conventional implicature via dependent type semantics

Introduction DTT DTS CI via DTS Solution Conclusion

CI via DTS(Conventional Implicature

via Dependent Type Semantics)

Daisuke Bekki1 Eric McCready2

1Ochanomizu University / CREST, Japan Science and Technology Agency /National Institute of Advanced Industrial Science and Technology / National

Institute of Informatics

2Aoyama Gakuin University

A guest lecture in ”Expressive Content” course(by Eric McCready and Daniel Gutzmann)

ESSLLI2015, Barcelona, August 14th (Fri), 2015.http://www.slideshare.net/kaleidotheater/

conventional-implicature-via-dependent-type-semantics 1 / 76


Introduction

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Conventional Implicatures (or expressive contents)

Conventional implicatures (CIs): (Part of the) nonassertedcontents conveyed by particular lexical items or linguisticconstructions (Grice (1975), Potts (2005)).

I Appositives: Lance Armstrong, an Arkansan , has won the2003 Tour de France!

I NRRCs: Lance Armstrong, who is an Arkansan , has won the2003 Tour de France!

I Expressive attributive adjectives: That bastard Jery showedup with no money.

I Speaker-oriented adverbs: Surprisingly , Jerry showed up withno money.

I Interjections, coloured expressions, particles, . . .

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Benchmarks of CI

In Potts (2005) and much subsequent works, CIs are characterizedas having at least the following properties:

B1 CI content is independent from at-issue content (inthe sense that the two are scopeless with respect toeach other)

B2 CIs do not modify CIs.

B3 Presupposition filters do not filter CIs

Problems pointed out by McCready (2010) and Gutzmann (2015):

P1 Functional mixed contents

P2 (More than) 2-place CIs

P3 Quantification problem

P4 Shunting

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[B1] CI content is independent from at-issue content

Both the sentences (1a) and (1b) entail the CI content LanceArmstrong is an Arkansan.

(1) a. Lance Armstrong, an Arkansan , has won the 2003Tour de France!

b. It is not the case that Lance Armstrong,

an Arkansan , has won the 2003 Tour de France!

CI content projects through logical operators such as negation.

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[B2] CIs do not modify CIs

As exemplified by (2), the speaker-oriented adverb surprisinglydoes not modify the expressive content induced by the bastard.

(2) Surprisingly , Jerry, the bastard , showed up with nomoney.

The bastardhood of Jerry is not surprising for the speaker.

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[B3] Presupposition filters do not filter CIs

The contrast between (3a) and (3b) exemplifies [B3].

(3) a. If Lance is a cyclist, then the Boston Marathon was

won by the cyclist .

b. # If Lance is a cyclist, then the Boston Marathon waswon by Lance, a cyclist .

In (3a), the presupposition Lance is a cyclist is filtered by theantecedent (the whole sentence does not have any presupposition).

In (3b), the CI Lance is a cyclist is not filtered by the sameantecedent thus projects over it (the whole sentence is infelicitousfor Gricean reasons).

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(Potts, 2005) on the benchmarks

Potts models these features in a two-dimensional semantics for CIsin which CIs are associated with special semantic types.

B1 Since CI content enters a dimension of meaningdistinct from that of at-issue content, no scoperelations are available, modeling.

B2 Characteristic [B2] follows from a lack of functionaltypes with CI inputs in the type system.

B3 Placing filters in the at-issue dimension also accountsfor [B3].

Although this system has been criticized for various reasons, itseems to be adequate for modeling the basic data associated withCIs.

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Problems: Interaction between at-issue and CI content

A fully separated multidimensional semantics has empiricalproblems: there is interaction between CIs andanaphora/presupposition (as Potts himself notes).

P5 CI content may serve as antecedent for lateranaphoric items and presupposition triggers:

P6 Preceding discourse may serve as antecedent foranaphora/presupposition in CI contexts

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[P5] CI content may serve as antecedent

Discourse referents introduced in CI contexts are accessible toanaphora/presupposition triggers, e.g. (4).

(4) a. Mary counseled John, who killed a coworker .

b. Unfortunately, Bill knows that he killed a coworker .

