1. Linguistics 187 Week 3 Coordination and Functional Uncertainty

2. Coordination Illustrates engineering interaction of –Linguistic phenomena –Description –Representation

3. Coordination phenomena Constituent: Coordinated elements are otherwise motivated constituents. [ S A girl saw Mary] and [ S a girl heard Bill].(Unreduced) A girl [ VP saw Mary] and [ VP heard Bill].(Reduced) A girl [ V saw] and [ V heard] Mary. Nonconstituent: Coordinated elements look like fragments Bill went to [ ? Chicago on Wednesday] and [ ? New York on Thursday]. (What motivates constituency? Transformations? Phonology? Semantics? Coordination? We’ll deal only with constituent coordination)

4. Descriptive problems First cut: Conjoin phrases of like category Assign expanded-form interpretation (?) (1)A girl [ VP saw Mary] and [ VP heard Bill]. interpreted like (2) [ S A girl saw Mary] and [ S a girl heard Bill]. see(girl,Mary) & hear(girl, Bill) But: Can coordinate some unlike categories: Bush is [ NP a Republican] and [ AP proud of it]. Can’t coordinate some like categories: [Bad] John [ V keeps] and [ V polishes] his car in the garage. [OK] John [ V washes] and [ V polishes] his car in the garage. And semantic entailments differ: One girl in (1)

5. Theoretical/engineering goal Get right syntactic and semantic results Without obscuring other generalizations: One account of passives, relatives, subcategorization…whether conjoined or not.

6. Coordination in LFG/XLE Functional representation: –A coordinate phrase corresponds to an f-structure set (Bresnan/Kaplan/Peterson; Kaplan/Maxwell) –For unreduced, add alternative to other S expansions S --> { NP VP | … | S: ! $ ^; CONJ S: ! $ ^ }.

7. Coordinate reduction Also sets, but … must distribute external elements across all set members E.g. single SUBJ satisfies conjoined VPs: A girl [ VP saw Mary] and [ VP heard Bill]. VP --> { V NP … | VP: ! $ ^; CONJ VP: ! $ ^ }. How does SUBJ distribute without modifying normal SUBJ equation?

8. Distribution If ^ denotes an f-structure f, then (^ SUBJ)=! Holds iff f has an attribute SUBJ with value ! What if ^ denotes a set f? –Without further specification, (^ SUBJ)=! is false. –Distribution: a formal/theoretical extension: For any (distributive) property P and set s, P(s) holds iff P(f) holds for all f in s. (^ SUBJ)=! is a (distributive) property, so If ^=s= {f 1 f 2 } and !=g, then (s SUBJ)=g iff (f 1 SUBJ)=g and (f 2 SUBJ)=g

9. (s SUBJ)=g s g Note: For defining equations, distribution is equivalent to generalization (Kaplan & Maxwell); distribution is better for existentials

10. Further consequences

11. Where’s the conjunction? Lexical entry: and CONJ * (^ COORD)=and. VP -> VP: !$^; CONJ: !$^; VP: !$^. PRED see SUBJ girl COORD and SUBJ girl PRED hear SUBJ girl VP -> VP: !$^; CONJ: !=^; VP: !$^. PRED see SUBJ girl COORD and PRED hear SUBJ girl COORD and PRED see SUBJ girl COORD and PRED hear SUBJ girl COORD *and/or PRED smell SUBJ girl COORD *and/or see and hear or smell

12. Solution: Nondistributives Observe: Coordination itself has properties NUM, PERS, GEND of coordination different from any/all conjuncts [sg] and [sg] ⇒ [pl] [fem] & [masc] ⇒ [masc] Coordination f-structure is hybrid – Elements and attributes – Attributes declared in grammar configuration NONDISTRIBUTIVES NUM PERS GEND COORD. PRED see SUBJ girl COORD and PRED smell SUBJ girl COORD or PRED hear SUBJ girl

13. Nondistributives: NP example Mary I PRED 'Mary' NUM sg PERS 3 PRED 'I' NUM sg PERS 1 Mary and I PRED 'Mary' NUM sg PERS 3 PRED 'I' NUM sg PERS 1 NUM pl, PERS 1, COORD and

14. METARULEMACRO Right-hand side of each grammar rule is the result of applying the macro to the rule METARULEMACRO(_CAT _BASECAT _RHS) = _RHS.

