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Dynamic Syntax in Type Theory with Records Robin Cooper and Staffan - - PowerPoint PPT Presentation

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Dynamic Syntax in Type Theory with Records Robin Cooper and Staffan Larsson Centre for Linguistic Theory and Studies in Probability (CLASP) Dept. of Philosophy, Linguistics and Theory of Science University of Gothenburg Supported by VR

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Dynamic Syntax in Type Theory with Records

Robin Cooper and Staffan Larsson Centre for Linguistic Theory and Studies in Probability (CLASP)

  • Dept. of Philosophy, Linguistics and Theory of Science

University of Gothenburg Supported by VR projects: 2009-1569, Semantic analysis of interaction and coordination in dialogue (SAICD); 2016-01162, Incremental Reasoning in Dialogue (IncReD); 2014-39, Centre for Linguistic Theory and Studies in Probability (CLASP)

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Outline

DS in TTR Using TTR contents in DS Adding speech events

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Outline

DS in TTR Using TTR contents in DS Adding speech events

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DS in TTR Using TTR contents in DS Adding speech events

Relating DS and TTR

◮ DS (Kempson et al., 2001) ◮ TTR (Cooper, in prep, 2012; Cooper and Ginzburg, 2015) ◮ adding TTR for semantic representation (Eshghi, 2015) ◮ What might it look like to do everything in TTR? ◮ Is it even possible?

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DS in TTR Using TTR contents in DS Adding speech events

John arrived in DS

“John arrived”

− →

♦, ?Ty(t) Ty(e), Fo(john′) Ty(e → t), λx.arrive(x)

plication of lexical actions is interspersed with

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DS in TTR Using TTR contents in DS Adding speech events

Tree nodes

Nodes seem to contain records of the type: type : Type cont : type

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DS in TTR Using TTR contents in DS Adding speech events

Tree nodes

Nodes seem to contain records of the type: type : Type cont : type

  • That is, in official notation:

type : Type cont : λv:Type.v, type

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DS in TTR Using TTR contents in DS Adding speech events

Daughters

But tree nodes may have daughters. Therefore we define a (basic, recursive) type Tree such that a:Tree iff a:   type : Type cont : type daughters : Tree*   Tree* is the type of strings of trees (cf. Kleene-*) including the empty string, ǫ

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DS in TTR Using TTR contents in DS Adding speech events

John arrived in DS (again)

“John arrived”

− →

♦, ?Ty(t) Ty(e), Fo(john′) Ty(e → t), λx.arrive(x)

plication of lexical actions is interspersed with

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DS in TTR Using TTR contents in DS Adding speech events

Type for the tree for John arrived

            type=t : Type cont : type daughters :   type=e : Type cont=john′ : type daughters=ǫ : Tree*   ⌢   type=e → t : Type cont=λx:e . arrive(x) : type daughters=ǫ : Tree*              

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DS in TTR Using TTR contents in DS Adding speech events

  • r more diagrammatically . . .

type=t : Type cont : type

  • type=e → t

: Type cont=λx:e . arrive(x) : type

  • type=e

: Type cont=john′ : type

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DS in TTR Using TTR contents in DS Adding speech events

  • r more diagrammatically . . .

type=t : Type cont : type

  • type=e → t

: Type cont=λx:e . arrive(x) : type

  • type=e

: Type cont=john′ : type

  • ◮ Note that this represents a tree type, not a tree

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DS in TTR Using TTR contents in DS Adding speech events

  • r more diagrammatically . . .

type=t : Type cont : type

  • type=e → t

: Type cont=λx:e . arrive(x) : type

  • type=e

: Type cont=john′ : type

  • ◮ Note that this represents a tree type, not a tree

◮ cf underspecified trees

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DS in TTR Using TTR contents in DS Adding speech events

  • r more diagrammatically . . .

type=t : Type cont : type

  • type=e → t

: Type cont=λx:e . arrive(x) : type

  • type=e

: Type cont=john′ : type

  • ◮ Note that this represents a tree type, not a tree

◮ cf underspecified trees ◮ a record type is fully specified iff all its fields are manifest

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DS in TTR Using TTR contents in DS Adding speech events

  • r more diagrammatically . . .

type=t : Type cont : type

  • type=e → t

: Type cont=λx:e . arrive(x) : type

  • type=e

: Type cont=john′ : type

  • ◮ Note that this represents a tree type, not a tree

◮ cf underspecified trees ◮ a record type is fully specified iff all its fields are manifest ◮ it is underspecified otherwise

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DS in TTR Using TTR contents in DS Adding speech events

  • r more diagrammatically . . .

type=t : Type cont : type

  • type=e → t

: Type cont=λx:e . arrive(x) : type

  • type=e

: Type cont=john′ : type

  • ◮ Note that this represents a tree type, not a tree

◮ cf underspecified trees ◮ a record type is fully specified iff all its fields are manifest ◮ it is underspecified otherwise ◮ this type is underspecified with respect to the path ‘cont’

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DS in TTR Using TTR contents in DS Adding speech events

More underspecification

type=t : Type cont : type

  • type=e

: Type cont=john′ : type

  • cf. D-theory (Marcus et al., 1983), functional uncertainty in LFG

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DS in TTR Using TTR contents in DS Adding speech events

Components in records

◮ An object, a, is a component of a record, r, in symbols, aεr,

just in case there is some path, π, in r such that r.π = a

◮ A string a⌢ 0 . . .⌢ an can be viewed as a record

   t0 = a0 . . . tn = an   

◮ Thus there are paths into strings occuring as a component in

a record

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DS in TTR Using TTR contents in DS Adding speech events

Types of objects containing a certain component

If a is an object of some type and T is a type, then Taε is a type. b : Taε iff b : T and aεb.

