Segmented Discourse Representation Theory Alex Tantos Segmented Discourse Representation Theory A theory of discourse interpretation 14/05 Course: “Computerlinguistik

Segmented Discourse Representation Theory Segmented Discourse Representation Theory Alex TantosAlex Tantos

Segmented Discourse Representation Segmented Discourse Representation Theory Theory

A theory of discourse interpretationA theory of discourse interpretation

14/05 14/05

Course: “Computerlinguistik II”Course: “Computerlinguistik II”

Alexandros Tantos Alexandros Tantos [email protected]@uni-konstanz.dekonstanz.de


The structure of the sessionThe structure of the session

• The placement of computational discourse The placement of computational discourse semantics and SDRT in NLPsemantics and SDRT in NLP

• The need for dynamic semantics in the The need for dynamic semantics in the discourse (inter-)(re-)presentation discourse (inter-)(re-)presentation (Discourse (Discourse Representation Theory: advantages and Representation Theory: advantages and drawbacks) drawbacks)

• Evidence for SDRT and rhetorical relationsEvidence for SDRT and rhetorical relations

• Possible NLP applications based on such a Possible NLP applications based on such a framework: what comes next?framework: what comes next?


The theory in our mind and in NLPThe theory in our mind and in NLP

MacrostructureMacrostructure of semantic “deep” NLP of semantic “deep” NLP applicationsapplications

Understanding Understanding

““Input”Input”

systemssystems

GenerationGeneration

““Output”-Output”-ResponseResponse

systemssystems

InterpretationInterpretation


Discourse semanticsDiscourse semantics

Static vs. Dynamic semanticsStatic vs. Dynamic semantics

Prehistory – Static approaches Prehistory – Static approaches

•Static semantics (sentential level): satisfaction of first-order Static semantics (sentential level): satisfaction of first-order logical (FOL) formulas in a model with respect to (x-variant) logical (FOL) formulas in a model with respect to (x-variant) assignment functions assignment functions

Every boy loves a girl. (2 readings nicely translated by FOL, Every boy loves a girl. (2 readings nicely translated by FOL, the one straightforwardly by syntax, the other by Montague’s the one straightforwardly by syntax, the other by Montague’s QR or by Cooper’s storage, etc..)QR or by Cooper’s storage, etc..)

1.1. x(boy(x)x(boy(x)y(girl(y)y(girl(y)loves(x,y)))loves(x,y)))

2.2. y(girl(y)y(girl(y)x(boy(x)x(boy(x)loves(x,y)))loves(x,y)))

But how to deal with indefinites and But how to deal with indefinites and anaphora in general?anaphora in general?


Interpretation of the Interpretation of the indefinite „a“indefinite „a“

No straightforward translation of „a“ in No straightforward translation of „a“ in FOL FOL

1.1. Scope over coordinatesScope over coordinates

• *John introduced [every new student]*John introduced [every new student]I I to the to the

chairperson, and Bill introduced himchairperson, and Bill introduced himI I to the dean.to the dean.

• John introduced [a new student]John introduced [a new student]j j to the chairperson, to the chairperson,

and Bill introduced himand Bill introduced himI I to the dean.to the dean.

2.2. Donkey sentences-Geach(1962) (Conditionals-When Donkey sentences-Geach(1962) (Conditionals-When clauses)clauses)

a.a. If John owns [a donkey]If John owns [a donkey]II, he beats it, he beats itII..

((xx(donkey(x)(donkey(x)John(y)John(y)owns(y,x))owns(y,x))beats(y,x))beats(y,x))

xx(donkey(x)(donkey(x)(John(y)(John(y)owns(y,x)owns(y,x)beats(y,x)))beats(y,x)))

a.a. When an [Italian is tall]When an [Italian is tall]jj, he, hejj is also blond. is also blond.


Intersentential anaphora Intersentential anaphora resolutionresolution

Diverse intersentential anaphoric Diverse intersentential anaphoric phenomena in NLphenomena in NL

Anaphora resolution is processed considering discourse Anaphora resolution is processed considering discourse factors.factors.

Until Kamp (1981), Heim (1982) compositional semantics Until Kamp (1981), Heim (1982) compositional semantics were assigned until the end of the sentence.were assigned until the end of the sentence.

