Dynamics, Dependency Grammar and Incremental Interpretation

Transcription

1 Dynamic, Dependency Grammar and Incremental Interpretation David Milward Iri Perkmann

2 Lexicalied Dependency Grammar: provide (flat) tree-tructure analye of entence. Dynamic Dependency Grammar: provide analye of entence a tranition between tate, according to axiom and deduction rule.

3 Dynamic Grammar

4 Dynamic Grammar Dynamic Grammar ha an infinite et of tate and a et of tranition between tate. A tate repreent the yntactic and emantic dependencie aborbed o far. Each word can add new dependencie and change the tate. A entence i grammatical, if it perform a tranition between a uitable initial and final tate.

5 Finite tate machine a logic b tart 0 a 1 c 2 b 3 grammatical: every tring of form ab*cb that map from 0 to 3.

6 Finite tate machine a logic b tart 0 a 1 c 2 b 3 Reformulation: State0 Str State1 0 a 1 1 b 1 2 b 3 1 c 2

7 Sequencing Tranition are combined uing a deduction rule, Sequencing: S 0 String a S 1 S 1 String b S 2 S 0 String a String b S 2

8 Sequencing Tranition are combined uing a deduction rule, Sequencing: S 0 String a S 1 S 1 String b S 2 S 0 String a String 2 S 2 0 a 1 1 b 1 2 b 3 1 c 2 1 bb 1 1 c 2 1 bbc 2 A tring i grammatical, if it ha uch a proof.

9 Proof Multiple proof for the ame tring are poible. 0 a 1 1 b 1 1 b 1 1 bb 1 1 c 2 1 bbc 2 0 abbc 2 2 b 3 0 abbcb 3

10 Lexicalied Dependency Grammar

11 Notation Notation of dependency tructure: John thought Mary howed Ben to Sue Thi can be hown a bracketed tructure: [John thought [Mary howed Ben [to Sue]]]

12 Aumption Adjacency Fixed order of dependent relative to the head and each other

13 Lexicalied Dependency Grammar Each head i a function with it dependent a argument. Contituent are formed by combining function with all their argument.

14 Tree tructure [John thought [Mary howed Ben [to Sue]]] np l np r np l np r np, pp np pp pp l r np np

15 Feature tructure repreentation of Lexical categorie howed: l np r np, pp bae type argument to the left argument to the right bae type: Type of contituent formed from the item and it argument (A noun phrae i een a a noun and it dependent, a entence a a verb and it dependent)

16 Feature tructure repreentation of Lexical categorie If the left and right argument lit are empty, categorie are aturated: X l = X r Argument mut be aturated categorie.

17 Lexicalied Dependency Grammar Propertie of LDG: 1 A finite et of bae type T 0,..T n (, np, pp etc.) 2 An infinite et of lexical categorie X where X i a bae type and L and R are lit of bae type. ll rr If L and R are empty, the category i identical to the bae type X. 3 A finite lexicon L which aign lexical categorie to word. 4 A pecial type T 0. If a tring ha thi category, it i grammatical. 5 A combination rule. Concatenation of all l and r element of a category X ha category X.

18 Dynamic Dependency Grammar

19 Dynamic Dependency Grammar Reformulation of LDG. State encode the yntax of the tring aborbed o far, they are labelled by the type of the tring: l l Sue aw l Ben r r l np r np r

20 Dynamic Dependency Grammar Reformulation of LDG. State encode the yntax of the tring aborbed o far, they are labelled by the type of the tring: l l Sue aw l Ben r r l np r np r unaturated

21 Dynamic Dependency Grammar A entence i grammatical, if the tatement hold true: l Str r The ame logic, axiom and deduction rule are ued a in LDG (for non-empty tring of word): S 0 String a S 1 S 1 String b S 2 S 0 String a String 2 S 2

22 Prediction and Application The et of axiom i infinite (neceary for cae like centre embedding). It i decribed by two chemata, Prediction and Application, dependent on whether or not the category found correpond to the category expected.

23 Prediction l l Sue r r l np r where Sue:np Prediction i ued when the encountered category doe not match the expected: The current tate expect a entence, but encounter an NP. The reulting tate till expect a entence, but without an NP on the left.

24 Prediction l l Y W Y r ll L R rr l X L R r r X where W: ll rr

25 Application l Ben where Ben:np r np An NP i expected and encountered.

26 Application l X W l r ll R rr R r X where W: ll rr

27 Determinim Reulting tate are uually determined by the current tate and the word. Non-determinim can arie from lexical ambiguity (e. g. thought + or thought + PP) or from the choice between Prediction and Application (Prediction i poible whenever Application i).

28 Determinim State are labelled by type, not tree tructure. Thu non-determinim can be kept low. Ben Sue aw np np l np, np r Ben Sue leep believe np np l np r l, np r

29 Determinim The two tructure can be treated a the ame, until the verb i encountered. Ben Sue l r l np, np r aw : Application leep : Prediction

30 Dynamic Dependency Grammar Propertie of DDG: 1 A et of categorie of the form X ll rr 2 Two axiom chemata, Application and Prediction 3 The lexicon L 4 One deduction rule, Sequencing 5 Two ditinguihed categorie, T 0 and T 0. l r T 0 A tring Str i grammatical, if: T 0 Str T 0 l r T 0

31 Incremental Interpretation

32 Incremental Interpretation Each tate can be aigned a emantic type and value. l l Sue aw l r r l np r np r t t (e t) t e t λq.q λp.p(ue ) λy.aw (ue,y) map to the emantic type t = truth-value; np to e = entity categorie with argument map to correponding functional type

33 Incremental Interpretation lexical categorie are extended by emantic value: e. g. aw ha the value λyλx.aw (X,Y) and the type e (e t).

34 Application

35 Application provide incremental paring and interpretation for LDG can be ued a link between the original grammar and a paring algorithm can be extended with axiom and deduction rule to cover difficult yntactic phenomena, like coordination, topicaliation and extrapoition: C 0 String a C 1 C 0 String b C 1 C 0 String a and String b C 1

36 quetion: Auming adjacency, how are problem like long-ditance dependencie handled? How hould analyi of ambiguou word work? thought+pp v. thought+? What about adjunct?

37 Milward, David (1992). Dynamic, Dependency Grammar and Incremental Interpretation. In: Proc. of COLING-92, Nante, Aug , 1992.