(5) (Intra-sentential case) Mary counseled John, who killed acoworker, without being informed that Bill knows that hekilled a coworker.

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[P6] Preceding discourse may serve as antecedent foranaphora/presupposition in CI contexts

They require access to their left contexts, as exemplified in themini-discourse (6) (see also Wang et al. (2005).).

(6) a. John killed a coworker .

b. Mary, who knows that he killed a coworker ,

counseled him.

(7) (Intra-sentential case) John actually killed a coworker 5days before Mary, who knows that he killed a coworker,counseled him.

In both (4) and (6), the factive presupposition “he (=John) killeda coworker” can be bound by the antecedent in the first sentence.

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Alternative approaches?

We need another ’channel’ for expressive contents:

I Potts introduced the second dimension, and McCreadyand Gutzmann introduced even more dimension(s) insemantic representations

I There is also a channel for naphora/presupposition(though CIs are not filtered by presupposition filters)

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Dependent Type Theory

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Three key concepts in dependent type theory

1. Curry-Howard Correspondence (between logic and typetheory)

2. Dependent types (vs. Simple types)

3. Proof-theoretic semantics (vs. Model-theoretic semantics)

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Typing rules for simply-typed lambda calculus (STLC) withbinary products

Type construction rules Type deconstruction rules

x : A....M : B

i

λx.M

function

: A→ B(LAM ),i

M : A→ B N : AMN : B

(APP)

M : A N : B(M,N)

pair

: A×B(PROD)

M : A×Bπ1(M) : A

(PROJ )M : A×Bπ2(M) : B

(PROJ )

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f : A→ B, x : A ` f : A→ B(VAR)

f : A→ B, x : A ` x : A(VAR)

f : A→ B, x : A ` fx : B(APP)

f : A→ B ` λx.fx : A→ B(LAM )

` λf.λx.fx : (A→ B)→ (A→ B)(LAM )

I The type of a term is determined by types of its subterm(s).

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f : A→ B, x : A ` f : A→ B(VAR)

f : A→ B, x : A ` x : A(VAR)

f : A→ B, x : A ` fx : B(APP)

f : A→ B ` λx.fx : A→ B(LAM )

` λf.λx.fx : (A→ B)→ (A→ B)(LAM )

I The typing tree of a term (in STLC) can be recovered fromthe (structure of) term. (cf. Milner (1978))

Fact 1

A term is an encoding of a typing tree.

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Curry-Howard Correspondence btw. function type andimplication

Introduction rules Elimination rules

Typing rules inSTLC

x : A....M : B

i

λx.M

function

: A→ B(LAM ),i


(APP)

Natural de-duction rulesin PL

A....B

i

A→ B(→I ),i

A→ B A

B(→E)

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Curry-Howard Correspondence btw. product type andconjunction


Typingrules inSTLC

M : A N : B(M,N)

pair

: A×B(PROD)

M : A×Bπ1(M) : A


(PROJ )

Naturaldeduc-tion rulesin PL

A B

A ∧B(∧I )

A ∧BA

(∧E)A ∧BB

(∧E)

Fact 2

Typing rules of STLC (almost exactly) correspond to naturaldeduction rules in logic.

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Fact 1

A term is an encoding of a typing tree.

+

Fact 2

Typing rules of STLC (almost exactly) correspond to naturaldeduction rules in logic.

⇓

Fact 3

A term of type A is also an encoding of a proof diagram of aproposition A (under the view that proposition is type)

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Fact 3

A term of type A is also an encoding of a proof diagram of aproposition A (under the view that proposition is type)

Fact 3’

I Functions encode proofs of →.

I Pairs encode proofs of ∧.