““The meaning of a sentence is the set of models it The meaning of a sentence is the set of models it satisfies.”satisfies.”

A man walked in. He was wearing a hat.A man walked in. He was wearing a hat.

Solution…the interpretation is assigned contextuallySolution…the interpretation is assigned contextually

Kamp (1981) introduced the Context Change Potential Kamp (1981) introduced the Context Change Potential (CCP) -- dynamic way of thinking about meaning…(CCP) -- dynamic way of thinking about meaning…


DRT-CCPDRT-CCP

Dynamic notion of meaningDynamic notion of meaning

Meaning a Meaning a relationrelation between a set of «input» between a set of «input» contexts which represents the content of the contexts which represents the content of the discourse prior to the sentence being processed, discourse prior to the sentence being processed, and a set of «output» contexts which represents and a set of «output» contexts which represents the content of the discourse including that the content of the discourse including that sentence.sentence.

A man walked in. He ordered a beer.A man walked in. He ordered a beer.

Input context Input context

OutputOutput contextcontext


DRT-basicsDRT-basics

Discourse Representation Structures Discourse Representation Structures (DRSs)(DRSs)

DRT-like notation (box representation)DRT-like notation (box representation)

DRSs: formal objects realising the dynamic DRSs: formal objects realising the dynamic notion of meaning in the interpretation of notion of meaning in the interpretation of discoursediscourse

DRSs consist of the universe (entities) and the DRSs consist of the universe (entities) and the conditions (relations between entities) conditions (relations between entities) supported by an «appropriate» modelsupported by an «appropriate» model


DRT: availability positionsDRT: availability positions

Anaphora resolution according to Anaphora resolution according to availability constraintsavailability constraints

DRS B1 is accessible from DRS B2 when: a. B1 equals B2 b. B1 subordinates B2 B1 subordinates B2 when:

a. B1 immediately subordinates B2b. There is some DRS B such that B1 subordinates B and B subordinates B2

B1 contains a condition of the form B2; orB1 contains a condition of the form B2B or BB2, for some DRS B; orB1 contains a condition of the form B2B (or some quantifier), for some DRS B; orB1B2 is a condition in some DRS B.


DRT: availability positionsDRT: availability positions

Accesibility constraintsAccesibility constraints

x1x1

1.1.

x2 x5 x2 x5

2. 5.2. 5.

x3 x4 many x6 x7,xx3 x4 many x6 x7,x

3. 4 x2 6. 7.3. 4 x2 6. 7.


DRT coping with indefinitesDRT coping with indefinites

Indefinites as free variables being Indefinites as free variables being outscoped by other quantifiers outscoped by other quantifiers

a.a. Every farmer who owns a donkey beats it.Every farmer who owns a donkey beats it.

x,yx,y

farmer(x), farmer(x), donkey(y)donkey(y)

Owns(x,y)Owns(x,y) beats(x,y)beats(x,y)

everyevery

xx


One more example of DRT´s One more example of DRT´s representationrepresentation

person(x), restaurant (r)person(x), restaurant (r)

ee

x,rx,r

a.a. Someone didn’t smoke in the restaurant.Someone didn’t smoke in the restaurant.

smoke(e,x), in(e,r) smoke(e,x), in(e,r)

rr

restaurant (r)restaurant (r)

x,ex,e

person(x) person(x)

smoke(e,x), in(e,r) smoke(e,x), in(e,r)

b.b. c.c.presuppositionpresupposition


DRT: what offersDRT: what offers

Kamp and Reyle (1993)Kamp and Reyle (1993)

• a way to handle intersentential anaphoric a way to handle intersentential anaphoric phenomenaphenomena

• a way to handle quantification effectivelya way to handle quantification effectively

• tense and aspect in most of the cases are tense and aspect in most of the cases are

captured by the theorycaptured by the theory

• pluralsplurals


Why DRT and dynamic semantics are Why DRT and dynamic semantics are not enoughnot enough

Drawbacks: no connection to pragmatic Drawbacks: no connection to pragmatic factorsfactors

• Constraints on anaphora both overgenerate andConstraints on anaphora both overgenerate and

undergenerate possible readings undergenerate possible readings

1.1.

a.a. Max had a great evening last night.Max had a great evening last night.

b.b. He had a great meal.He had a great meal.

c.c. He ate salmon.He ate salmon.

d.d. He devoured cheese.He devoured cheese.

e.e. He then won a dancing competition.He then won a dancing competition.

f.f. ?It was a beautiful pink. ?It was a beautiful pink.


