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Lexical-Functional Grammar,A Formal System for Grammatical Representation Kaplan and Bresnan, 1982 Erin Fitzgerald NLP Reading Group October 18, 2006,10/18/2006,Lexical-Functional Grammars,LFG History,Developed by J. Bresnan and R. Kaplan in early 1970s Believed Chomskyan approach doesnt 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 about that he was sick for days. We talked about the fact that he was sick for days.,“Syntax is not just structure-based”,10/18/2006,Lexical-Functional Grammars,How its 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.,10/18/2006,Lexical-Functional Grammars,How its 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,10/18/2006,Lexical-Functional Grammars,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, 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,10/18/2006,Lexical-Functional Grammars,Correspondence Between Levels,C(onstituent)-structure: varies across languages F(unctional)-structure: Universal properties Structures arent isomorphic, but related by different correspondences,string,c-structure,f-structure,discourse structure,semantic structure,?,10/18/2006,Lexical-Functional Grammars,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,10/18/2006,Lexical-Functional Grammars,C-Structure,S,NP,VP,DET,N,NP,V,N,DET,DET,N,NP,a,girl,handed,the,baby,a,toy,S NP VP (SUBJ)= = NP DET N VP V NP NP (OBJ)= (OBJ2)=,Immediate Domination Metavariables: : mother f-structure : self f-structure,i.e. head,Set specifiers: S S CONJ S Adjuncts also use set indicators,10/18/2006,Lexical-Functional Grammars,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,10/18/2006,Lexical-Functional Grammars,F-structure,10/18/2006,Lexical-Functional Grammars,F-structure: Attributes and Values,10/18/2006,Lexical-Functional Grammars,F-structure: Attributes and Values,10/18/2006,Lexical-Functional Grammars,F-structure: Primitives,Symbols,Semantic Forms,Embedded Structures,10/18/2006,Lexical-Functional Grammars,F-structure: Input to Semantic Interp,Agent,Theme,Goal,10/18/2006,Lexical-Functional Grammars,C-Structure to F-Description,S,NP,VP,DET,N,NP,V,N,DET,DET,N,NP,a,girl,handed,the,baby,a,toy,S NP VP (SUBJ)= = NP DET N VP V NP NP (OBJ)= (OBJ2)=,a: DET, (SPEC) = A girl: N, (NUM) = SG,(NUM) = SG,(PRED) = GIRL,10/18/2006,Lexical-Functional Grammars,C-Structure to F-Description,S,the,baby,a,toy,NP; (SUBJ)=,VP; =,(OBJ) = NP,(NUM) = SG (PRED) = GIRL N,(TENSE) = PAST (PRED) = HAND V,(SPEC) = A (NUM) = SG DET,(OBJ) = NP,(SPEC) = DET,(NUM) = SG (PRED) = BABY N,(SPEC) = (NUM) = SG DET,(NUM) = SG (PRED) = TOY N,a,girl,handed,f1,f2,f4,f5,f3,(f4 SPEC) = THE (f4 NUM) = SG (f4 PRED) = BABY,(f3 TENSE) = past,(f2 SPEC) = A (f2 NUM) = SG (f2 NUM) = SG (f2 PRED) = GIRL,Etc.,f1= f3,(f1 SUBJ) = f2,10/18/2006,Lexical-Functional Grammars,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 of two sets (if conflicts dont 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,10/18/2006,Lexical-Functional Grammars,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,f1,10/18/2006,Lexical-Functional Grammars,F-structure: equations,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,f2,10/18/2006,Lexical-Functional Grammars,F-structure: equations,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,f2,f4,10/18/2006,Lexical-Functional Grammars,F-structure: equations,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,f2,f4,f5,10/18/2006,Lexical-Functional Grammars,F-structure: lexically derived eqns,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,f2,f4,f5,10/18/2006,Lexical-Functional Grammars,F-structure: lexically derived eqns,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,f2,f4,f5,MERGE CONFIRMED,10/18/2006,Lexical-Functional Grammars,F-structure: lexically derived eqns,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,f2,f4,f5,10/18/2006,Lexical-Functional Grammars,F-structure: lexically derived eqns,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,f2,f4,f5,10/18/2006,Lexical-Functional Grammars,F-structure: lexically derived eqns,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,f2,f4,f5,MERGE CONFIRMED,10/18/2006,Lexical-Functional Grammars,F-structure: lexically derived eqns,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,f2,f4,f5,10/18/2006,Lexical-Functional Grammars,F-structure: lexically derived eqns,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,f2,f4,f5,10/18/2006,Lexical-Functional Grammars,A Unique Solution?,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,f2,f4,f5,Prefer minimal solution,10/18/2006,Lexical-Functional Grammars,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.,10/18/2006,Lexical-Functional Grammars,Principles Regulating F-Structures,Uniqueness: Every attribute has a unique value Note: Uniqueness doesnt 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,10/18/2006,Lexical-Functional Grammars,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,Lexical item requires governed functions OBJ and OBJ2,10/18/2006,Lexical-Functional Grammars,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,10/18/2006,Lexical-Functional Grammars,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,10/18/2006,Lexical-Functional Grammars,Changing structure, but not meaning,S,NP,VP,DET,N,NP,V,N,DET,DET,N,NP,a,girl,handed,a,toy,the,baby,VP V NP NP PP* (OBJ)= (OBJ2)= (PCASE)= PP P NP (OBJ)= NP DET N S NP VP (SUBJ)= =,PP,to,P,10/18/2006,Lexical-Functional Grammars,Changing structure, but not meaning,THE,SG,SG,BABY,Dativizing Rule: ( OBJ2) ( OBJ) ( OBJ) ( TO OBJ),From (PCASE)=,10/18/2006,Lexical-Functional Grammars,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 PARTICIPLE) = PRESENT ( VCOMP SUBJ) = ( SUBJ),( VCOMP PARTICIPLE) =c PRESENT,Single, progressive arg,Functional control,Constraint Schema,10/18/2006,Lexical-Functional Grammars,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 ( VCOMP TO) =c + ( VCOMP SUBJ) = ( OBJ),10/18/2006,Lexical-Functional Grammars,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 ( VCOMP TO) =c + ( VCOMP SUBJ) = ( SUBJ),10/18/2006,Lexical-Functional Grammars,( PARTICLE) = PASSIVE ( PRED) = PROMISE ( VCOMP TO) =c + ( VCOMP SUBJ) = ( BY OBJ),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 ( VCOMP TO) =c + ( VCOMP SUBJ) = ( SUBJ),Doesnt conform to Fn Control Restrictions,10/18/2006,Lexical-Functional Grammars,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,10/18/2006,Lexical-Functional Grammars,Long Distance Dependencies,The girl wondered who the baby saw _. Instance of constituent control Decompose into chain of functional identities,10/18/2006,Lexical-Functional Grammars,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,10/18/2006,Lexical-Functional Grammars,C-Structure for Long-Distance Dependencies,the,baby,saw,(Q-FOCUS)= = NP,= S,(OBJ) = NP,(PRED) = WHO N,= VP,(SPEC) = DET,(NUM) = SG (PRED) = BABY N,(TENSE) = PAST (PRED) = SEE V,(OBJ) = NP,who,f1,(SCOMP)= S,e,= NP,Bounded Domination Metavariables: : bounded above (longer path) : bounding node,10/18/2006,Lexical-Functional Grammars,More Precisely,Shell
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