The Formal Architecture of. Lexical-Functional Grammar. Ronald M. Kaplan and Mary Dalrymple

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1 The Formal Architecture of Lexical-Functional Grammar Ronald M. Kaplan and Mary Dalrymple Xerox Palo Alto Research Center 1. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

2 Architectural Issues Representation: Formal encoding of linguistic dependencies Modularity: Factoring independent generalizations Mathematical tractability: Provable mathematical properties Implementability: Transparent, efficient computation 2. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

3 LFG: Formal Concepts Structure Structural Description Structural Correspondence (Projection) Architectural themes: Importance of partial specification Factor generalizations on related but dissimilar representations 3. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

4 Variation in External Structure The small children are chasing the dog. English: S S Japanese: VP V DET Adj N V N P Adj N P oikaketa chase The small children V V Det N inu dog o ACC tiisai small kodomotati children ga NOM are chasing the dog Warlpiri: S Aux V N kapala Pres N wajilipinyi chase N kurdujarrarlu children maliki dog witajarrarlu small 4. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

5 Invariance in Internal Structure The small children are chasing the dog. Common f-structure for English, Japanese, and Warlpiri: PRED chase PRED children SPEC the SUBJ MODS PRED small OBJ PRED dog SPEC the 5. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

6 Structure = Set + Relations + Properties Examples: Strings A. B. C W = Set of words < W W precedence Trees A E B C D N = Set of nodes M: N N mother function < N N precedence λ : N L label function F-Structures Q R S T U V W S = Set of symbols F = S + (S f F) hierarchical finite functions (f s): F S F function application (Kaplan, 1975) 6. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

7 Structures can be described by their properties and relations Structure Description n 2 He S n 1 M(n 2 )=n 1 VP n 3 V n 4 saw n 5 it λ(n 1 )=S λ(n 2 )= M(n 3 )=n 1 λ(n 3 )=VP n 2 <n f1 Subj Pred f2 Pred ball Num Sg fell (f 1 Subj)=f 2 (f 2 Pred)=ball (f 2 Num)=Sg (f 1 Pred)=fell 7. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

8 Description language: Formal expressions that structures may satisfy Trees: 1. Boolean combinations of primitive descriptors M(n 1 )=n 2 M(n 2 )=n 3 n 2 =n 3 2. Context-free rewriting rules (node admissibility) S VP Det N F-structures: Boolean combinations of primitive equalities [(f 1 Num)=SG (f 2 Num)=Pl] (f 3 Subj)=f 1 Choose language for convenience: expressive power, solvability 8. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

9 Satisfiability of Equality Constraints Conjunctions of equalities (and disequalities) (f 1 SUBJ)=f 2 (f 2 NUM)=SG f 1 =f 3 (f 3 NUM)=PL Solvable by Rewriting Unification Deductive closure + Any other methods for Quantifier-free equality theory Disjunctions of constraints Convert to Disjunctive Normal Form, then use Conjunctive Method (f 1 SUBJ)=f 2 (f 1 SUBJ)=f 2 (f 1 SUBJ)=f 2 [(f 2 NUM)=SG (f 2 PERS)=3] f 1 =f 3 (f 2 NUM)=SG f 1 =f 3 (f 2 PERS)=3 f 1 =f 3 (f 3 NUM)=PL (f 3 NUM)=PL (f 3 NUM)=PL 9. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

10 Structures of different types may be set in correspondence by element-wise functions φ: N F S n 1 SUBJ f2 PRED girl NUM SG n 2 VP n 3 f1 PRED OBJ see f5... V n 4 n 5 Descriptions of range can then be stated in terms of domain relations (f 1 SUBJ)=f 2 (φmn 2 SUBJ)=φn 2 since f 1 =φn 1 =φmn 2 (f 2 NUM)=SG (φn 2 NUM)=SG (f 1 OBJ)=f 5 (φmmn 5 OBJ)=φn 5? Correspondences transfer constraints 10. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

11 A correspondence can be many-to-one φ S n 1 SUBJ f2 PRED girl NUM SG n 2 VP n 3 f1 f3 f4 PRED OBJ see f5... V n 4 n 5 F-structure elements represent information mutually shared by nodes. Gives formal account of : head-of-construction discontinuous "constituents" (e.g Dutch) (functional information distributed in string) 11. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

12 A correspondence need not be onto φ S SUBJ PRED PRO V VP VP V surprised N SUBJ PRED TENSE OBJ PRED SEE<...> OBJ PRED ME SURPRISE<...> PAST PRED MARY Seeing N me Mary No dummy Gives formal account of null/zero anaphors (e.g. English gerunds, Japanese "pro-drop") 12. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