Dynamic semantics: drawbacksDynamic semantics: drawbacks

2.2.

a.a. One plaintiff was passed over for promotion three One plaintiff was passed over for promotion three times.times.

b.b. Another didn’t get a raise for five years.Another didn’t get a raise for five years.

c.c. A third plaintiff was given a lower wage compared A third plaintiff was given a lower wage compared to males who were doing the same work.to males who were doing the same work.

d.d. But the jury didn’t believe this. But the jury didn’t believe this.


Temporal phenomena Temporal phenomena

Kamp and Reyle (1993) - syntax determines the Kamp and Reyle (1993) - syntax determines the aktionsart of the sentence aktionsart of the sentence

• Max entered the room. The room became dark.Max entered the room. The room became dark.

• Max entered the room. The room was dark.Max entered the room. The room was dark.

For a: eFor a: et (the event is within the reference time)t (the event is within the reference time)

t’t’t (for forward movement in narratives)t (for forward movement in narratives)

ttn (past tense) n (past tense)

For b: t’ For b: t’ s (the state may still be ongoing), t’s (the state may still be ongoing), t’n n

c.c. Max fell. John helped him up.Max fell. John helped him up.

d.d. Max fell. John pushed him.Max fell. John pushed him.

Not even pure default world-knowledge can help us...Not even pure default world-knowledge can help us...

Pushings-fallings events...Pushings-fallings events...


PresuppositionPresupposition

Van der Sandt (1992) (constraints on Van der Sandt (1992) (constraints on accommodation are too weak) accommodation are too weak)

Beaver (1996) (no precise definition of the “most Beaver (1996) (no precise definition of the “most plausible pragmatic interpretation”)plausible pragmatic interpretation”)

a.a. If David scuba dives, he will bring his regulator.If David scuba dives, he will bring his regulator.

b.b. If David scuba dives, he will bring his dog.If David scuba dives, he will bring his dog.

c.c. I doubt that the knowledge that this seminal logic I doubt that the knowledge that this seminal logic paper was written by a computer program running on a PC paper was written by a computer program running on a PC will confound the editors.will confound the editors.


Lexical disambiguationLexical disambiguation

a.a. The judge demanded to know where the defendant was.The judge demanded to know where the defendant was.

b.b. The barrister apologized and said that he was drinking The barrister apologized and said that he was drinking across the street.across the street.

c.c. The court bailiff found him asleep beneath the The court bailiff found him asleep beneath the barbar..

Solutions provided only by data-intensive linguistics (Guthrie, Solutions provided only by data-intensive linguistics (Guthrie, 1991)1991)

Pr(sense(w)=s|C)Pr(sense(w)=s|C)

What would they say in case of c’ instead of c?What would they say in case of c’ instead of c?

c’.c’. But the bailiff found him slumped underneath the bar.But the bailiff found him slumped underneath the bar.

Clearly, we need hybrid approaches where semantic, Clearly, we need hybrid approaches where semantic, pragmatic and statistical factors are involved…pragmatic and statistical factors are involved…


Why SDRT (Asher (1993), Why SDRT (Asher (1993), Asher and Lascarides Asher and Lascarides

(2003)) ?(2003)) ?a.a. It provides rhetorical relations (Narration, Elaboration, It provides rhetorical relations (Narration, Elaboration, Parallel, Contrast, Explanation, Background, etc.)Parallel, Contrast, Explanation, Background, etc.)

b.b. It does not exclude pragmatics or AI techniques for the It does not exclude pragmatics or AI techniques for the representation of knowledge…it only formalize them in a representation of knowledge…it only formalize them in a better way and face more effectively the problemsbetter way and face more effectively the problems

c.c. It keeps things modular…every source of knowledge is It keeps things modular…every source of knowledge is kept separate and interactivekept separate and interactive

d.d. It separates the logic of information content and the logic It separates the logic of information content and the logic of information packagingof information packaging

e.e. And…assumes underspecification appropriate for And…assumes underspecification appropriate for composition relying on constraint-based frameworks…composition relying on constraint-based frameworks…(HPSG, LFG)(HPSG, LFG)