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The correspondence between the notions of logic and type theory :

Logic Type Theory

proposition typeproof term (or program)axiom constant symbolassumption variablelogical connective type constructor

implication functional typeconjunction product typedisjunction direct sum type

absurdity empty typeintroduction constructorelimination destructorprovability inhabitancecut substitutionnormalization reduction

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Dependent function type


function type→ in STLC

x : A....M : B

i

λx.M

function

: A→ B(LAM ),i


(APP)

Dependentfunction type(Π) in DTT

A : type

x : A....M : B

i

λx.M

function

: (x:A)→ B(ΠI ),i

M : (x:A)→ B N : A

MN : B[N/x](ΠE)

Scope: (x:A)→ B

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Dependent sum type


producttype × inSTLC

M : A N : B(M,N)

pair

: A×B(PROD)

M : A×Bπ1(M) : A


(PROJ )

Dependentsum type(Σ) inDTT

M : A N : B[M/x]

(M,N)

pair

:[x:AB

] (ΣI )M :

[x:AB

]π1(M) : A

(ΣE)

M :[x:AB

]π2(M) : B[π1(M)/x]

(ΣE)

Scope:

[x:AB

]

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Dependent types

Dependent types Standard notation x 6∈ fv(B) x ∈ fv(B)(x:A)→ B (Πx : A)B A→ B (∀x : A)B[x:AB

](Σx : A)B A ∧B (∃x : A)B

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Dependent Type Semantics

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E-type anaphora: Ranta (1994)

(8) A man entered. He whistled.u:

x:entity[man(x)enter(x)

] whistle( π1(u) )

Note:

[x:AB

]is a type for pairs of A and B[x].

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Donkey anaphora: Sundholm (1986)

(9) Every farmer who owns a donkey beats it .

(x:entity)→

u:

farmer(x) y:entitya[

donkey(y)own(x, y)

] → beat(x, π1π2(u) )

Note: (x:A)→ B is a type for functions from A to B[x].

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Accessibility: Ranta (1994)

(10) Every man entered. * He whistled.u: (x:entity)→ man(x)→ enter(x)

whistle( ? )

In this case, the pronoun CANNOT pick up the entity (=the manwho entered) from u, since u is a function. This explains thefollowing cases uniformly, since both implication and negation areinstances of dependent functional types:

(11) a. If John owns a car, it must be a Porsche. *It is red.

b. John did not buy a car. *It is a Porsche.

This accounts for accessibility, based on the structure of a proof.

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Local context and context passing: Bekki (2014)

Definition (Dynamic conjunction and disjunction)

M ;Ndef≡ λc.

[u:McN(c, u)

]M |N

def≡ λc. (u:¬Mc)→ N(c, u)

(8) A man entered. He whistled.

λc.


] ; λc.whistle( @1 c))

underspecified term

= λc.

u:


]whistle( @1 (c, u))

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Presupposition projection as type checking/inference

Felicity condition

`

u:


]whistle(@1((), u))

: type

⇓ Type checking/inference

` @1 :

>x:entity[

man(x)enter(x)

]→ entity

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Presupposition resolution as proof search

` @1 :

>x:entity[

man(x)enter(x)

]→ entity

I If the hearer chooses to bind the presupposition, he/she hasto find a term to replace @1 (for example, λx.π1π2(x) is sucha term). In other words, anaphora/presupposition resolutionreduces to proof search.

I Or the hearer may choose to accommodate the presupposition:in that case, he/she abandons tng proof search and add a newvariable of the above type to the global context.

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Recent works on DTS

I Generalized Quantifiers: Tanaka et al. (2013), Tanaka (2014)

I Double-Negated Antecedents: Bekki (2013)

I Modal Subordination: Tanaka et al. (2014)

I Conventional Implicature: Bekki and McCready (2014)

I Honorification in Japanese: Watanabe et al. (2014)

I Type checking/inference in DTS and its implementation:Bekki and Sato (2015)

I Factive Presupposition: Tanaka et al. (2015)

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Interim summary

I DTS is a framework of natural language semantics based ondependent type theory, following the line of Sundholm (1986),Ranta (1994).

I Dependent types work well for representing discourseanaphora (or presupposition in general) in a parallel mannerto syntactic structures.

I DTS is a compositionalized (or lexicalized) version ofdependent-type-oriented semantics, which adopts amechanism such as local contexts, context passing, andunderspecified terms.

I In DTS, the calculation of presupposition projection reducesto type checking/inference. This algorithm has not beenformulated nor implemented until this work is done!

