1 / 52

Lexical-Functional Grammar

Lexical-Functional Grammar. A Formal System for Grammatical Representation Kaplan and Bresnan, 1982 Erin Fitzgerald NLP Reading Group October 18, 2006. LFG History. “Syntax is not just structure-based”. Developed by J. Bresnan and R. Kaplan in early 1970’s

xenos
Télécharger la présentation

Lexical-Functional Grammar

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related