But first let’s see…what the rhetorical relations look like and But first let’s see…what the rhetorical relations look like and what they can do…what they can do…


Rhetorical relations..what are Rhetorical relations..what are they?they?

a.a. Anaphoric connectors of the discourseAnaphoric connectors of the discourse

b.b. Carriers of illocutionary force sourcing from the Carriers of illocutionary force sourcing from the discourse itselfdiscourse itself

c.c. Connectors of labels or Connectors of labels or speech act discourse speech act discourse referentsreferents and not of propositions…tokens of and not of propositions…tokens of propositions and not types (identity criteria, propositions and not types (identity criteria, etc..)etc..)

d.d. Validate the defeasibility floating around in Validate the defeasibility floating around in language production..language production..

a.a. Max fell. John pushed him.Max fell. John pushed him.

b.b. John and Max were at the edge of the cliff. John and Max were at the edge of the cliff. Max felt a sharp blow to the back of his neck. Max felt a sharp blow to the back of his neck. Max fell. John pushed him. Max rolled over Max fell. John pushed him. Max rolled over the edge of the cliff.the edge of the cliff.


Rhetorical relations-MDCRhetorical relations-MDCUse of Maximise Discourse Coherence (MDC), the Use of Maximise Discourse Coherence (MDC), the

strongest principle of SDRT with monotonic strongest principle of SDRT with monotonic consequences, which:consequences, which:

a.a. formalizes the notion of relevance introduced formalizes the notion of relevance introduced informally [by Sperber and Wilson’s informally [by Sperber and Wilson’s Relevance Theory (1986)] by defining Relevance Theory (1986)] by defining “scalar” coherence…“scalar” coherence…

b.b. Overrides conflicting world knowledge.Overrides conflicting world knowledge.

According to MDC:According to MDC:

1.1. The more rhetorical connections between the The more rhetorical connections between the segments of text..the more coherent is the text segments of text..the more coherent is the text meaningmeaning

2.2. The more anaphoric expressions are resolved the The more anaphoric expressions are resolved the higher the qualityhigher the quality

3.3. Some relations are inherently scalar..(Narration, Some relations are inherently scalar..(Narration, Contrast)..we are looking for the interpretation Contrast)..we are looking for the interpretation that maximises the quality of the relation under that maximises the quality of the relation under questionquestion


Rhetorical relationsRhetorical relationsHow are semantically to be understood? How are semantically to be understood?

The definition of a veridical rhetorical relationThe definition of a veridical rhetorical relation

A relation R is veridical iff the following axiom is A relation R is veridical iff the following axiom is valid:valid:

R(R(α,βα,β))(K(KααΚβ)Κβ)

is to be understood dynamically and not as is to be understood dynamically and not as logical conjunctionlogical conjunction

How is it satisfied?How is it satisfied?

(w,f)[[R((w,f)[[R(π1,π2)]]π1,π2)]]MM(w’,g) iff(w’,g) iff

(w,f)[[K(w,f)[[Kπ1 π1 KKπ2 π2 φφR(R(π1,π2π1,π2)]])]]MM(w’,g)(w’,g)

What does this mean?What does this mean?

a.a. They change context…they are interpreted as They change context…they are interpreted as speech acts..speech acts..


Anaphora resolutionAnaphora resolution

a.a. Max had a great evening last night.Max had a great evening last night.

b.b. He had a great meal.He had a great meal.

c.c. He ate salmon.He ate salmon.

d.d. He devoured cheese.He devoured cheese.

e.e. He then won a dancing competition.He then won a dancing competition.

f.f. ?It was a beautiful pink.?It was a beautiful pink.



Max had a lovely eveningMax had a lovely evening

ElaborationElaboration

He had a great meal He won a He had a great meal He won a dancingdancing

NarrationNarration competition competition


He ate salmon He ate salmon NarrationNarration He devoured cheese He devoured cheese



Observations:Observations:

• Right-frontier constraint on the discourse tree Right-frontier constraint on the discourse tree (Polanyi, 1985)(Polanyi, 1985)

• Hierarchical structure in the representation of Hierarchical structure in the representation of discoursediscourse

subordinating, coordinating relations..subordinating, coordinating relations..

c.c. Captures successfully the fact that there is Captures successfully the fact that there is incoherence going on in case (f) is addedincoherence going on in case (f) is added

d.d. Different approach to discourse update process Different approach to discourse update process from that of DRT (which is simple amending from that of DRT (which is simple amending DRSs)…take a look at the copy…DRSs)…take a look at the copy…


Temporal phenomenaTemporal phenomena

a.a. Max fell. John pushed him.Max fell. John pushed him.

