qn × A → Q is the partial transition function. such that the underlying graph (Q, E) with edge set E = {{qi, q}|∃a ∈ A, qi ∈ {q1, . . . , qn} : δ(q1, . . . qn, a) = q} is connected.

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 2

L Carpenter 1992 L Petersen 2007

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SLIDE 4

frames as atribute-value structures

tree trunk crown bark crown trunk bark

tree-frame

tree trunk bark trunk bark

trunk (of)-frame

class person person class class

classmate (of)-frame

Given a set of types T and a set of atributes A. A basic frame over (T, A) is a tuple Q, ¯ q, arg,θ,δ with Q is a finite set of nodes. ¯ q ∈ Q is the central node arg ⊆ Q argument nodes. ind ⊆ Q individual nodes. θ : Q → T is the typing function δ : Qn × A → Q is the partial transition function. such that the underlying graph (Q, E) with edge set E = {{qi, q}|∃a ∈ A, qi ∈ {q1, . . . , qn} : δ(q1, . . . qn, a) = q} is connected.

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 2

L Carpenter 1992 L Petersen 2007

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SLIDE 5

Remarks

The definition and the notation differs slightly from the one we used the last days frames are connected, directed graphs with labeled nodes (by types) and arcs (by atributes) argument nodes are represented as rectangular nodes individual nodes are marked by small pointing arrows the central node is marked by a double line the restriction that every node can be reached via directed arcs from an argument

  • r the central node is dropped

the types are writen inside the nodes

locomotion man path walking a c t

  • r

m

  • v

e r p a t h manner

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 3

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Definition (Subsumption) A frame F1 = Q1, ¯ q1,θ1,δ1 subsumes a frame F2 = Q2, ¯ q2,θ2,δ2 (F ⊑ F ′) iff there is a total function h : Q1 → Q2 with h(¯ q1) = ¯ q2, ∀q ∈ Q1 : θ1(q) ⊑ θ2(h(q)), if δ1(f , q) is defined, then h(δ1(f , q)) = δ2(f , h(q)). Definition (Equivalence) Two frames F1 and F2 are equivalent (F1 ∼ F2), if F1 ⊑ F2 and F2 ⊑ F1.

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 4

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SLIDE 7

Definition (Subsumption) A frame F1 = Q1, ¯ q1,θ1,δ1 subsumes a frame F2 = Q2, ¯ q2,θ2,δ2 (F ⊑ F ′) iff there is a total injective function h : Q1 → Q2 with h(¯ q1) = ¯ q2, ∀q ∈ Q1 : θ1(q) ⊑ θ2(h(q)), if δ1(f , q) is defined, then h(δ1(f , q)) = δ2(f , h(q)). Definition (Equivalence) Two frames F1 and F2 are equivalent (F1 ∼ F2), if F1 ⊑ F2 and F2 ⊑ F1.

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 4

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Adaption of subsumption relation

child person

FATHER

⊑

child person child

FATHER F A T H E R

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 5

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SLIDE 9

Adaption of subsumption relation

child person

F A T H E R

⊒

child person child

F A T H E R FATHER

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 5

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SLIDE 10

concept classification

person, pope, house, verb, sun, Mary, wood, brother, mother, meaning, distance, spouse, argument, entrance

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 6

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SLIDE 11

concept classification: relationality

non-relationalperson, pope, house, verb, sun, Mary, wood relational brother, mother, meaning, distance, spouse, argument, entrance

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 7

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concept classification: uniqueness of reference

non-unique reference unique reference non-relationalperson, house, verb, wood Mary, pope, sun relational brother, argument, entrance mother, meaning, distance, spouse

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 8

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concept classification

non-unique reference unique reference non-relationalsortal concept individual concept λx. P(x) λx. x = ιu. P(u) relational proper relational concept functional concept λyλx. R(x, y) λyλx. x = f (y)

L¨

  • bner (2011): ‘Concept Types and Determination’ Journal of Semantics 28: 279-333
  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 9

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concept classification

non-unique reference unique reference non-relationalsortal concept individual concept λx. P(x) λx. x = ιu. P(u) ιu. P(u) relational proper relational concept functional concept λyλx. R(x, y) λyλx. x = f (y) λy. f (y)

L¨

  • bner (2011): ‘Concept Types and Determination’ Journal of Semantics 28: 279-333
  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 9

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frames and functional concepts

tree trunk crown bark numeric trunk c r

  • w

n bark diameter

atributes describe functional relations, i.e., they represent functions atributes correspond to functional concepts ⇒ frames decompose concepts into functional concepts ⇒ functional concepts embody the concept type on which categorization is based

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 10

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sortal concepts

tree-Frame

tree trunk crown bark numeric trunk crown bark diameter

λx. crown(crown(x)) ∧ bark(bark(trunk(x))) ∧ numeric(diameter(trunk(x))) ∧ . . .

tree trunk-Frame

tree trunk bark numeric trunk b a r k d i a m e t e r

λx. trunk(εu. x = trunk(u)) ∧ bark(bark(x)) ∧ numeric(diameter(x)) ∧ . . . λx∃u. x = trunk(u) ∧ bark(bark(x)) ∧ numeric(diameter(x)) ∧ . . .