15. Coordination without METARULEMACRO Want to coordinate any constituent Coordination macro (Same Category COORD) SCCOORD(_CAT) = [ _CAT: ! $ ^; COMMA]* _CAT: ! $ ^; CONJ _CAT: ! $ ^. Put invocation in each rule: NP: { (DET) AP* N PP* |@(SCCOORD NP)}. Engineering problem: –forget to invoke –put in wrong category

16. Coordination with METARULEMACRO Call SCCOORD as part of MRM METARULEMACRO(_CAT _BASECAT _RHS) = { _RHS | @(SCCOORD _CAT)}. Base NP rule: NP: (DET) AP* N PP*. Expanded: NP: { (DET) AP* N PP* |@(SCCOORD NP}. MRM = NP: { (DET) AP* N PP* | [ NP: ! $ ^; COMMA]* SCOORD NP: ! $ ^; CONJ NP: ! $ ^. } _CAT_RHS

17. Ambiguity with coordination Boys and girls jumped. 3 c-structures: NP coord, NPadj coord, N coord boysand girls NP NPadj N NP NPadj N NP boysand girls NPadj N N NP NPadj boysand girls NN NP NPadj N CCC

18. Solution, as before: PUSHUP If non-branching, push up to highest node. METARULEMACRO(_CAT _BASECAT _RHS) = { _RHS | _CAT: @PUSHUP }. Recall –Designator to test existence of sister nodes: * MOTHER SISTER PUSHUP = { (* MOTHER LEFT_SISTER) |(* MOTHER RIGHT_SISTER) ~(* MOTHER LEFT_SISTER) |~(* MOTHER MOTHER) }.

19. Different categories … Republican and proud of it. MCATS: Mixable categories MCATS = {VP S AP NP PP}. MCOORD = [ @MCATS: ! $ ^; COMMA]* @MCATS: ! $ ^; CONJ @MCATS: ! $ ^.

20. Functional Uncertainty Linguistic Issue: Long distance dependencies –Questions: Who do you think Mary saw? –Relative Clauses: The boy who I think Mary saw jumped. –Topicalization: The little boy, I think Mary saw.

21. The Problem What is Mary's within clause function or role –Mary, John saw. –Mary, John said Bill saw. –Mary, John said Bill claimed Henry saw. Mary is the argument/function of a distant predicate/clause. Not just any distant predicate though: –*Mary, John said the man who saw surprised Ken. (relative clause island) How to characterize such dependencies?

22. Phrase structure solutions: Guess a tree TG, GPSG, ATN, PATR, original LFG Link fronted phrase with trace/gap Infer role from trace position Node configuration gives island constraints

23. Example: Kaplan/Bresnan 82 NP Mary S' S NP John VP V saw NP:obj t TOPIC Mary1 PRED see TENSE past SUBJ John OBJ 1 M*   Long-distance path in c-str (M*) induces long-distance identity in f-str via c-str to f-str correspondence φ

24. Categorial generalizations? Perhaps: bad category mismatches –She'll grow that tall/*height. –She'll reach that height/*tall. –The girl wondered how tall she would grow/*reach. –The girl wondered what height she would reach/*grow. But these differ in function and control as well as category

25. Grow vs. Reach grow: (^ PRED)='grow ' (^ XCOMP SUBJ)=(^ SUBJ) reach: (^ PRED)='reach ' PRED 'grow ' SUBJ [ girl ] 1 XCOMP PRED 'tall ' SUBJ 1 PRED 'reach ' SUBJ [ girl ] OBJ [ height ]

26. But: some mismatches are required 1)He didn't think of that problem. (oblique NP) 2)He didn't think that he might be wrong. (S complement) 3)*He didn't think of that he might be wrong. (mismatch) 4)*That he might be wrong he didn't think. (match!) 5)That he might be wrong he didn't think of. (mismatch!) Simple functional account: –Think takes either of-oblique (1) or S complement (2) –Sentences cannot be PP objects in English (3) –English doesn't permit complement extraction (4) –But fronted S can be "linked" to oblique object (5)

27. Functional solution: guess a function Directly encode functional relations via f-str description language S' --> NP: (^ TOPIC)=! (^ TOPIC)=(^ OBJ); S NP Mary S' S NP John VP V saw TOPIC Mary1 PRED see TENSE past SUBJ John OBJ 1 

28. Problem: Infinite role uncertainty Infinite role uncertainty gives infinite disjunction –Mary, John saw. (^ TOPIC)=(^ OBJ) –Mary, John said Bill saw. (^ TOPIC)=(^ COMP OBJ) –Mary, John said Bill claimed Henry saw. (^ TOPIC)=(^ COMP COMP OBJ) –etc. Can't have direct functional encoding in a finite grammar.

29. Functional Uncertainty Extend description language to characterize, not enumerate, infinite role possibilities. Normal LFG function application (f s)=v iff f is an f-str, s is a symbol, and ∈ f Extended to strings: (f sy)=((f s) y) for sy a string of symbols (f  )=f (  denotes the empty string)

30. Extended to sets of strings (possibly infinite) (f  )=v iff (f x)=v for some string x in string-set  (choice of x gives uncertainty) If  is regular, can be defined by regular predicates (^ TOPIC)=(^ COMP* OBJ) hold iff one of (^ TOPIC)=(^ OBJ) (^ TOPIC)=(^ COMP OBJ) (^ TOPIC)=(^ COMP COMP OBJ)… holds. Regular predicates define accessibility and islands in functional terms.