π0π0

π1, π2π1, π2

π0π0: e: eπ1, π1, t, xt, x eeπ2, π2, t’, y, zt’, y, z

π1π1: max(x) : max(x) π2π2: john(y): john(y)

fall(efall(eπ1,π1, x) push(e x) push(eπ2,π2, y, z) y, z)

holds(eholds(eπ1π1, t) z=x, t) z=x

ttnow holds(enow holds(eπ2π2, t’), t’)

t’t’nownow

Explanation(Explanation(π1, π2)π1, π2)


Temporal phenomenaTemporal phenomena

By the semantics of Explanation…we have..By the semantics of Explanation…we have..

• φφExplanation(Explanation(α,β)α,β) ( (eeααeeββ))

• φφExplanation(Explanation(α,β)α,β) (event(e (event(eββ) ) e eββeeα)α)

Let’s take a look at where we are…check the copy..Let’s take a look at where we are…check the copy..


Cognitive plausibility mattersCognitive plausibility matters

Pragmatics (Grice (1975), Searle (1969), Sperber and Pragmatics (Grice (1975), Searle (1969), Sperber and Wilson(1986,1995)) and AI techniques (Hobbs et Wilson(1986,1995)) and AI techniques (Hobbs et al. (1993), Grosz and Sidner(1993)):al. (1993), Grosz and Sidner(1993)):

Direct interpretation of “intended” meaning both in Direct interpretation of “intended” meaning both in pragmatics and AI…pragmatics and AI…

PragmaticsPragmatics

Meaning is what speakers intend to say under what Meaning is what speakers intend to say under what they expressthey express

Full access to the cognitive state of the speakerFull access to the cognitive state of the speaker

AIAI

Hobbs et al. (1993) unmodular architecture of the Hobbs et al. (1993) unmodular architecture of the information flow between the participants in the information flow between the participants in the conversation..conversation..


Cognitive plausibility mattersCognitive plausibility matters

Obvious Drawbacks:Obvious Drawbacks:

• No formal way of inferring implicatures No formal way of inferring implicatures

• Static full access to the logic of cognitive states, Static full access to the logic of cognitive states, which apparently complicates the interpretation which apparently complicates the interpretation task and base the inferencetask and base the inference

c.c. Computability issueComputability issue

d.d. Fail to provide explanation about the dramatic Fail to provide explanation about the dramatic changes in the interpretation provided by small changes in the interpretation provided by small changes in the surface (no contact to linguistic changes in the surface (no contact to linguistic evidence-dynamic semantics)evidence-dynamic semantics)


Rhetorical Rhetorical relations...continuedrelations...continued


• Blair has caused chaos in Iraq. He sent his troops Blair has caused chaos in Iraq. He sent his troops and killed the hopes of the people there.and killed the hopes of the people there.

Temporal consequence of Elaboration:Temporal consequence of Elaboration:

φφElaboration(Elaboration(α,β)α,β) Part-of(e Part-of(eα,α,eeββ))

Properties:Properties:

1) Transitivity and 2) Distributivity1) Transitivity and 2) Distributivity

1)1) Elaboration(Elaboration(π1, π2π1, π2)) Elaboration( Elaboration(ππ22, , ππ3))3))Elaboration(Elaboration(π1,π3)π1,π3)

2)2) Elaboration(Elaboration(α,βα,β))Coord(Coord(β,γ)β,γ)I-outscopes(I-outscopes(δ,γ)δ,γ) Elaboration(Elaboration(α,δ)α,δ)

Check at the first classical example with the Check at the first classical example with the salmon…salmon…



Narration—Scalar coherenceNarration—Scalar coherence

Semantic constraints:Semantic constraints:

1.1. Spatiotemporal constraintSpatiotemporal constraint

If Narration(If Narration(π1,π2)π1,π2), then the poststate of e, then the poststate of eπ1π1 must overlap the prestate of emust overlap the prestate of eπ2π2

a.a. The terrorist Blair planted a mine near the The terrorist Blair planted a mine near the bridge. bridge.