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 11

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individual concepts

Mary-frame predicate constant ‘Mary’:

Mary

λx. x = ιy. (y = Mary) pope-frame predicate constant ‘pope’:

RCC head

λx. x = head(ιy. y = RCC)

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 12

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individual concepts

Mary-frame predicate constant ‘Mary’:

Mary

λx. x = ιy. (y = Mary) individual constant ‘Mary’:

Mary

ιx. x = Mary pope-frame predicate constant ‘pope’:

RCC head

λx. x = head(ιy. y = RCC) individual constant ‘pope’:

RCC head

ιx. x = head(RCC)

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 12

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Summary: non-relational concepts

sortal concepts

  • ne open argument

individual concepts

  • ne open argument

there is a direct path from a definite node to the central node

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 13

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SLIDE 20

proper relational concepts

classmate-frame

class person person class class

λyλx. class(x) = class(y) ∧ . . .

child-frame

person person mother

λyλx. y = mother(x) ∧ person(x) ∧ person(y)

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 14

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functional concepts

head-frame

predicate constant ‘head’:

head

λyλx. x = head(y)

haircolor-frame

predicate constant ‘haircolor’:

hair color

λyλx. x = color(hair(y))

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 15

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functional concepts

head-frame

predicate constant ‘head’:

head

λyλx. x = head(y) function constant ‘head’:

head

λy. head(y)

haircolor-frame

predicate constant ‘haircolor’:

hair color

λyλx. x = color(hair(y)) function constant ‘haircolor’:

hair color

λy. color(hair(y))

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 15

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Summary: relational concepts

proper relational concepts two open arguments no direct path from the other open argument to the central node functional concepts two open arguments there is a direct path from the other open argument to the central node

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 16

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Summary: concept classes and frames

sortal concepts default frame: λx. P(x) e, t

  • ne open node = central node

Examples: stone, teenager, tree individual concepts default frame: ιu. P(u) e no open node Examples: pope, Mary proper relational concepts default frame: λyλx. R(x, y) e, e, t two open nodes, central node is open and not reachable from second open node Examples: sister, son, finger functional concepts default frame: λy. f (y) e, e central node reachable from an open node, central node not open. Examples: mother, trunk, color

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 17

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type shifs: non-relational → relational

sortal individual proper relational functional

flat person person tenant housing

  • wner

sortal concept flat: “Many flats are offered in the newspaper.”

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 18

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type shifs: non-relational → relational

sortal individual proper relational functional

flat person person tenant housing

  • wner

proper relational concept flat: “This flat is a flat of John, he owns more than five.”

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 18

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type shifs: non-relational → relational

sortal individual proper relational functional

flat person person t e n a n t housing

  • wner

functional concept flat: “The flat of Mary is huge and the rent is reasonable.”

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 18

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type shifs: relational → non-relational

sortal individual proper relational functional

tree trunk bark numeric trunk b a r k diameter

functional concept trunk: “She sat with her back against the trunk of an oak.”

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 19

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type shifs: relational → non-relational

sortal individual proper relational functional

tree trunk bark numeric trunk b a r k diameter

sortal concept trunk: “They rested and sat on a trunk.”

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 19

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Metonymic Shifs

State Bulgaria Rumen Radew area team law name president soccer team g e

  • g

r . r e g i

  • n

law

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 20

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Metonymic Shifs

State Bulgaria Rumen Radew area team law name president soccer team

  • geogr. region

l a w “Bulgaria won 2:3”

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 21

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Metonymic Shifs

State Bulgaria Rumen Radew area team law name president soccer team

  • geogr. region

law “Bulgaria allows to vote from the age of 18 on”

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 22

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Metonymic Shifs

State Bulgaria Rumen Radew area team law name president soccer team

  • geogr. region

l a w “Bulgaria speaks afer Latvia”

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 23

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Metonymic Shifs

State Bulgaria Rumen Radew area team law name president soccer team

  • geogr. region

l a w “This bus goes to Bulgaria.”

  • R. Osswald & W. Petersen

Semantic Modeling with Frames | Part 5 | ESSLLI 2018 | Sofia 24