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

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)

Outline DS in TTR Using TTR contents in DS Adding speech events

Outline DS in TTR Using TTR contents in DS Adding speech events

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? 4 / 28

DS in TTR Using TTR contents in DS Adding speech events John arrived in DS “John arrived” �− → ♦ , ? Ty ( t ) Ty ( e ) , Ty ( e → t ) , Fo ( john ′ ) λx.arrive ( x ) plication of lexical actions is interspersed with 5 / 28

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 6 / 28

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 : � λ v : Type . v , � type �� 6 / 28

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  type :  Type a : Tree iff a : cont : type   daughters : Tree * Tree * is the type of strings of trees ( cf. Kleene-*) including the empty string, ǫ 7 / 28

DS in TTR Using TTR contents in DS Adding speech events John arrived in DS (again) “John arrived” �− → ♦ , ? Ty ( t ) Ty ( e ) , Ty ( e → t ) , Fo ( john ′ ) λx.arrive ( x ) plication of lexical actions is interspersed with 8 / 28

DS in TTR Using TTR contents in DS Adding speech events Type for the tree for John arrived type= t :  Type  cont : type     type= e :   Type    cont= john ′  daughters : : type  ⌢      daughters= ǫ : Tree *       type= e → t : Type     cont= λ x : e . arrive ( x ) : type     daughters= ǫ : Tree * 9 / 28

DS in TTR Using TTR contents in DS Adding speech events or more diagrammatically . . . � type= t � : Type cont : type � type= e � type= e → t : � : � Type Type cont= john ′ : type cont= λ x : e . arrive ( x ) : type 10 / 28

DS in TTR Using TTR contents in DS Adding speech events or more diagrammatically . . . � type= t � : Type cont : type � type= e � type= e → t : � : � Type Type cont= john ′ : type cont= λ x : e . arrive ( x ) : type ◮ Note that this represents a tree type , not a tree 10 / 28

DS in TTR Using TTR contents in DS Adding speech events or more diagrammatically . . . � type= t � : Type cont : type � type= e � type= e → t : � : � Type Type cont= john ′ : type cont= λ x : e . arrive ( x ) : type ◮ Note that this represents a tree type , not a tree ◮ cf underspecified trees 10 / 28

DS in TTR Using TTR contents in DS Adding speech events or more diagrammatically . . . � type= t � : Type cont : type � type= e � type= e → t : � : � Type Type cont= john ′ : type cont= λ x : e . arrive ( x ) : 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 10 / 28

DS in TTR Using TTR contents in DS Adding speech events or more diagrammatically . . . � type= t � : Type cont : type � type= e � type= e → t : � : � Type Type cont= john ′ : type cont= λ x : e . arrive ( x ) : 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 10 / 28

DS in TTR Using TTR contents in DS Adding speech events or more diagrammatically . . . � type= t � : Type cont : type � type= e � type= e → t : � : � Type Type cont= john ′ : type cont= λ x : e . arrive ( x ) : 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’ 10 / 28

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 11 / 28

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, a ε r , just in case there is some path, π , in r such that r .π = a 0 . . . ⌢ a n can be viewed as a record ◮ A string a ⌢   t 0 = a 0 . .   .   t n = a n ◮ Thus there are paths into strings occuring as a component in a record 12 / 28

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 T a ε is a type. b : T a ε iff b : T and a ε b . 13 / 28

DS in TTR Using TTR contents in DS Adding speech events Type for the tree with unattached node   type= t : Type cont : type   Tree * � type= e   daughters :   � : Type   ε cont= john ′ : type 14 / 28

DS in TTR Using TTR contents in DS Adding speech events Lexical entry for John john: ? Ty ( e ) IF put ( Ty ( e ) ) THEN put ( Fo ( john ′ ) ) abort ELSE 15 / 28

DS in TTR Using TTR contents in DS Adding speech events Lexical entries as update rules � type=e � : Type If T i = , cont : type � type=e � : Type then set T i +1 to be cont= john ′ : type 16 / 28

DS in TTR Using TTR contents in DS Adding speech events Lexical entries as type refinements � type=e � type=e � � : Type : Type ⇒ cont : type cont= john ′ : type Type rewrite rule which is a type refinement because RHS ⊑ LHS 17 / 28

DS in TTR Using TTR contents in DS Adding speech events More general version of type refinement rule � type=e � : Type If T ⊑ : cont : type � type=e � : Type T ⇒ T ∧ . cont= john ′ : type 18 / 28

Outline DS in TTR Using TTR contents in DS Adding speech events

DS in TTR Using TTR contents in DS Adding speech events Alternative using TTR-style content � type= � type= � � � � � � x: Ind : Type x: Ind : Type ⇒ � � cont : type cont= x=john : type 20 / 28

DS in TTR Using TTR contents in DS Adding speech events Type for John arrived with TTR content  type= RecType : Type  � x=john: Ind �   cont= :type p:arrive(x) � type= � � �  � �  x: Ind : Type type=( x: Ind → RecType ): Type � � � x= r .x: Ind � cont= x=john :type  � �  cont= λ r : x: Ind . :type p:arrive(x) 21 / 28

Outline DS in TTR Using TTR contents in DS Adding speech events

DS in TTR Using TTR contents in DS Adding speech events Split utterances A. You burned . . . B. . . . myself 23 / 28

DS in TTR Using TTR contents in DS Adding speech events Speech events   sp : Ind au : Ind     SEvent = e : Phon     c sp : speaker(e,sp)   c au : audience(e,au) 24 / 28

DS in TTR Using TTR contents in DS Adding speech events Indexical pronouns  s-event :  SEvent  ⇒ � � I, me 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 25 / 28

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 26 / 28

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 27 / 28