Examples of Accessibility Constraint Modelling Sylvain Pogodalla - - PowerPoint PPT Presentation

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Examples of Accessibility Constraint Modelling

Sylvain Pogodalla INRIA Nancy Grand-Est Calligramme May 14th

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car.

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. ∃x car x ∧ own j x

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. It is red. ∃x car x ∧ own j x

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. It is red. ∃x car x ∧ own j x ∧ red x

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. It is red. ∃x car x ∧ own j x ∧ red x John doesn’t own a car.

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. It is red. ∃x car x ∧ own j x ∧ red x John doesn’t own a car. ¬(∃x car x ∧ own j x)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. It is red. ∃x car x ∧ own j x ∧ red x John doesn’t own a car. ∗It is red. ¬(∃x car x ∧ own j x)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. It is red. ∃x car x ∧ own j x ∧ red x John doesn’t own a car. ∗It is red. ¬(∃x car x ∧ own j x) ∧ red x

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. It is red. ∃x car x ∧ own j x ∧ red x John doesn’t own a car. ∗It is red. ¬(∃x car x ∧ own j x) ∧ red x John doesn’t own a car.

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. It is red. ∃x car x ∧ own j x ∧ red x John doesn’t own a car. ∗It is red. ¬(∃x car x ∧ own j x) ∧ red x John doesn’t own a car. ¬(∃x car x ∧ own j x)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. It is red. ∃x car x ∧ own j x ∧ red x John doesn’t own a car. ∗It is red. ¬(∃x car x ∧ own j x) ∧ red x John doesn’t own a car. He is ecology-minded. ¬(∃x car x ∧ own j x)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. It is red. ∃x car x ∧ own j x ∧ red x John doesn’t own a car. ∗It is red. ¬(∃x car x ∧ own j x) ∧ red x John doesn’t own a car. He is ecology-minded. ¬(∃x car x ∧ own j x) ∧ ecolo j

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric pronouns and their antecedents

Example (Existentials, proper nouns, and negation) John owns a car. It is red. ∃x car x ∧ own j x ∧ red x John doesn’t own a car. ∗It is red. ¬(∃x car x ∧ own j x) ∧ red x John doesn’t own a car. He is ecology-minded. ¬(∃x car x ∧ own j x) ∧ ecolo j What we’ve learned from DRT: Indefinite noun phrases (existentials) introduce discourse referents Negation limits the accessibility of discourse referents (existentials = proper nouns)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric Pronouns and Their Antecedents

Example (Hierarchical structure of the discourse [Busquets et al.(2001)]) Jean est ` a l’hˆ

• pital.

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric Pronouns and Their Antecedents

Example (Hierarchical structure of the discourse [Busquets et al.(2001)]) Jean est ` a l’hˆ

• pital.

Marie lui a cass´ e le nez.

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric Pronouns and Their Antecedents

Example (Hierarchical structure of the discourse [Busquets et al.(2001)]) Jean est ` a l’hˆ

• pital.

Marie lui a cass´ e le nez. Pierre lui a cass´ e le bras..

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric Pronouns and Their Antecedents

Example (Hierarchical structure of the discourse [Busquets et al.(2001)]) Jean est ` a l’hˆ

• pital.

Marie lui a cass´ e le nez. Pierre lui a cass´ e le bras.. Il l’a mˆ eme mordu.

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric Pronouns and Their Antecedents

Example (Hierarchical structure of the discourse [Busquets et al.(2001)]) Jean est ` a l’hˆ

• pital.

Marie lui a cass´ e le nez. Pierre lui a cass´ e le bras..

∗Elle l’a mˆ

eme mordu.

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric Pronouns and Their Antecedents

Example (Hierarchical structure of the discourse [Busquets et al.(2001)]) Jean est ` a l’hˆ

• pital.

Marie lui a cass´ e le nez. Pierre lui a cass´ e le bras.. Il l’a mˆ eme mordu.

Jean est ` a l’hˆ

• pital

Marie lui a cass´ e le nez Pierre lui a cass´ e le bras Il l’a mˆ eme mordu

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric Pronouns and Their Antecedents

Example (Hierarchical structure of the discourse [Busquets et al.(2001)]) Jean est ` a l’hˆ

• pital.

Marie lui a cass´ e le nez. Pierre lui a cass´ e le bras..

∗Elle l’a mˆ

eme mordu.

Jean est ` a l’hˆ

• pital

Marie lui a cass´ e le nez Pierre lui a cass´ e le bras

∗Elle l’a mˆ

eme mordu

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

Anaphoric Pronouns and Their Antecedents

Example (Hierarchical structure of the discourse [Busquets et al.(2001)]) Jean est ` a l’hˆ

• pital.

