Lexical-Functional Grammar & Flexible Composition Ash Asudeh - PowerPoint PPT Presentation

Lexical-Functional Grammar & Flexible Composition Ash Asudeh Oxford University & Carleton University

Goals • Provide an overview of Lexical-Functional Grammar • Provide an overview of Glue Semantics • Provide an introduction to an approach to argument structure that builds on these two theories, part of what I call Flexible Composition

Lexical-Functional Grammar

History • LFG was developed by Joan Bresnan, a syntactician, and Ron Kaplan, a social psychologist by training but then a computational linguist, as a constraint-based/declarative alternative to transformational/procedural theories of the time. • Desiderata: • Formal precision • Psychological plausibility • Computational tractability

Overview • At the heart of LFG remain its two syntactic structures: • C(onstituent)-structure • ‘Concrete syntax’: Precedence, dominance, constituency • F(unctional)-structure • ‘Abstract syntax’: Morphosyntactic features, grammatical functions, predication, subcategorization, local dependencies (agreement, control, raising), unbounded dependencies, anaphoric syntax (binding)

The ɸ correspondence function • Elements of the c-structure are mapped to (put into correspondence with) elements of the f-structure by the ɸ correspondence function (sometimes called a projection function ). • This is accomplished by adding functional descriptions to the nodes in the c-structure tree. • These equations use the ↑ (“up arrow”) and ↓ (“down arrow”) metavariables. • A ↑ on a c-structure node n refers to the f-structure of the (c-structure) mother of n . • A ↓ on a c-structure node n refers to the f-structure of node n. • Examples: • ↑ = ↓ on n means that n and n ’s mother map to the same f-structure. • ( ↑ SUBJECT ) = ↓ on n means that the f-structure of n is the value of the SUBJECT attribute in the f-structure of n ’s mother.

Example: 
 That kid is eating cake Lexical entries C-structure IP that , D 0 ( ↑ DEFINITE ) = + ( ↑ SUBJ ) = ↓ ( ↑ DEIXIS ) = DISTAL ↑ = ↓ ( ↑ NUMBER ) = SG DP I ′ ( ↑ PERSON ) = 3 ↑ = ↓ ↑ = ↓ ↑ = ↓ kid , N 0 ( ↑ PRED ) = ‘kid’ I 0 D ′ VP ( ↑ NUMBER ) = SG ( ↑ PERSON ) = 3 is ↑ = ↓ ↑ = ↓ ↑ = ↓ D 0 NP V ′ is , I 0 ( ↑ SUBJ NUMBER ) = SG ( ↑ SUBJ PERSON ) = 3 That ( ↑ OBJ ) = ↓ ↑ = ↓ ↑ = ↓ ( ↑ TENSE ) = PRESENT N 0 V 0 DP ( ↑ PARTICIPLE ) = c PRESENT eating , V 0 kid eating ( ↑ PRED ) = ‘eat ⟨ SUBJ , OBJ ⟩ ’ ↑ = ↓ ( ↑ ASPECT ) = PROGRESSIVE NP ( ↑ PARTICIPLE ) = PRESENT ↑ = ↓ cake , N 0 ( ↑ PRED ) = ‘cake’ N 0 ( ↑ NUMBER ) = SG ( ↑ PERSON ) = 3 cake e metavariables are instantiated as follows. Each

Example: 
 That kid is eating cake (66) IP 1   ‘eat ⟨ SUBJ , OBJ ⟩ ’ PRED     ‘kid’ PRED ( f 1 SUBJ ) = f 2 f 1 = f 7 f 1 f 2     I ′ DP 2 DEIXIS DISTAL f 7 f 3     7     + f 8 f 4 DEFINITE  SUBJ        f 9 f 5 f 2 = f 3 f 7 = f 8 f 7 = f 9     NUMBER SG     I 0 f 6 D ′ VP 9 f 10   3 PERSON 3 8   f 11       ‘cake’ f 12 PRED f 3 = f 4 f 3 = f 5 is f 9 = f 10     f 13 OBJ  NUMBER SG  D 0 NP 5 V ′     4 10   f 14 3  PERSON      That f 5 = f 6 f 10 = f 11 ( f 10 OBJ ) = f 12 TENSE PRESENT   N 0 V 0   DP 12 ASPECT PROGRESSIVE   6 11   PARTICIPLE PRESENT kid eating f 12 = f 13 NP 13 f 13 = f 14 N 0 14 cake

Flexibility in mapping Finnish Common (subsumptive) f-structure English IP IP   ‘drink ⟨ SUBJ , OBJ ⟩ ’ PRED I ′ I ′ DP  TENSE PAST        ‘pro’ PRED   VP I 0 VP   I 1  SUBJ  PERSON       V ′   Joi- n V ′ � NUMBER SG         ‘water’ PRED DP V 0 DP     3 OBJ PERSON         vett¨ a drank NUMBER SG water