13 LFG Summary (Kaplan & Bresnan, 1982) 1. Structures of different formal types: Trees represent constituent structure Indicate surface phrase configurations Concrete: No empty nodes F-structures represent abstract syntactic dependencies Grammatical relations Agreement 2. A correspondence φ maps c-structure nodes to f-structure units 3. φ is many-to-one (heads, discontinuous constituents, control) but not onto (null anaphors). 4. Phrase-structure constraints describe c-structure. 5. F-structure description comes from c-structure properties via φ. 13. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

14 C-Structure constraints play 2 roles (1) Determine acceptable trees (as usual): Given the rule S VP, S VP is an allowable configuration of nodes 14. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

15 (2) Analyze tree relations to generate f-structure description Match tree against annotated rules: (Description by Analysis) S (φ(m(n)) SUBJ)=φ(n) VP φ(m(n))=φ(n) where n denotes the matching node S n 1 n VP 2 n 3 S (φ(m(n)) SUBJ)=φ(n) VP φ(m(n))=φ(n) Yields (φ(m(n 2 )) SUBJ)=φ(n 2 ) φ(m(n 3 )=φ(n 3 ) Simplify to familiar LFG notation: Define φ(m(n)), φ(n) Then S ( SUBJ)= VP = 15. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

16 Extensions and Applications To Structural Domains Symbol subsumption: lexical generalizations Sets and generalization: coordination To Correspondence Configuration Multiple correspondences: syntax, semantics, discourse, translation Codescription, Inverse description To Description Languages Regular predicates for C-structure rules: ID/LP Functional Uncertainty: long-distance dependencies quantifier scope, anaphora Functional precedence: anaphora, loose order Restriction: manipulation of substructure 16. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

17 Extensions to the Structural Domain Subsumption of symbols: Underspecification Original LFG: Symbols only have identity property Distinct symbols are not equal (SUBJ OBJ) Lexical redundancy rules for passives, datives, etc. SUBJ OBL-AG (passive) OBJ SUBJ Bresnan & Kanerva (1989): Underspecification Lexical items marked with generalized grammatical functions [ r]=subj, OBJ [+r]=obj θ, OBL θ [ o]=subj, OBL θ [+o]=obj, OBJ θ Subsumption lattice: OBJ SUBJ OBL θ [ r] [ o] Basic principles predict correct instantiation: Subject required, function-argument biuniqueness 17. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

18 Sets in the F-Structure domain Original LFG: Sets represent non-unique adjuncts and modifiers: { [big] [tall] [green] } Description language augmented with : ( ADJ) Bresnan/Kaplan/Peterson: A coordinate phrase corresponds to an f-structure set For constituent coordination, add simple alternative to other rules: S S CONJ S φ S...saw... S CONJ and S...heard... PRED see<girl, Mary> SUBJ girl OBJ Mary PRED heard<girl, Bill> SUBJ girl OBJ Bill 18. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

19 Sets as Functions (Kaplan/Maxwell 1988) Original (LFG) function application: (f a) =v iff f is an f-structure, a is a symbol, and <a,v> f (s a) undefined if s is a set of f-structures. Extend to sets of f-structures via generalization: (s a)= f s (f a) if s is a set of f-structures, Generalization: where is the generalization operator on f-structures f 1 f 2 f 1 if f 1 =f 2 {<a, (f 1 a) (f 2 a)> a DOM(f 1 ) DOM(f 2 )} if f 1 and f 2 are f-structures otherwise f 1 f 2 subsumes both f 1 and f 2 --it s the greatest lower bound. f 1 f 2 has all/only the common attribute-value pairs of f 1 and f Kaplan and Dalrymple, ESSLLI 1995, Barcelona

20 Multiple correspondences/projections relate independently motivated structures (Halvorsen/Kaplan 1988) Constituent structure: Phrase order, grouping Functional structure: Syntactic dependencies (agreement, case) Semantic structure: Truth and entailment Discourse structure: Topic/focus etc. Structures may not be isomorphic, but are related by different correspondences (e. g. φ, σ, δ...) Form Meaning semantic structure π φ σ?.... string c-structure f-structure δ discourse structure 20. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

21 Example: Coordination in Functional and Semantic Structures C-Structure F-Structure S-Structure φ σ S VP PRED SUBJ jump they REL ARG1 and REL ARG1 jump they N They V V CONJ V PRED SUBJ swim ARG2 REL ARG1 swim they jump and swim groups distributes organizes 21. Kaplan and Dalrymple, ESSLLI 1995, Barcelona

22 Modes of description for abstract correspondences Co-description: Uses composition of correspondences σ = σ(φ(m(*))) = [σ o φ](*) Semantic and functional descriptions generated in the same analysis of the c-structure. Description-by-analysis: Analyze one structure to produce the description of another Recursion/analysis of tree gives function description. Separate recursion/analysis of f-structure gives semantic description. In effect, quantification over f-structure: For all f-structures f, if (f SUBJ)=g, then (σf ARG1)=σg 22. Kaplan and Dalrymple, ESSLLI 1995, Barcelona