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  1. Lexical-Functional Grammar A Formal System for Grammatical Representation Kaplan and Bresnan, 1982 Erin Fitzgerald NLP Reading Group October 18, 2006

  2. LFG History “Syntax is not just structure-based” • Developed by J. Bresnan and R. Kaplan in early 1970’s • Believed Chomskyan approach doesn’t model psychological reality of language • Other motivations: • Supported in wider variety of languages than other formalisms (ex nonconfigurational languages with ~free word order/ case marks) • Movement paradoxes: • That he was sick we talked about __ for days. • *We talked aboutthat he was sick for days. • We talked aboutthe factthat he was sick for days. Lexical-Functional Grammars

  3. How it’s different from Chomsky X’ • Requires a higher level of mathematical precision • Subject, Object, etc considered primitives, not defined from positions in tree • Empty categories and funct. projections avoided • No movement • Unification-based • Levels of representation not strictly derived from each other • Not assumed that phonological, etc contents are derived from syntactic structure in any way. Lexical-Functional Grammars

  4. How it’s different from HPSG • No hierarchical classification to deal with vertical and horizontal redundancy • LFG focuses on the processing and psychological reality of language • HPSG combines all syntactic, phonological, etc information into a single level Lexical-Functional Grammars

  5. Generative Power of LFG • Not as powerful as general rewriting system or Turing Machine (LF languages are context-sensitive) • But, greater generative capacity than CFG (lower bound) • Allows anbncn, ωω non-CF languages • Sources of generative power: • Functional Composition: Helps encode range of tree properties • Equality Predicate: Enforces a match between properties encoded from different nodes Lexical-Functional Grammars

  6. Correspondence Between Levels • C(onstituent)-structure: varies across languages • F(unctional)-structure: Universal properties • Structures aren’t isomorphic, but related by different correspondences semantic structure σ π φ ? δ string c-structure f-structure discourse structure Lexical-Functional Grammars

  7. C-Structure • Composed of • Terminal strings • Syntactic categories • Dominance/precedence relations • Expressed through phrase structure trees • Determined by CF phrase structure rules • Regulated by a version of X’ theory Lexical-Functional Grammars

  8. C-Structure S  NP VP(↑SUBJ)=↓ ↑=↓ NP  DET N VP  V NP NP(↑OBJ)=↓ (↑OBJ2)=↓ i.e. head S NP VP DET N V NP NP Set specifiers: S  S CONJ S↓є↑ ↓є↑ Adjuncts also use set indicators DET N DET N a girl handed the baby a toy Immediate Domination Metavariables: ↑: mother f-structure ↓: self f-structure Lexical-Functional Grammars

  9. F-structure • Composed of • Grammatical function names • Semantic forms • Feature symbols • Models internal structure of language where grammatical relations are represented • Formalized through matrix of attributes, viewable as mathematical function • Lexical schemata determine content of lexical items Lexical-Functional Grammars

  10. F-structure Lexical-Functional Grammars

  11. F-structure: Attributes and Values Lexical-Functional Grammars

  12. F-structure: Attributes and Values Lexical-Functional Grammars

  13. F-structure: Primitives Symbols Semantic Forms Embedded Structures Lexical-Functional Grammars

  14. F-structure: Input to Semantic Interp Agent Theme Goal Lexical-Functional Grammars

  15. C-Structure to F-Description S  NP VP(↑SUBJ)=↓ ↑=↓ NP  DET N VP  V NP NP(↑OBJ)=↓ (↑OBJ2)=↓ S NP VP DET N V NP NP a: DET,(↑SPEC) = A girl: N,(↑NUM) = SG (↑NUM) = SG DET N DET N (↑PRED) = ‘GIRL’ a girl handed the baby a toy Lexical-Functional Grammars

  16. C-Structure to F-Description S (f1 SUBJ) = f2 f1= f3 f1 NP; (↑SUBJ)=↓ VP; ↑=↓ f2 f3 (↑NUM) = SG(↑PRED) = ‘GIRL’ N (↑TENSE) = PAST(↑PRED) = ‘HAND<>’ V (↑OBJ) = ↓ NP (↑OBJ) = ↓ NP (↑SPEC) = A(↑NUM) = SG DET f4 f5 (f3 TENSE) = past Etc. (↑SPEC) = ↓ DET (↑NUM) = SG(↑PRED) = BABY N (↑SPEC) = ↓(↑NUM) = SG DET (↑NUM) = SG(↑PRED) = TOY N (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ toy a girl handed the baby a Lexical-Functional Grammars

  17. F-Description to F-Structure • Locate Operator • Obtain value for designator • Merge Operator (*Unify*) • If left and right values exist,check if values are equal • Else, create new entity(if properties are compatible) • Similar to taking the union oftwo sets (if conflicts don’t exist) • Start clean; build until full f-description analyzed f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) = ‘HAND<>’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ Lexical-Functional Grammars

  18. F-structure f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) = ‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ f1 Lexical-Functional Grammars