Example: the book that she likes C-structure rules C-structure and corresponding f-structure D 0 ) ) a. DP − NP → f DP ↑ = ↓ ↑ = ↓ ADJ � = ¯ � = ¯ b. NP − NP CP → D 0 NP f ↑ = ↓ ↓ ∈ ( ↑  ) ¯ Î ( � ADJ) the � = ¯ NP CP N ′ c. NP − → ↑ = ↓ � = ¯ that she likes N d. N ′ − N 0 → � = ¯ ↑ = ↓ N 0 book

Example: the book that she likes Lexical entries C-structure with lexical information and instantiated f-structure she , D 0 ) ( ↑  ) = ‘pro’ DP f 1 ( ↑  ) =  ‘book’ PRED ( ↑  ) =  f 1 NUM SG f 2 ( ↑  ) =  f 1 = f 2 f 1 = f 3 + DEF f 3 D 0 f 2 NP f 3 ) likes , V 0 ( ↑  ) = ‘like ⟨  ,  ⟩ ’ f 4 ‘the’ PRED SPEC f 5 ( ↑  ) =  the f 3 = f 4 f 7 Î (f 3 ADJ ) f 6 f 7 ... ADJ ( ↑   ) =  (f 2 SPEC PRED ) = ‘the’ NP f 4 CP f 7 (f 2 def ) = + ( ↑   ) =  f 4 = f 5 the , D 0 ) ( ↑   ) = ‘the’ N ¢ f 5 that she likes ( ↑  ) = + ) book , N 0 ( ↑  ) = ‘book’ f 5 = f 6 N 0 f 6 ( ↑  ) =  book (f 6 PRED ) = ‘book’ (f 6 NUM ) = SG

Example: the book that she likes Penultimate f-structure ‘book’ PRED NUM SG + DEF ‘the’ SPEC PRED ‘like’ PRED Notes: 
 b 1. I often adopt the practice ‘pro’ PRED of labelling f-structures mnemonically with the first 3 PERS p l letter of the PRED value. 
 ADJ SUBJ NU M SG 2. I often leave the subcategorization out of the GEND FEM PRED. (There’s a principled reason for this; we can TENSE PRES discuss it in question time.)

General wellformedness constraints on f-structures • Completeness 
 All subcategorized grammatical functions in a PRED feature must be present in the f-structure. • Coherence 
 All grammatical functions that are present in the f- structure must be subcategorized by a PRED feature. • Consistency (a.k.a. Uniqueness ) 
 Each f-structure attribute has one value.

Example: 
 Violations of Completeness , Coherence , Consistency Completeness Coherence Consistency " # ) NUM SG ‘like SUBJ , OBJ ’ ‘like SUBJ , OBJ ’ PRED PRED NUM PL SUBJ SUBJ 2 3 h i OBJ ‘hello’ SUBJ PRED 6 7 h i 4 5 ‘world’ PRED SUBJ OBL

Example: the book that she likes Penultimate f-structure ‘book’ PRED NUM SG + DEF ‘the’ SPEC PRED Not complete: 
 ‘like’ OBJ of ‘like’ missing PRED b ‘pro’ PRED 3 PERS p l ADJ SUBJ NU M SG GEND FEM TENSE PRES


 Unbounded dependencies • Extended Coherence Condition 
 ( ↑ UDFPATH ) = ( ↑ COMP ∗ GF ) An UNBOUNDED DEPENDENCY FUNCTION ( UDF ) must be linked (1) Who did you see? to the semantic predicate argument structure of the (2) Who did Kim say that you saw? sentence in which it occurs, (3) Who did Kim claim that Sandy either by functionally or by alleged that you saw? anaphorically binding an argument. 
 C ′ CP − → { XP } | Â ( ↑  ) = ↓ ( ↑   ) = ‘pro’ ↑ = ↓ ( ↑  ) = ( ↑  P  ) ( ↑  ) = ( ↑  P  )

Example: the book that she likes Final f-structure ‘book’ PRED NUM SG + DEF ‘the’ SPEC PRED ‘like’ PRED p1 PRED ‘pro’ UDF b ‘pro’ PRED 3 PERS l ADJ p2 SUBJ NUM SG GEND FEM OBJ TENSE PRES

Language as a form–meaning mapping: The Correspondence Architecture G = w o i o s o l o a o r o m o p f ψ Form Meanin g m r p a s i w l phonological morphological prosodic constituent argument functional semantic information model string structure structure structure structure structure structure structure

Templates: 
 Generalizations over named descriptions • An LFG template is nothing more than a named functional description (i.e., a set of equations that describe linguistic structures). • For any LFG grammar defined in terms of templates, we could construct a completely equivalent grammar which does not use templates, simply by replacing each template with the description that it abbreviates. • The same grammatical descriptions would be associated with words and phrases in each of the two grammars, and the grammars would produce the same c-structures and f-structures for the words and phrases of the language. • However, the grammar without templates would lack the means of expressing generalizations across lexical entries and grammar rules which templates make available. • In sum: • Templates name LFG grammatical descriptions such that the same description can be used in different parts of the grammar. • The semantics of template calling/invocation is just substitution: The grammatical description that the template names is substituted where the template is called.