20m south, he planted another.20m south, he planted another.

b.b. The terrorist Blair planted a mine near The terrorist Blair planted a mine near the bridge.the bridge.

Then he planted another.Then he planted another.

Narration(Narration(α,β)α,β)overlap(prestate(eoverlap(prestate(eβ),β),AdvAdvββ(postst(poststate(eate(eα)))α)))



Narration—Scalar coherenceNarration—Scalar coherence

Semantic constraints:Semantic constraints:

2.2. Common TopicCommon Topic

Both the speech act discourse referents must Both the speech act discourse referents must indicate a common topicindicate a common topic

a.a. My car broke down. Then the sun set.My car broke down. Then the sun set.

b.b. My car broke down. Then the sun set and My car broke down. Then the sun set and I knew I was in trouble.I knew I was in trouble.

φφNarration(Narration(α,β)α,β)(K(KααKKβ)β)



BackgroundBackground

• Max entered the room. It was pitch dark. Max entered the room. It was pitch dark. (Background)(Background)

• Max switched off the light. It was pitch dark. Max switched off the light. It was pitch dark. (Narration)(Narration)

Temporal consequence of Background:Temporal consequence of Background:

φφBackground(Background(α,βα,β)) overlap(e overlap(eβ,β,eeα)α)

Topic constraint like Narration but in Background the Topic constraint like Narration but in Background the eeαα maintains available for anaphoric binding maintains available for anaphoric binding since it is considered the “main story line”since it is considered the “main story line”



BackgroundBackground

1.1. π1π1 A burglar broke into Mary’s apartment.A burglar broke into Mary’s apartment.

π2π2 Mary was asleep.Mary was asleep.

π3π3 He stole the silver.He stole the silver.

2.2. π1π1 A burglar broke into Mary’s apartment.A burglar broke into Mary’s apartment.

π2π2 A police woman visited her the next day.A police woman visited her the next day.

π3π3 ??He stole the silver.??He stole the silver.

repeating the common topic…set union of repeating the common topic…set union of π1, π2π1, π2

Introduce Introduce Foreground-Background Pair Foreground-Background Pair subordinate relation (FBP) subordinate relation (FBP)



Background Background

π’π’

π’’, ππ’’, π

π’’π’’: K: Kπ1π1KKππ22

FBPFBP((π’’,π)π’’,π)

π’π’:: π1,π2 π1,π2

π1π1: K: Kπ1, π2π1, π2: K: Kπ2π2

ππ: Background(: Background(π1,π2) π1,π2)



Contrast-EvidenceContrast-Evidence

Ducrot (1984)Ducrot (1984)

a.a. John speaks French. Bill speaks German. (formal John speaks French. Bill speaks German. (formal contrast)contrast)

b.b. John loves sport. But he hates football. (violation John loves sport. But he hates football. (violation of expectation)of expectation)

An example of the second case…An example of the second case…

a.a. If Molly sees a stray cat, she pets it.If Molly sees a stray cat, she pets it.

b.b. But if Dan sees it, he takes it home.But if Dan sees it, he takes it home.



Contrast-Evidence Contrast-Evidence

a.a.

ΠαΠα

π1,π2 π1,π2 z1,z2z1,z2

ΠαΠα:: π1 π1: Molly(x), cat(y) : Molly(x), cat(y) π2π2: pets(z1,z2): pets(z1,z2)

see(x,y) z1=x,z2=ysee(x,y) z1=x,z2=y

ConsequenceConsequence((π1,π2) π1,π2)



Contrast-EvidenceContrast-Evidence

bb..

π0π0

ππbb

π3,ππ3,π44

z,z3 w1,z4z,z3 w1,z4

π0π0:: π πb:b: π3π3: Dan(z), see(z,z3) : Dan(z), see(z,z3) π4π4: take-home(w1,z: take-home(w1,z44))

z3= ? w1=?, z4=?z3= ? w1=?, z4=?

Consequence(Consequence(π3,π4)π3,π4)

Contrast(?,Contrast(?,ππb)b)



ContrastContrast

ContrastContrast

παπα ππbb

π1π1:: Conseq Conseq π2π2: : π3π3: Conseq : Conseq π4π4::

[Molly sees cat] [Molly pets cat] [Dan sees ?] [Dan takes home ?] [Molly sees cat] [Molly pets cat] [Dan sees ?] [Dan takes home ?]