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CI via DTS

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The CI operator: Bekki and McCready (2014)

A given bit of CI content A (of type type) can be properlyrepresented in terms of DTS by using intensional equality type(Nordstrom et al. (1990)):

Definition (The CI operator)

Let A be a type and @i be an underspecified term with anindex i:

CI(@i : A)def≡ @i =A @i

The CI operator is in common with presupposition triggers, butunlike presupposition triggers, the CI operator does not respect itslocal context.

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Intensional equality type in dependent type theory

Definition (Id-formation and introduction rules)

M : A N : AM =A N : type

(IdF )M : A

reflA(M) : M =A M(IdI )


@i : A @i : A@i =A @i : type

(IdF )@i : A

reflA(@i) : @i =A @i(IdI )

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@i : A @i : A@i =A @i : type

(IdF )@i : A


I CI(@i : A) is always provable under any context by the (IdI)rule (=the reflexivity law).

I CI(@i : A) inhabits a canonical proof reflA(@i) (i.e.` reflA(@i) : @i =A @i).

I This means that the CI operator CI(@i : A) does notcontribute anything to at-issue content.

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@i : A @i : A@i =A @i : type

(IdF )@i : A


I However, the type checking of a semantic representationwhich contains CI(@i : A) requires that the @i =A @i has atype type, which in turn requires that the underspecified term@i has the type A.

I Therefore, the proposition A must have a proof term @i oftype A (i.e. A must be true), which projects, regardless of theconfiguration in which it is embedded.

I Moreover, unlike the cases of anaphora and presupposition, anunderspecified term for a CI does not take any local contextas its argument. This explains why CIs do not respect theirlocal contexts.

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[B1] Independence from at-issue content

First, consider the independence of CI content from at-issuecontent.

(12) a. Lance Armstrong, an Arkansan , has won the 2003Tour de France!

b. It is not the case that Lance Armstrong,

an Arkansan , has won the 2003 Tour de France!

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LanceNP

: lance

anS\NP/N

: id

ArkansanN

: λx.λc.arkansan(x)

S\NP: λx.λc.arkansan(x)

>

S/(S\NP)\NP

: λx.λp.λc.[pxcCI(@1 : arkansan(x))

] (IA1 )

S/(S\NP)

: λp.λc.[p(lance)cCI(@1 : arkansan(lance))

] <

has won the 2003 Tour de FranceS\NP

: λx.λc.won(x)

S

: λc.[

won(lance)CI(@1 : arkansan(lance))

] >

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This embedding for an indefinite appositive construction is done byapplying the following Indefinite Appositive Rule.

Definition (Indefinite Appositive Rule)

S\NP: M

S/(S\NP)\NP

: λx.λp.λc.[pxcCI(@i : Mxc)

] (IAi )

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The proposition Lance Armstrong is an Arkansan is represented inDTS as a type (=proposition) arkansan(lance). If it is embeddedwithin the CI type as in CI(@1 : arkansan(lance)), this propositionis a CI content, and @1 is its proof term.

λc.

[won(lance)CI(@1 : arkansan(lance))

]This resulting SR entails arkansan(lance), because it contains theCI type CI(@1 : arkansan(lance)) and type checking of this SRrequires that the underspecified term @1 is of typearkansan(lance).

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won : entity→ type(Con)

lance : entity(Con)

won(lance) : type(ΠE)

@1 : arkansan(lance)

CI(@1 : arkansan(lance)) : type(IdF )[


]: type

(ΣF )

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In contrast, a derivation of (12b) is shown below:

It is not the case thatS/S

: λp.λc. ¬ pc

Lance, an Arkansan, has won the 2007 Tour de FranceS

: λc.[


]S

: λc. ¬[


] >

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However, type checking of this SR is not affected by the existenceof the negation operator ¬ that encloses it. So it also requiresthat the proposition that Lance is an Arkansan is inhabited.

won : entity→ type(Con)

lance : entity(Con)

won(lance) : type(ΠE)

@1 : arkansan(lance)

CI(@1 : arkansan(lance)) : type(IdF )[


]: type

(ΣF )

¬[


]: type

(¬F )

The CI content is predicted to be independent from at-issuecontent (as expected).