31. Possible Paths The paths can be any of the regular expressions that are used for the c-structure (see the XLE documentation) Some common ones: Kleene * (^ XCOMP* OBJ)=! (0 or or more) Kleene + (^ COMP+ OBJ) = ! (1 or more) {} (^ { COMP | XCOMP } OBJ) =! (disjunction) These can be combined: –(^ { ACOMP | NCOMP }+ { SUBJ | OBL OBJ }) = !

32. Subcategorization Subcategorization eliminates possibilities Mary, he told/failed to stop. Topicalization uncertainty: (^ TOPIC)=(^ XCOMP* { SUBJ | OBJ }) Satisfactory uncertainty strings: intransitive stop: OBJ (only with told) transitive stop: XCOMP OBJ (only with failed)

33. Intransitive stop TOPIC [ Mary ] 1 SUBJ [ he ] PRED 'tell ' OBJ 1 XCOMP SUBJ 1 PRED 'stop ' TOPIC [ Mary ] 1 SUBJ [ he ] 2 PRED 'fail ' OBJ 1 XCOMP SUBJ 2 PRED 'stop ' TOPIC=OBJ: failed is Incoherent TOPIC=XCOMP OBJ: stop is Incoherent TOPIC=XCOMP SUBJ: Inconsistent TOPIC=OBJ “Mary he failed to stop.” “Mary he told to stop.”

34. Transitive stop TOPIC [ Mary ] 1 SUBJ [ he ] PRED 'tell ' OBJ [---]2 XCOMP SUBJ 2 PRED 'stop ' OBJ 1 TOPIC [ Mary ] 1 SUBJ [ he ] 2 PRED 'fail ' XCOMP SUBJ 2 PRED 'stop ' OBJ 1 TOPIC=XCOMP OBJ failed TOPIC=OBJ: stop is Incomplete TOPIC=XCOMP OBJ: told is Incomplete “Mary he failed to stop.” “Mary he told to stop.”

35. Uncertainty for English topics (^ TOPIC)=(^ {COMP|XCOMP}* [GF-COMP]) Topic clause can be OBJ but not COMP He didn't think of that problem. He didn't think that he might be wrong. *He didn't think of that he might be wrong. *That he might be wrong he didn't think. That he might be wrong he didn't think of.

36. No need for empty nodes S' --> NP: (^ TOPIC)=! (^ TOPIC)=(^ COMP* GF); S where GF={SUBJ|OBJ|OBJ2|OBL} VP --> V (NP: (^ OBJ)=!) … TOPIC Mary1 PRED see TENSE past SUBJ John OBJ 1  NP Mary S' S NP John VP V saw 

37. No empty nodes cont. Object NP is independently optional (for intransitives) Long-distance identity in f-structure is directly specified C-structure is closer to concrete phonology

38. Satisfiability Given a system of equations with functional uncertainty, there is an algorithm that: –determines if the system is satisfiable –finds all minimal solutions Problems: –Strings chosen from different uncertainties can interact –Infinite choices ==> Finite case analysis doesn’t work

39. Satisfiability example Which strings produce a satisfiable system? (f XCOMP* {SUBJ|OBJ})=c1 (f XCOMP* {SUBJ|OBJ|OBJ2})=c2 [c2≠c1] Satisfiability depends on the particular strings chosen –satisfiable: (f XCOMP SUBJ)=c1 (f OBJ)=c2 –not satisfiable: (f XCOMP SUBJ)=c1 (f XCOMP SUBJ)=c2

40. Satisfiability example cont. Solution: A finite characterization of dependencies: (f XCOMP*)=g ∧ (g {SUBJ|OBJ})= c1 ^ (g XCOMP+ {SUBJ|OBJ|OBJ2})=c2  (g XCOMP+ {SUBJ|OBJ}=c1 ^ (g {SUBJ|OBJ|OBJ2})=c2  (g SUBJ)=c1 ^ (g {OBJ|OBJ2})=c2  (g OBJ)=c1 ^ (g {SUBJ|OBJ2})=c2

41. Inside-out functional uncertainty Just saw "outside-in" for (f  )=v The uncertainty can be anchored on v and lead outside it to an enclosing f. (  g)=f iff (f  )=g for some f-structure f iff (f x)=g for some f-structure f and some string x in  Used for: –quantifier scope –anaphora –in-situ wh words

42. Inside-out FU example ((XCOMP* OBJ ^) SUBJ NUM)=sg SUBJ [NUM sg] XCOMP [XCOMP [OBJ ^ […] ]

43. Functional Uncertainty Summary Characterizes long-distance dependencies Basic form: (^ PATH GF)=… XLE implements both outside-in (typical) and inside-out functional uncertainty Functional uncertainty can be inefficient, especially when multiple uncertainties interact