Marie lui a cass´ e le nez. Pierre lui a cass´ e le bras..

∗Elle l’a mˆ

eme mordu.

Jean est ` a l’hˆ

• pital

Marie lui a cass´ e le nez Pierre lui a cass´ e le bras

∗Elle l’a mˆ

eme mordu

What we’ve learned from theories on rhetorical structure Segments of the discourse stand in relation to each other Depending on the relation (coordinating, subordinating), discourse markers are accessible or not

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Formal framework

Motivations

Requirement: Standard notions of interpretation Unlike DRT/DPL:

Dynamic scoping Destructive assignment

SDRT: idem Requirement: Declarative approach to accessibility constraints Accessibility defined on the representation language, not on a meta-level.

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Aims

Adapting [de Groote(2006)] Management of proper nouns Negation and accessibility of discourse referents

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Aims

Adapting [de Groote(2006)] Management of proper nouns Negation and accessibility of discourse referents Modelling of other theories We do not commit ourselves with any specific theory. Consequently, our approach is independent of the target logic that is used to express the meaning of the

• expressions. [de Groote(2006)]

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Aims

Adapting [de Groote(2006)] Management of proper nouns Negation and accessibility of discourse referents Modelling of other theories We do not commit ourselves with any specific theory. Consequently, our approach is independent of the target logic that is used to express the meaning of the

• expressions. [de Groote(2006)]

Modelling the RFC

Outline

1

Motivations Accessibility According to DRT Accessibility According to Discourse Hierarchy Theoretical Framework

2

Aims Adapting [de Groote(2006)] Modelling of Other Theories: the RFC

3

Context Management: [de Groote(2006)]’s approach General Ideas Negation Negation Revisited

4

Application to the RFC Its Modelling

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Interpretation of sentences s = γ → (γ → t) → t

e:γ

z }| { S

φ:γ→t

z }| { | {z }

t

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ)

e::γ

z }| { S1. S2

φ:γ→t

z }| { | {z }

λe′.S2 e′ φ:γ→t

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car j y car y

• wn j y

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car j y car y

• wn j y

λeφ.∃y.car y ∧ own j y ∧ φ (y :: e)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car j y car y

• wn j y

λeφ.∃y.car y ∧ own j y ∧ φ (y :: e) it

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car j y car y

• wn j y

λeφ.∃y.car y ∧ own j y ∧ φ (y :: e) it z=?

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car j y car y

• wn j y

λeφ.∃y.car y ∧ own j y ∧ φ (y :: e) it z=? λPeφ.P (sel e) e φ

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car j y car y

• wn j y

λeφ.∃y.car y ∧ own j y ∧ φ (y :: e) it z=? λPeφ.P (sel e) e φ it is red

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car j y car y

• wn j y

λeφ.∃y.car y ∧ own j y ∧ φ (y :: e) it z=? λPeφ.P (sel e) e φ it is red z red z z =?

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car j y car y

• wn j y

λeφ.∃y.car y ∧ own j y ∧ φ (y :: e) it z=? λPeφ.P (sel e) e φ it is red z red z z =? λeφ.red(sel e) ∧ φ e

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car j y car y

• wn j y

λeφ.∃y.car y ∧ own j y ∧ φ (y :: e) it z=? λPeφ.P (sel e) e φ it is red z red z z =? λeφ.red(sel e) ∧ φ e John owns a car it is red

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car j y car y

• wn j y

λeφ.∃y.car y ∧ own j y ∧ φ (y :: e) it z=? λPeφ.P (sel e) e φ it is red z red z z =? λeφ.red(sel e) ∧ φ e John owns a car it is red j y z car y

• wn j y

red z z = y

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Accessibility

The Context (Accessible Discourse Referents) as an Argument

Composition of sentences S1.S2 = λeφ.S1 e (λe′.S2 e′ φ) Example John owns a car j y car y

• wn j y

λeφ.∃y.car y ∧ own j y ∧ φ (y :: e) it z=? λPeφ.P (sel e) e φ it is red z red z z =? λeφ.red(sel e) ∧ φ e John owns a car it is red j y z car y

• wn j y

red z z = y λeφ.∃y.car y ∧ own j y ∧ red(sel y :: e) ∧φ (y :: e)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Lexical Semantics

Lexicon John = λPeφ.P j e φ

• wns

= λOS.S(λx.O(λye′φ′.own x y ∧ φ′ e′)) a = λPQeφ.∃y.P y (y :: e) φ ∧ Q y (y :: e) φ car = λxeφ.car x