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(13) a. If Lance is a cyclist, then the Boston Marathon was

won by the cyclist . (presupposition)

b. # If Lance is a cyclist, then the Boston Marathon waswon by Lance, a cyclist . (CI)

There are various ways in which this infelicity could be viewed, butto us a violation of Quantity or Manner, in that the conditionalclause is uninformative, as it is pre-satisfied by the appositivecontent. Let us explain how this contrast is predicted in DTS.

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First, the derivation of (13a) is as follows:

If Lance is a cyclistS/S

: λp.λc. (u:cyclist(lance))→ p(c, u)

the BMNP: bm

was won byS\NP/NP

: λy.λx.λc.win(y, x)

the cyclistS\NP\(S\NP/NP)

: λp.λx.λc.p(π1

(@1c :

[y:entitycyclist(y)

]))xc

S\NP

: λx.λc.win

(π1

[y:entity@1c : cyclist(y)

], x

) <

S

: λc.win

(π1

(@1c :

[y:entitycyclist(y)

],BM

)) <

λc. (u:cyclist(lance))→ win

(π1

(@1(c, u) :

[y:entitycyclist(y)

],BM

)) >

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Then the type checking rules apply to the resulting SR under theinitial context ():

(u:cyclist(lance))→ win

(π1

(@1(c, u) :

[y:entitycyclist(y)

],BM

)): type

which require that the underspecified term @1 satisfies thefollowing judgment.

Γ, u : cyclist(lance) ` @1 :[>cyclist(lance)

]→[y:entitycyclist(y)

]In other words, the type checking launches a proof search, whichtries to find a term of type:[

>cyclist(lance)

]→[y:entitycyclist(y)

]under a given context.We assume that the hearer knows thatLance exists, i.e. we assume that the global context Γ includes theentry lance : entity. Then the presupposition can be bound.

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In the case of CI, the situation is different. The derivation of (13b)is as follows:

If Lance is a cyclistS/S

: λp.λc. (u:cyclist(lance))→ p(c, u)

the BMNP: bm

was won byS\NP/NP

: λy.λx.λc.win(y, x)

Lance, a cyclistT \(T /NP)

: λp.λx.λc.[p(lance)xcCI(@2 : cyclist(lance))

]S\NP

: λx.λc.[

win(lance, x)CI(@2 : cyclist(lance))

] <

S

: λc.[

win(lance,BM )CI(@2 : cyclist(lance))

] <

λc. (u:cyclist(lance))→

[win(lance,BM )CI( @2 : cyclist(lance))

] >

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Type checking rules apply to the resulting SR under the initialcontext ():

(u:cyclist(lance))→


]: type

which requires that the underspecified term @2 satisfies thefollowing judgment.

Γ, u : cyclist(lance) ` @2 : cyclist(lance)

It seems that the variable u is an immediate candidate that canreplace @2, but this is not licenced: the underspecified term @2

should not contain the free occurrence of u.

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I Thus, there is no binding option for the CI in (13b) unless theglobal context Γ provides some knowledge that allows itsinference.

I Otherwise, the hearer has to update Γ accordingly, i.e.accommodate it.

I The simplest way is to use the following updated globalcontext Γ′ (x is some variable chosen so that x /∈ Γ).

Γ′def≡ Γ, x : cyclist(lance)

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I The difference between the two cases:I Presuppositions: The underspecified term is given a local

context as its argument, and so is able to bind it by means ofinformation deduced from the local context.

(u:cyclist(lance))→ win

(π1

(@1(c, u) :

[y:entitycyclist(y)

],BM

)): type

I CIs: The underspecified term does not take a local context asits argument, and so cannot refer to it

(u:cyclist(lance))→


]: type

I This way, DTS predicts that antecedents of conditionals,which are of course presupposition filters, do not filter CIcontents, thus deriving one of the empirical differencesbetween these types of content.

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It is also predicted in DTS that the sentence (13b) is pragmaticallyinfelicitous.

(13b) # If Lance is a cyclist, then the Boston Marathon was won

by Lance, a cyclist .