  19. F-structure: equations f2 f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) = ‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ f1 f3 Lexical-Functional Grammars

  20. F-structure: equations f2 f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) = ‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ f4 f1 f3 Lexical-Functional Grammars

  21. F-structure: equations f2 f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) = ‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ f4 f5 f1 f3 Lexical-Functional Grammars

  22. F-structure: lexically derived eqns f2 f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) = ‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ f4 f5 f1 f3 Lexical-Functional Grammars

  23. F-structure: lexically derived eqns f2 f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) = ‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ MERGECONFIRMED f4 f5 f1 f3 Lexical-Functional Grammars

  24. F-structure: lexically derived eqns f2 f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) = ‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ f4 f5 f1 f3 Lexical-Functional Grammars

  25. F-structure: lexically derived eqns f2 f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) = ‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ f4 f5 f1 f3 Lexical-Functional Grammars

  26. F-structure: lexically derived eqns f2 f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) = ‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ f4 f5 f1 f3 MERGECONFIRMED Lexical-Functional Grammars

  27. F-structure: lexically derived eqns f2 f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) = ‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ f4 f5 f1 Lexical-Functional Grammars

  28. F-structure: lexically derived eqns f2 f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) =‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ f4 f5 f1 Lexical-Functional Grammars

  29. A Unique Solution? f2 f1= f3(f1 SUBJ) = f2(f3 OBJ) = f4(f3 OBJ2) = f5 (f2 SPEC) = A(f2 NUM) = SG (f2 NUM) = SG(f2 PRED) = ‘GIRL’ (f3 TENSE) = PAST(f3 PRED) =‘HAND...’ (f4 SPEC) = THE (f4 NUM) = SG(f4 PRED) = ‘BABY’ (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = SG(f5 PRED) = ‘TOY’ f4 f5 f1 Prefer minimal solution Lexical-Functional Grammars

  30. Principles Regulating F-Structures • Uniqueness: • Every attribute has a unique value • Completeness: • Every function designated by a PRED must be present in the f-structure of that PRED • Coherence: (converse) • Every argument in an f-structure must be designated by a PRED A string is grammatical only if it is assigned a complete and coherent f-structure, and its f-struct is consistent and determinate. Lexical-Functional Grammars

  31. Principles Regulating F-Structures • Uniqueness: • Every attribute has a unique value • Note: Uniqueness doesn’t prevent different attributes from sharing values A girl handed the baby a toys. (f5 SPEC) = A(f5 NUM) = SG (f5 NUM) = PL(f5 PRED) = ‘TOYS’ Lexical-Functional Grammars

  32. Principles Regulating F-Structures • Completeness: • Every function designated by a PRED must be present in the f-structure of that PRED An f-structure is locally complete iff it contains all governable grammatical functions that its predicate governs. A girl handed. PRED ‘HAND<(↑ SUBJ)(↑ OBJ2)(↑ OBJ)>’ Lexical item requires governed functions OBJ and OBJ2 Lexical-Functional Grammars

  33. Principles Regulating F-Structures • Coherence: • Every argument in an f-structure must be designated by a PRED An f-structure is locally coherent iff all governable functions are governed. The girl fell the apple the dog. PRED ‘FELL<(↑ SUBJ)>’ Lexical-Functional Grammars

  34. Principles Regulating F-Structures • Uniqueness: • Every attribute has a unique value • Completeness: • Every function designated by a PRED must be present in the f-structure of that PRED • Coherence: (converse) • Every argument in an f-structure must be designated by a PRED A string is grammatical only if it is assigned a complete and coherent f-structure, and its f-struct is consistent and determinate. Exception: Adjunct grammatical functions are not specified in PRED and no reqmt of mutual syntactic compatibility, so excluded from Uniqueness and Coherence Conditions Lexical-Functional Grammars

  35. Changing structure, but not meaning VP  V NP NP PP*(↑OBJ)=↓ (↑OBJ2)=↓ (↑(↓PCASE))=↓ PP  P NP (↑OBJ)=↓ NP  DET N S  NP VP(↑SUBJ)=↓ ↑=↓ S NP VP DET N V NP PP DET N P NP DET N a girl handed a toy to the baby Lexical-Functional Grammars

  36. Changing structure, but not meaning Dativizing Rule: (↑OBJ2)  (↑ OBJ) (↑ OBJ)  (↑ TO OBJ) From (↑(↓PCASE))=↓ THE SG SG ‘BABY’ Lexical-Functional Grammars

  37. Defining vs. Constraining Schema • Consider: • The girl is handing the baby the toy. • *The girl is hands the baby the toy. VP  V NP NP PP* VP’(↑OBJ)=↓ (↑OBJ2)=↓ (↑(↓PCASE))=↓ (↑VCOMP)=↓ VP’  (to) VP ↑=↓ is: V, (↑ TENSE) = PRESENT (↑ SUBJ NUM) = SG (↑ PRED) = ‘PROG<(↑ VCOMP)>’ (↑ VCOMP PARTICIPLE) = PRESENT (↑ VCOMP SUBJ) = (↑ SUBJ) Single, progressive arg Functional control (↑ VCOMP PARTICIPLE) =c PRESENT Lexical-Functional Grammars Constraint Schema