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Lexical Semantics

Lexicon John = λPeφ.P j e φ

• wns

= λOS.S(λx.O(λye′φ′.own x y ∧ φ′ e′)) a = λPQeφ.∃y.P y (y :: e) φ ∧ Q y (y :: e) φ car = λxeφ.car x Example a car = λQeφ.∃y.car y ∧ Q y (y :: e) φ

• wns(a car)

= λS.S(λx.(λQeφ.∃y.car y ∧ Q y (y :: e) φ) (λye′φ′.own x y ∧ φ′ e′)) = λS.S(λx.(λeφ.∃y.car y ∧ (λye′φ′.own x y ∧ φ′ e′) y (y :: e) φ)) = λS.S(λx.(λeφ.∃y.car y ∧ (own x y ∧ φ (y :: e))))

• wns(a car)John

= (λPeφ.P j e φ)(λx.(λeφ.∃y.car y ∧ (own x y ∧ φ (y :: e)))) = (λeφ.(λx.(λeφ.∃y.car y ∧ (own x y ∧ φ (y :: e)))) j e φ) = λeφ.∃y.car y ∧ (own j y ∧ φ (y :: e))

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Existentials and negation [de Groote(2007)]

Existential quantification Σx.Px

∆

= λeφ.∃x.P x (x :: e) φ

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Existentials and negation [de Groote(2007)]

Existential quantification Σx.Px

∆

= λeφ.∃x.P x (x :: e) φ Negation ˜A

∆

= λeφ.¬(A e (λe.⊤)) ∧ φ e

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Existentials and negation [de Groote(2007)]

Existential quantification Σx.Px

∆

= λeφ.∃x.P x (x :: e) φ Negation ˜A

∆

= λeφ.¬(A e (λe.⊤)) ∧ φ e Problems with the negation No new discourse referent is added to the environment given to the continuation But proper nouns should be added

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

The Negation Revisited

Reminder: Negation ˜A

∆

= λeφ.¬(A e (λe.⊤)) ∧ φ e

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

The Negation Revisited

Reminder: Negation ˜A

∆

= λeφ.¬(A e (λe.⊤)) ∧ φ e Alternative proposals ˜A

∆

= λeφ.¬(A e (λe′.φ e))

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

The Negation Revisited

Reminder: Negation ˜A

∆

= λeφ.¬(A e (λe.⊤)) ∧ φ e Alternative proposals ˜A

∆

= λeφ.¬(A e (λe′.φ e)) ˜A

∆

= λeφ.¬(A e (λe′.¬(φ e)))

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

The Negation Revisited

Reminder: Negation ˜A

∆

= λeφ.¬(A e (λe.⊤)) ∧ φ e Alternative proposals ˜A

∆

= λeφ.¬(A e (λe′.φ e)) ˜A

∆

= λeφ.¬(A e (λe′.¬(φ e))) ˜A

∆

= λe1e2φ.¬(Ae1e2(λe′

1e′ 2.¬(φe′ 1e2)))

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

The Negation Revisited

Reminder: Negation ˜A

∆

= λeφ.¬(A e (λe.⊤)) ∧ φ e Alternative proposals ˜A

∆

= λeφ.¬(A e (λe′.φ e)) ˜A

∆

= λeφ.¬(A e (λe′.¬(φ e))) ˜A

∆

= λe1e2φ.¬(Ae1e2(λe′

1e′ 2.¬(φe′ 1e2)))

• wns

= λOS.S(λx.O(λye′φ′.own x y ∧ φ′ e′))

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

The Negation Revisited

Reminder: Negation ˜A

∆

= λeφ.¬(A e (λe.⊤)) ∧ φ e Alternative proposals ˜A

∆

= λeφ.¬(A e (λe′.φ e)) ˜A

∆

= λeφ.¬(A e (λe′.¬(φ e))) ˜A

∆

= λe1e2φ.¬(Ae1e2(λe′

1e′ 2.¬(φe′ 1e2)))

• wns

= λOS.S(λx.O(λye′φ′.own x y ∧ φ′ e′)) Our proposal s

∆

= κ → γ → γ → (κ → γ → γ → o) → o (κ

∆

= o → o → o) ˜A

∆

= λce1e2φ.¬(A (¬c) e1 e2(λc′e′

1e′ 2.¬(φc′e′ 1e2)))

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

The Negation Revisited

Reminder: Negation ˜A

∆

= λeφ.¬(A e (λe.⊤)) ∧ φ e Alternative proposals ˜A

∆

= λeφ.¬(A e (λe′.φ e)) ˜A

∆

= λeφ.¬(A e (λe′.¬(φ e))) ˜A

∆

= λe1e2φ.¬(Ae1e2(λe′

1e′ 2.¬(φe′ 1e2)))