I In order to accept (13b) as a felicitous sentence, one has toadd the entry x : cyclist(lance) to his/her global context inmost cases.

I It is then inappropriate to assume that Lance is a cyclist, as in(13b), which is redundant, since it is immediately derivablefrom the global context.

This is one way to implement the idea of the infelicity of (13b) asa Gricean violation of the kind mentioned above.

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Solution

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[P5] A CI can serve as an antecedent for the subsequentanaphora/presuppositions

MaryNP

: mary

counselledS\NP/NP

: λy.λx.λc.counsel(x, y)

JohnNP

: john

, who1

T \(T /NP)\NP/(S\NP)

: λr.λz.λp.λ~x.λc.[pz~xcCI(@1 : rzc)

] killed a coworkerS\NP

: λx.λc.killC(x)

T \(T /NP)\NP

: λz.λp.λ~x.λc.[pz~xcCI(@1 : killC(z))

] >

T \(T /NP)

: λp.λx.λc.[pjohnxcCI(@1 : killC(john))

] <

S\NP

: λx.λc.[

counsel(x, john)CI(@1 : killC(john))

]S

: λc.

[counsel(mary , john)CI(@1 : killC(john))

] <

;

BillNP: bill

knows2 thatS\NP/S

: λp.λx.λc.know(x,@2c : pc)

he3 killed a coworkerS

: λc.killC(@3c)

S\NP: λx.λc.know(x,@2c : killC(@3c))

>

S: λc.know(bill ,@2c : killC(@3c))

>

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(4) Mary counseled John, who killed a coworker .

Unfortunately, Bill knows that he killed a coworker .

Dynamic conjunction−−−−−−−−−−−−→ λc.

u:

[counsel(mary , john)CI( @1 : killC(john))

]know(bill , @2 (u, c) : killC( @3 (u, c))

The resulting discourse representation contains threeunderspecified terms:I @1 for the CI content

I @2 for the factive presupposition of “knows”

I @3 for the pronoun “he”

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(14)

λc.

u:

[counsel(mary , john)CI( @1 : killC(john))

]know(bill , @2 (u, c) : killC( @3 (u, c))

I Type checking requires the term @1 to be of type

killC(john) (⇒ accommodated as new information to thehearer.)

I The term @3 can be independently resolved as@3 = λc.john (if it is intended to be coreferential to “John”)

I Then the term @2 can be bound, which is required to have

type killC(john), just by being identified with @1 .

In this way, what is introduced as a CI can bind the subsequentpresuppositions, although it does not participate in the at-issuecontent. 58 / 76


[P6] Anaphora/Presupposition inside CIs receive their localcontexts

The semantic representation for (6) is derived as follows.JohnNP

: john

killed a coworkerS\NP

: λx.λc.killC(x)

S: λc.killC(john)

>

;

MaryNP

: mary

, who1

T /(T \NP)\NP/(S\NP)

: λr.λz.λp.λ~x.λc.[pz~xcCI(@1 : rzc)

]

knows2 thatS\NP/S

: λp.λx.λc.know(x,@2c : pc)

John killed a coworkerS

: λc.killC(john)

S\NP: λx.λc.know(x,@2c : killC(john))

>

T /(T \NP)\NP

: λz.λp.λc.[pzcCI(@1 : know(z,@2c : killC(john)))

] >

T /(T \NP)

: λp.λc.[pmarycCI(@1 : know(mary ,@2c : killC(john)))

] <

counselled him3

S\NP: λx.λc.counsel(x,@3c)

S

: λc.[

counsel(mary ,@3c)CI(@1 : know(mary ,@2c : killC(john)))

] >

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(6) John killed a coworker. Mary,

who knows that he killed a coworker , counseled him .

Dynamic conjunction−−−−−−−−−−−−→ λc.

u:killC(john)[CI( @1 : know(mary , @2 (c, u) : killC(john)))counsel(mary , @3 (c, u))

]The resulting discourse representation contains threeunderspecified terms:

I @2 for the factive presupposition triggered by “know” whichstates that John killed a coworker

I @1 for the NRRC that Mary knows it

I @3 for the pronoun “him”

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λc.

u:killC(john)[CI( @1 : know(mary , @2 (c, u) : killC(john)))counsel(mary , @3 (c, u))

]The factive presupposition @2 , embedded within the CI forNRRC, still receives its local context (c, u) (= a pair of the localcontext for this mini discourse and the proof of the first sentence).