For the mapping between the For the mapping between the ππs see Asher (1993)s see Asher (1993)



MicrostructureMicrostructure

Some words about the connectives between two Some words about the connectives between two fully specified formulas:fully specified formulas:

,,,,…DRT’s truth functional approach…DRT’s truth functional approach

In SDRT, they are represented by rhetorical In SDRT, they are represented by rhetorical relations…relations…

Consequence, Alternation and no conjunction…Consequence, Alternation and no conjunction…conjunction is too poor…conjunction is too poor…

What does it mean that the compositional semantics What does it mean that the compositional semantics of two clauses are true and nothing more?of two clauses are true and nothing more?



MicrostructureMicrostructure

A 3A 3rdrd connector… connector…

>: means defeasible consequence…or conditional of >: means defeasible consequence…or conditional of normality (normally if…then..)normality (normally if…then..)

Used heavily in the logic of information packaging, Used heavily in the logic of information packaging, where defaults are placed and defeated when where defaults are placed and defeated when new information comes to play…new information comes to play…

An exampleAn example on applying the relational-dynamic on applying the relational-dynamic semantics of SDRT on an intentional model…semantics of SDRT on an intentional model…

M=<AM=<Aμ,μ,WWμ ,μ ,**μ,μ,IIμ>μ>

Tasha is a cat.Tasha is a cat.

**μμ(w,[[(w,[[π]]π]]))

The SDRS KThe SDRS Kπ π for the sentence…under the special for the sentence…under the special element *element *μμ gives us all the output contexts gives us all the output contexts where the cat is a normal one..(has a tail, four where the cat is a normal one..(has a tail, four legs, two eyes…)legs, two eyes…)


Unpacking truth conditions:Unpacking truth conditions:

a.a. Max fell. Max fell.

b.b. Either John pushed him orEither John pushed him or

c.c. He slipped on a banana peel.He slipped on a banana peel.


Unpacking truth conditions:Unpacking truth conditions:π0π0

π1,π2π1,π2

e1,x,t1e1,x,t1

ππ1: 1: max(x), fall(e1,x),max(x), fall(e1,x),

holds(e1,t1), t1<nowholds(e1,t1), t1<now

π3,π4π3,π4

ππ0: y,e3,x1,t3 z,x2,e4,t40: y,e3,x1,t3 z,x2,e4,t4

john(y), banana(z),john(y), banana(z),

π2π2: : π3π3: push(e3,y,x1),x1=x, : push(e3,y,x1),x1=x, π4π4: slip(e4,x2,z),x2=x,: slip(e4,x2,z),x2=x,

holds(e3,t3), holds(e4,t4),holds(e3,t3), holds(e4,t4),

t3<now t4<nowt3<now t4<now

Alternation(Alternation(π3,π4)π3,π4)

Explanation(Explanation(π1,π2)π1,π2)



Use of the satisfaction schema and recursively unpacking:Use of the satisfaction schema and recursively unpacking:

(w,f)[[Explanation((w,f)[[Explanation(π1,π2)]]π1,π2)]]M(w,g) iffM(w,g) iff

(w,f)[[K(w,f)[[Kπ1 π1 KKπ2 π2 ExplanationExplanation((π1,π2π1,π2)]])]]MM(w’,g)(w’,g)

By the semantics of By the semantics of there are variable assignment there are variable assignment functions h and i such that:functions h and i such that:

a)a) (w,f)[[K(w,f)[[Kπ1]]π1]]MM(w,h)(w,h)

b)b) (w,h)[[K(w,h)[[Kππ22]]]]MM(w,i); and(w,i); and

c)c) (w,i)[[Explanation(w,i)[[Explanation((π1,π2π1,π2)]])]]MM(w,g)(w,g)

Let’s take the first condition:Let’s take the first condition:

(a)(a) Holds only if:Holds only if:

1.1. Dom(h)=dom(f)Dom(h)=dom(f){e1,x,t1} and (w,h) satisfies the {e1,x,t1} and (w,h) satisfies the SDRSs conditions..SDRSs conditions..

2.2. <h(x)><h(x)>IIMM(max)(w), <h(e1),h(x)>(max)(w), <h(e1),h(x)>IIMM(fall)(w),etc..(fall)(w),etc..