• wns

= λOS.S(λx.O(λye′φ′.own x y ∧ φ′ e′)) Our proposal s

∆

= κ → γ → γ → (κ → γ → γ → o) → o (κ

∆

= o → o → o) ˜A

∆

= λce1e2φ.¬(A (¬c) e1 e2(λc′e′

1e′ 2.¬(φc′e′ 1e2)))

s1.s2 = λce1e2φ.s1 c e1 e2(λc′e′

1e′ 2.s2c′e′ 1e′ 2φ)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Example

Lexicon John = λPce1e2φ.P j c (j :: e1) e2 φ doesn’t = λVSce1e2φ.¬((V S) (¬c) e1 e2(λc′e′

1e′ 2.¬(φ c′ e′ 1 e2)))

• wns

= λOS.S(λx.O(λyc′e′

1e′ 2φ′.c′(own x y)(φ′ c′ e′ 1 e′ 2)))

a = λPQce1e2φ.∃x.[λφ′.(P x c e1 e2 φ′) ∧ (Q x c e1 e2 φ′)](λc′e′

1e′ 2.φce′ 1(x :: e′ 2))

car = λxce1e2φ.c(car x)(φ c e1 e2) he = λPce1e2φ.P (sel e1 ∪ e2) it = λPce1e2φ.P (sel e1 ∪ e2) is = λAS.S(λxc′e′

1e′ 2φ′.c′(A(λyc′′e′′ 1 e′′ 2 φ′′.⊤)x c′ e′ 1 e′ 2 φ′)(φ′ c′ e′ 1 e′ 2))

red = λPxce1e2φ.(P x c e1 e2 φ) ∧ (red x)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Example

Lexicon John = λPce1e2φ.P j c (j :: e1) e2 φ doesn’t = λVSce1e2φ.¬((V S) (¬c) e1 e2(λc′e′

1e′ 2.¬(φ c′ e′ 1 e2)))

• wns

= λOS.S(λx.O(λyc′e′

1e′ 2φ′.c′(own x y)(φ′ c′ e′ 1 e′ 2)))

a = λPQce1e2φ.∃x.[λφ′.(P x c e1 e2 φ′) ∧ (Q x c e1 e2 φ′)](λc′e′

1e′ 2.φce′ 1(x :: e′ 2))

car = λxce1e2φ.c(car x)(φ c e1 e2) he = λPce1e2φ.P (sel e1 ∪ e2) it = λPce1e2φ.P (sel e1 ∪ e2) is = λAS.S(λxc′e′

1e′ 2φ′.c′(A(λyc′′e′′ 1 e′′ 2 φ′′.⊤)x c′ e′ 1 e′ 2 φ′)(φ′ c′ e′ 1 e′ 2))

red = λPxce1e2φ.(P x c e1 e2 φ) ∧ (red x) Example (d=John doesn’t own a car. ∗It is red) d (∧) nil nil φe = (¬∃y.(car y ∧ owe j y)) ∧ red(sel (j :: nil)) with φe = λce1e2.¬(c ⊤⊥)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Example

Lexicon John = λPce1e2φ.P j c (j :: e1) e2 φ doesn’t = λVSce1e2φ.¬((V S) (¬c) e1 e2(λc′e′

1e′ 2.¬(φ c′ e′ 1 e2)))

• wns

= λOS.S(λx.O(λyc′e′

1e′ 2φ′.c′(own x y)(φ′ c′ e′ 1 e′ 2)))

a = λPQce1e2φ.∃x.[λφ′.(P x c e1 e2 φ′) ∧ (Q x c e1 e2 φ′)](λc′e′

1e′ 2.φce′ 1(x :: e′ 2))

car = λxce1e2φ.c(car x)(φ c e1 e2) he = λPce1e2φ.P (sel e1 ∪ e2) it = λPce1e2φ.P (sel e1 ∪ e2) is = λAS.S(λxc′e′

1e′ 2φ′.c′(A(λyc′′e′′ 1 e′′ 2 φ′′.⊤)x c′ e′ 1 e′ 2 φ′)(φ′ c′ e′ 1 e′ 2))

red = λPxce1e2φ.(P x c e1 e2 φ) ∧ (red x) Example (d=John doesn’t own a car. He is ecology-minded) d (∧) nil nil φe = (¬∃y.(car y ∧ owe j y)) ∧ ecolo(sel(j :: nil)) with φe = λce1e2.¬(c ⊤⊥)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