The most salient resolution is @2 = λc.π2c, which returns theproof of the first sentence.

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The lexical entry of “who” passes the local context it receives to

the relative clause, while the CI content @1 that it introducesdoes not receive it.

, who1

T /(T \NP)\NP/(S\NP)

: λr.λz.λp.λ~x.λc.

[pz~x c

CI( @1 : rz c )

]In the DTS framework, the at-issue contents and the CI contentsare not separated representation-wise, unlike Potts (2005)’stwo-dimensional theory.

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[P1] Honorification in Japanese: Watanabe et al. (2014)

John-sensei-gaS/(S\NPga)

: λp.p(j )

irassyaruS\NPga

: λx.λc.[

come(x)CI(@1 : honor(sp, x)))

]S

: λc.[

come(j )CI(@1 : honor(sp, j )))

] >

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[P1&P2] 2-place functional mixed content

Hansh

anglotzen

λy.λx.λc.

[look-at(x, y)CI(@1 : bad(look-at(x, y)))

] Tinat

λx.λc.

[look-at(x, t)CI(@1 : bad(look-at(x, t)))

] >

λc.

[look-at(h, t)CI(@1 : bad(look-at(h, t)))

] <

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[P3] Quantification problem

Hansh

anglotzen

λy.λx.λc.

[look-at(x, y)CI(@1 : bad(look-at(x, y)))

] every girlλp.λx.λc. (y:entity)→ (v:girl(y))→ pyx(c, (y, v))

λx.λc. (y:entity)→ (v:girl(y))→[

look-at(x, y)CI(@1 : bad(look-at(x, y)))

] >

λc. (y:entity)→ (v:girl(y))→[

look-at(h, y)CI(@1 : bad(look-at(h, y)))

] <

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[P4] Shunting

yokumoS/S

: λp.λc.CI(@1 : pc)

· · · sita-naS: φ

S: λc.CI(@1 : φc)

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Conclusion

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Conclusion

Our work: an analysis of conventional implicature in the frameworkof DTS.

I DTS: phenomena such as anaphora resolution andpresupposition are viewed in terms of proof search;

I together with suitable constraints on CIs, this naturally derivesCI behaviorI semantic operatorsI and interaction between at-issue and CI content.

We think the resulting picture is attractive, not least in that it isfully integrated with compositional, subsentential aspects ofmeaning derivation.

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Conclusion

One direction for future expansion of this work:

I Simons et al. (2011): the projection behavior of not-at-issuecontent depends on the relation of that content to the currentQuestion Under Discussion, or QUD Roberts (1996).

I In outline: QUD-related content doesn’t project,QUD-irrelevant content does.

We are sympathetic to the idea that projection behavior should berelativized in some manner to the discourse context, eg. the QUD.

I At least in principle: more work is needed to clarify theempirical situation.

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Conclusion

This view seems closely related to the DTS formalism.

I Discourse context makes various sorts of content available.

I If that content contains such things as goals and QUDs, thenthey ought to play a role in proof search as well;

I so different projection behavior is to be expected.

How to spell this out? It depends on (+ the empirical facts) . . .

I the analysis of questions,

I the proper analysis of denial and other relational speech acts,

I the form of QUDs and their proof-theoretic correspondence:

I What kind of resource is a QUD?

We believe that exploring these issues is an exciting next step forthe present project.

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Reference I

Bekki, D. (2013) “A Type-theoretic Approach to Double NegationElimination in Anaphora”, In the Proceedings of Logic andEngineering of Natural Language Semantics 10 (LENLS 10).Tokyo.

Bekki, D. (2014) “Representing Anaphora with Dependent Types”,In the Proceedings of N. Asher and S. V. Soloviev (eds.):Logical Aspects of Computational Linguistics (8th internationalconference, LACL2014, Toulouse, France, June 2014Proceedings), LNCS 8535. Toulouse, pp.14–29, Springer,Heiderburg.