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DS in TTR Using TTR contents in DS Adding speech events

Type for the tree with unattached node

     type=t : Type cont : type daughters : Tree* type=e : Type cont=john′ : type

  • ε

    

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DS in TTR Using TTR contents in DS Adding speech events

Lexical entry for John

john: IF ?Ty(e) THEN put(Ty(e)) put(Fo(john′)) ELSE abort

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DS in TTR Using TTR contents in DS Adding speech events

Lexical entries as update rules

If Ti = type=e : Type cont : type

  • ,

then set Ti+1 to be type=e : Type cont=john′ : type

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DS in TTR Using TTR contents in DS Adding speech events

Lexical entries as type refinements

type=e : Type cont : type

  • ⇒

type=e : Type cont=john′ : type

  • Type rewrite rule which is a type refinement because RHS⊑LHS

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DS in TTR Using TTR contents in DS Adding speech events

More general version of type refinement rule

If T ⊑ type=e : Type cont : type

  • :

T ⇒ T∧ . type=e : Type cont=john′ : type

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Outline

DS in TTR Using TTR contents in DS Adding speech events

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DS in TTR Using TTR contents in DS Adding speech events

Alternative using TTR-style content

type=

  • x:Ind
  • :

Type cont : type

  • ⇒

type=

  • x:Ind
  • :

Type cont=

  • x=john
  • :

type

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DS in TTR Using TTR contents in DS Adding speech events

Type for John arrived with TTR content

  type=RecType:Type cont= x=john:Ind p:arrive(x)

  • :type

    type=(

  • x:Ind
  • →RecType):Type

cont=λr:

  • x:Ind
  • .

x=r.x:Ind p:arrive(x)

  • :type

  type=

  • x:Ind
  • :Type

cont=

  • x=john
  • :type
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Outline

DS in TTR Using TTR contents in DS Adding speech events

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DS in TTR Using TTR contents in DS Adding speech events

Split utterances

A. You burned . . . B. . . . myself

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DS in TTR Using TTR contents in DS Adding speech events

Speech events

SEvent =       sp : Ind au : Ind e : Phon csp : speaker(e,sp) cau : audience(e,au)      

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DS in TTR Using TTR contents in DS Adding speech events

Indexical pronouns

I, me   s-event : SEvent type=

  • x:Ind
  • :

Type cont : type   ⇒   s-event : SEvent type=

  • x:Ind
  • :

Type cont=

  • x=s-event.sp
  • :

type  

◮ different s-event for each incremental item, therefore

potentially different speakers for different incremental items

◮ sign-based approach

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DS in TTR Using TTR contents in DS Adding speech events

Still to be done

◮ a neat solution for the focus, ♦ – possibly just an additional

field

◮ linked nodes ◮ . . . ◮ working out (and implementing) a detailed grammar based on

these ideas

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DS in TTR Using TTR contents in DS Adding speech events

Why?

◮ because we can (or perhaps, ultimately, cannot) ◮ TTR would like to bill itself as a foundation for various

linguistic theories

◮ . . . allowing integration of analyses in different theories or

pointing up relations between them

◮ Perhaps there are elements in TTR which DS would find useful

in addition to the use of TTR for semantic representation

◮ In general, the more theoretical light from different

perspectives we can shed on incremental processing of language, the better

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DS in TTR Using TTR contents in DS Adding speech events

Support from VR projects:

◮ 2009-1569, Semantic analysis of interaction and coordination

in dialogue (SAICD)

◮ 2016-01162, Incremental Reasoning in Dialogue (IncReD) ◮ 2014-39, Centre for Linguistic Theory and Studies in

Probability (CLASP)

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References

Bibliography I

Cooper, Robin (2012) Type Theory and Semantics in Flux, in R. Kempson, N. Asher and T. Fernando (eds.), Handbook of the Philosophy of Science, Vol. 14: Philosophy of Linguistics, pp. 271–323, Elsevier BV. General editors: Dov M. Gabbay, Paul Thagard and John Woods. Cooper, Robin (in prep) Type theory and language: from perception to linguistic communication. Draft of book chapters available from https://sites.google.com/site/ typetheorywithrecords/drafts. Cooper, Robin and Jonathan Ginzburg (2015) Type Theory with Records for Natural Language Semantics, in S. Lappin and C. Fox (eds.), The Handbook of Contemporary Semantic Theory, second edition, pp. 375–407, Wiley-Blackwell.

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References

Bibliography II

Eshghi, Arash (2015) DS-TTR: An incremental, semantic, contextual parser for dialogue, pp. 172–173. Kempson, Ruth, Wilfried Meyer-Viol and Dov Gabbay (2001) Dynamic syntax: the flow of language understanding, Blackwell. Marcus, Mitchell P., Donald Hindle and Margaret M. Fleck (1983) D-theory: Talking About Talking About Trees, in Proceedings of the 21st Annual Meeting on Association for Computational Linguistics, pp. 129–136, Association for Computational Linguistics, Stroudsburg, PA, USA.

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