The RFC

Its modelling

Jean est ` a l’hˆ

• pital

Marie lui a cass´ e le nez Pierre lui a cass´ e le bras Il l’a mˆ eme mordu/Elle l’a mˆ eme mordu

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

The RFC

Its modelling

Jean est ` a l’hˆ

• pital

Marie lui a cass´ e le nez Pierre lui a cass´ e le bras Il l’a mˆ eme mordu/Elle l’a mˆ eme mordu Coordinating and Subordinating Sentence Composition Two compositions: −.c− and −.s− κ

∆

= γ → γ → γ s

∆

= κ → γ → γ → (κ → γ → γ → t) → t Coord = λlastdom.dom and Sub = λlastdom.last ∪ dom s1.ss2 = λclastdomφ.s1 c last dom(λc′last 1dom2.s2 Sub last 1 (c last dom) φ) s1.cs2 = λclastdomφ.s1 c last dom(λc′last 1dom2.s2 Coord last 1 (c last dom) φ)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

The RFC

Its modelling

Jean est ` a l’hˆ

• pital

Marie lui a cass´ e le nez Pierre lui a cass´ e le bras Il l’a mˆ eme mordu/Elle l’a mˆ eme mordu Coordinating and Subordinating Sentence Composition Two compositions: −.c− and −.s− κ

∆

= γ → γ → γ s

∆

= κ → γ → γ → (κ → γ → γ → t) → t Coord = λlastdom.dom and Sub = λlastdom.last ∪ dom s1.ss2 = λclastdomφ.s1 c last dom(λc′last 1dom2.s2 Sub last 1 (c last dom) φ) s1.cs2 = λclastdomφ.s1 c last dom(λc′last 1dom2.s2 Coord last 1 (c last dom) φ) Hypothesis: John est ` a l’hˆ

• pital.s(Marie lui a cass´

e le nez.cPierre lui a cass´ e le bras.cIl l’a mˆ eme mordu)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Subordinating and coordinating composition

Coord = λlastdom.dom and Sub = λlastdom.last ∪ dom s1.ss2 = λclastdomφ.s1 c last dom(λc′last 1dom2.s2 Sub last 1 (c last dom) φ) s1 s2 s1.ss2Sub = λlastdomφ.s1 Sub last dom(λc′last 1dom2.s2 Sub last 1 (last ∪ dom) φ)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Subordinating and coordinating composition

Coord = λlastdom.dom and Sub = λlastdom.last ∪ dom s1.ss2 = λclastdomφ.s1 c last dom(λc′last 1dom2.s2 Sub last 1 (c last dom) φ) s1 s2 s1.ss2Coord = λlastdomφ.s1 Coord last dom(λc′last 1dom2.s2 Sub last 1 (dom) φ)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Subordinating and coordinating composition

Coord = λlastdom.dom and Sub = λlastdom.last ∪ dom s1.cs2 = λclastdomφ.s1 c last dom(λc′last 1dom2.s2 Coord last 1 (c last dom) φ) s1 s2 s1.cs2Sub = λlastdomφ.s1 Sub last dom(λc′last 1dom2.s2 Coord last 1 (last ∪ dom) φ)

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

Subordinating and coordinating composition

Coord = λlastdom.dom and Sub = λlastdom.last ∪ dom s1.cs2 = λclastdomφ.s1 c last dom(λc′last 1dom2.s2 Coord last 1 (c last dom) φ) s1 s2 s1.cs2Coord = λclastdomφ.s1 Coord last dom(λc′last 1dom2.s2 Coord last 1 (dom) φ)

Conclusion

Summary Extension of [de Groote(2006)]’s modelling of negation Different contexts according to their accessibility properties Account of the RFC Perspectives Negation? Anaphora hierarchy Complex discourse structures (Discourse pops, DAG rhetorical structures) Interaction with lexical semantics (cf. contrast, parallel)/salience feature

Motivations Aims Context Management: [de Groote(2006)]’s approach Application to the RFC

• J. Busquets, L. Vieu, and N. Asher.

La SDRT : une approche de la coh´ erence du discours dans la tradition de la s´ emantique dynamique. Verbum, 23(1), 2001.

• P. de Groote.

Towards a montagovian account of dynamics. In Proceedings of Semantics and Linguistic Theory XVI, 2006. http://research.nii.ac.jp/salt16/proceedings/degroote.new.pdf.

• P. de Groote.

Yet another dynamic logic. Presentation at the 4th Lambda Calculus and Formal Grammar workshop, September 18-19 2007. http://www.loria.fr/equipes/calligramme/acg/workshops/lcfg-04/slides/ lcfg04-degroote.pdf.