  38. Raising Verbs • The girl persuaded the baby to go. • The girl persuaded the baby that the baby (should) go. • Link via co-indexing, or arguments assumed distinct VP  V NP NP PP* VP’(↑OBJ)=↓ (↑OBJ2)=↓ (↑(↓PCASE))=↓ (↑VCOMP)=↓ VP’  to VP(↑TO) = ↓ ↑=↓(↑INF)= ↓ ↑=↓ persuaded: V, (↑ TENSE) = PAST (↑ PRED) = ‘PERSUADE<(↑SUBJ)(↑OBJ)(↑VCOMP)>’ (↑ VCOMP TO) =c + (↑ VCOMP SUBJ) = (↑ OBJ) Lexical-Functional Grammars

  39. Raising Verbs • The girl promised the baby to go. • The girl promised the baby that the girl (should) go. VP  V NP NP PP* VP’(↑OBJ)=↓ (↑OBJ2)=↓ (↑(↓PCASE))=↓ (↑VCOMP)=↓ VP’  to VP(↑TO) = ↓ ↑=↓(↑INF)= ↓ ↑=↓ promised: V, (↑ TENSE) = PAST (↑ PRED) = ‘PERSUADE<(↑SUBJ)(↑OBJ)(↑VCOMP)>’ (↑ VCOMP TO) =c + (↑ VCOMP SUBJ) = (↑ SUBJ) Lexical-Functional Grammars

  40. Raising Verbs: Passivization • The baby was persuaded to go by the girl. • *The baby was promised to go by the girl. persuaded: V, promised: V, (↑ PARTICLE) = PASSIVE (↑ PRED) = ‘PERSUADE<(↑BY OBJ)(↑SUBJ)(↑VCOMP)>’ (↑ VCOMP TO) =c + (↑ VCOMP SUBJ) = (↑ SUBJ) (↑ PARTICLE) = PASSIVE (↑ PRED) = ‘PROMISE<(↑BY OBJ)(↑SUBJ)(↑VCOMP)>’ (↑ VCOMP TO) =c + (↑ VCOMP SUBJ) = (↑ BY OBJ) Doesn’t conform to Fn Control Restrictions Lexical-Functional Grammars

  41. F-Level Distinct from Semantics • No quantifier or VP scope specification • Raising vs. Equi Verbs (All have semantic role) • The girl persuaded the baby to go. • The girl expected the baby to go. Same f-structure, very different semantics Lexical-Functional Grammars

  42. Long Distance Dependencies • The girl wondered [who the baby saw __]. • Instance of constituent control • Decompose into chain of functional identities Lexical-Functional Grammars

  43. Bound Domination Metavariables • Aim to provide a formal mechanism to represent long-dist constituent dependencies • No unmotivated grammatical functions or features • Allow unbounded # of controllees for single constituent • Succinctly show generalizations Lexical-Functional Grammars

  44. C-Structure for Long-Distance Dependencies Bounded Domination Metavariables: ▲: bounded above (longer path) ▼: bounding node (↑SCOMP)=↓ S’ f1 (↑Q-FOCUS)=↓↓=▼NP ↑=↓S (↑PRED) = WHO N (↑OBJ) = ↓ NP ↑= ↓ VP (↑SPEC) = ↓ DET (↑NUM) = SG(↑PRED) = BABY N (↑TENSE) = PAST(↑PRED) = ‘SEE<>’ V (↑OBJ) = ↓ NP ↑=▲ NP who the baby saw e Lexical-Functional Grammars

  45. More Precisely • She’ll grow that tall/*height. • She’ll reach that *tall/height. • The girl wondered how tall she would grow/*reach ___. • The girl wondered what height she would *grow/reach ___. • These examples show that some bounding should be further constrained to specify POS Follow by AP Follow by NP (e: ↓=▼AP) (e: ↓=▼NP) Lexical-Functional Grammars

  46. Thanks!

  47. More (unfinished) slides Lexical-Functional Grammars

  48. Bounding Convention • A node M belongs to a control domain with root node R iff R dominates M and there are no bounding nodes on the path from M up to but not including R • Pg 245 Lexical-Functional Grammars

  49. Unification with Complex Expressions • See packet pg 10/22 • Outside-in • Combine feature structures at their roots and work top-down • Inside-out • Begin with two distinct f-structs sharing a substructure, and recursively combine up • Req’d for analyses like topicalization and anaphoric binding Lexical-Functional Grammars

  50. Subject-Auxiliary Inversion in LFG • Pg 228 • A girl is handing the baby a toy. • Is a girl handing the baby a toy? • *Is a girl is handing the baby a toy. • Prevented by “distinctiveness of semantic form instances” Lexical-Functional Grammars