Bekki, D. and E. McCready. (2014) “CI via DTS”, In theProceedings of LENLS11. Tokyo, pp.110–123.

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Reference II

Bekki, D. and M. Sato. (2015) “Calculating Projections via TypeChecking”, In the Proceedings of TYpe Theory and LExicalSemantics (TYTLES), ESSLLI2015 workshop. Barcelona, Spain.

Grice, H. P. (1975) “Logic and conversation”, In: P. Cole and J. L.Morgan (eds.): Syntax and Semantics 3: Speech Acts. London,Academic Press, pp.41–58.

Gutzmann, D. (2015) Use-conditional meaning, Vol. 6 of Studiesin Semantics and Pragmatics, Oxford Studies in Semantics andPragmatics. Oxford, Oxford University Press.

Loh, A., C. McBride, and W. Swierstra. (2010) “A TutorialImplementation of a Dependently Typed Lambda Calculus”,Fundamenta Informaticae - Dependently Typed Programming102(2), pp.177–207.

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Reference III

McCready, E. (2010) “Varieties of Conventional Implicature”,Semantics and Pragmatics 3(8), pp.1–57.

Milner, R. (1978) “A Theory of Type Polymorphism inProgramming” Journal of Computer and System Science(JCSS)(17), pp.348–374.

Nordstrom, B., K. Petersson, and J. Smith. (1990) Programmingin Martin-Lof’s Type Theory. Oxford University Press.

Potts, C. (2005) The Logic of Conventional Implicatures. OxfordUniversity Press.

Ranta, A. (1994) Type-Theoretical Grammar. Oxford UniversityPress.

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Reference IV

Roberts, C. (1996) “Information Structure: Towards an integratedformal theory of pragmatics”, In: OSUWPL Volume 49: Papersin Semantics. The Ohio State University Department ofLinguistics.

Simons, M., J. Tonhauser, D. Beaver, and C. Roberts. (2011)“What Projects and Why”, In the Proceedings of Proceedings ofSALT 20. pp.309–327, CLC Publications.

Sundholm, G. (1986) “Proof theory and meaning”, In: D. Gabbayand F. Guenthner (eds.): Handbook of Philosophical Logic, Vol.III. Reidel, Kluwer, pp.471–506.

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Reference V

Tanaka, R. (2014) “A Proof-Theoretic Approach to GeneralizedQuantifiers in Dependent Type Semantics”, In the Proceedingsof R. de Haan (ed.): the ESSLLI 2014 Student Session, 26thEuropean Summer School in Logic, Language and Information.Tubingen, Germany, pp.140–151.

Tanaka, R., K. Mineshima, and D. Bekki. (2014) “Resolving ModalAnaphora in Dependent Type Semantics”, In the Proceedings ofthe Eleventh International Workshop on Logic and Engineeringof Natural Language Semantics (LENLS11), JSAI InternationalSymposia on AI 2014. Tokyo, pp.43–56.

Tanaka, R., K. Mineshima, and D. Bekki. (2015) “Factivity andPresupposition in Dependent Type Semantics”, In theProceedings of TYpe Theory and LExical Semantics (TYTLES),ESSLLI2015 workshop.

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Reference VI

Tanaka, R., Y. Nakano, and D. Bekki. (2013) “ConstructiveGeneralized Quantifiers Revisited”, In the Proceedings of Logicand Engineering of Natural Language Semantics 10 (LENLS 10).Tokyo, pp.69–78.

Wang, L., B. Reese, and E. McCready. (2005) “The ProjectionProblem of Nominal Appositives”, Snippets 11, pp.13–14.

Watanabe, N., E. McCready, and D. Bekki. (2014) “JapaneseHonorification: Compositionality and Expressivity”, In theProceedings of S. Kawahara and M. Igarashi (eds.): FAJL 7:Formal Approaches to Japanese Linguistics, the MIT WorkingPapers in Linguistics 73. International Christian University,Japan, pp.265–276.

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