Condition (b) for KCondition (b) for Kπ2π2 contains a complex SDRS containing contains a complex SDRS containing an Alternation relation…an Alternation relation…

So either e3 happens or e4 in the KSo either e3 happens or e4 in the Kπ2π2::

(w,h)[[Alternation((w,h)[[Alternation(ππ33,π,π44)]])]]M(w,i) iffM(w,i) iff

(w,h)[[K(w,h)[[Kππ33 KKππ44]]]]MM(w,i)(w,i)

Reminder: KReminder: Kπ1 π1 is connected to Kis connected to Kπ2 π2 and not to Kand not to Kππ3 or to3 or to KKππ4. K4. Kπ2π2 is dependent on the truth conditions of K is dependent on the truth conditions of Kππ3 3 and Kand Kππ4.4.

For the condition (c)…the meaning postulate of explanation For the condition (c)…the meaning postulate of explanation must hold…must hold…

φφExplanation(Explanation(α,β)α,β) ( (eeααeeββ))


Some words about Some words about UnderspecificationUnderspecification

What is underspecification?What is underspecification?

A way to deal with ambiguity phenomena unable to be A way to deal with ambiguity phenomena unable to be covered by the grammar…the most classic one:covered by the grammar…the most classic one:

scope ambiguitiesscope ambiguities

What does underspecification really do?What does underspecification really do?

Keeps “labels” or “holes” in the semantic representation Keeps “labels” or “holes” in the semantic representation and fills them with the adequate candidates..and fills them with the adequate candidates..

In essence, it is a way of delaying things until the bits of In essence, it is a way of delaying things until the bits of information have been provided…information have been provided…

Approaches of underspecification: [Reyle(1993), Bos(1995), Approaches of underspecification: [Reyle(1993), Bos(1995), Bos et al. (1996), Asher and Fernando(1997), Egg et al.Bos et al. (1996), Asher and Fernando(1997), Egg et al.(2001) and Copestake et al.(1999)](2001) and Copestake et al.(1999)]

To the point with “labels”…To the point with “labels”…



Many problems preoccupy every politician.Many problems preoccupy every politician.

• many(x,problem(x),many(x,problem(x),(y,politician(y),preoccupy(x,y)))(y,politician(y),preoccupy(x,y)))

(y,politician(y),many(x,problem(x),preoccupy(x,y)))(y,politician(y),many(x,problem(x),preoccupy(x,y)))

manymany

x problem x problem

x y politician preoccupyx y politician preoccupy

y x y y x y



Many problems preoccupy every politician.Many problems preoccupy every politician.

• many(x,problem(x),many(x,problem(x),(y,politician(y),preoccupy(x,y)))(y,politician(y),preoccupy(x,y)))

(y,politician(y),many(x,problem(x),preoccupy(x,y)))(y,politician(y),many(x,problem(x),preoccupy(x,y)))

y politician manyy politician many

y x problem preoccupyy x problem preoccupy

x x yx x y



l1: many l2: l1: many l2:

x problem l4 y politician l5x problem l4 y politician l5

x l3: preoccupy y x l3: preoccupy y

x y x y

l4l4l5( l1: many(x, problem(x), l4) l5( l1: many(x, problem(x), l4)

l2: l2: (y, politician(y), l5) (y, politician(y), l5)

l3: preoccupy(x, y) l3: preoccupy(x, y)

outscopes(l1, l3) outscopes(l1, l3) outscopes(l2, l3)) outscopes(l2, l3))


What is next?What is next?

SDRT is a new theory..it does not include…SDRT is a new theory..it does not include…

• Implicatures that follow from social status, gender and Implicatures that follow from social status, gender and so onso on

• The contents of dialogues where discourse participants The contents of dialogues where discourse participants have different communicative agendashave different communicative agendas

• The repair strategies that occur when dialogue The repair strategies that occur when dialogue participants realise they have interpreted the dialogue participants realise they have interpreted the dialogue differentlydifferently

Do you want some more?Do you want some more?

Contact me…[email protected] me…[email protected]

Documents

Segmented Discourse Representation Theory Alex Tantos Segmented Discourse Representation Theory A theory of discourse interpretation 14/05 Course: “Computerlinguistik