Equality and Subsumption Ron Kaplan with Annie Mary

Equality and Subsumption Ron Kaplan (with Annie, Mary, John…) Bergen, October 2001

Syntactic asymmetry • Transformational grammar More things move up than down Cycles permit raising of constituents, not lowering Kayne: “The Asymmetry of Syntax” • Constraint-based grammar Mathematically rigorous formalization* Equality as basic predicate does not reflect asymmetry intuition • What about subsumption? ( OBJ) = ( XCOMP SUBJ) vs. ( OBJ) ( XCOMP SUBJ) [In XLE: ( OBJ) << ( XCOMP SUBJ) ] *except for HPSG

Equality and Subsumption Equality: f = g iff Symbols: f and g are identical F-structures: Dom(f ) = Dom(g) and for all a Dom(f ): (f a) = (g a) A B C + D - = E C + D - A B E Sets: Card(f ) = Card(g) and every element of f = some element of g Subsumption: f << g iff Symbols: f and g are identical F-structures: Dom(f ) Dom(g) and for all a Dom(f ): (f a) << (g a) f = A C + << A B C + D - = g E Sets: Card(f ) Card(g) and every element of f << some element of g f = g iff f << g and g << f (symmetry)

C-structure accidents conceal undesired symmetry Consider fictitious English-X allowing post-verbal subjects in VP: Went Bill. VP (to) I expected Bill to go. but *I expected to go Bill. ‘expect SUBJ XCOMP OBJ’ ( OBJ) = ( XCOMP SUBJ) S NP V NP = ( SUBJ) = VP John expected NP VP Bill to go PRED ‘expect SUBJ XCOMP OBJ’ SUBJ PRED ‘John’ OBJ XCOMP PRED ‘Bill’ PRED ‘go SUBJ PRED ‘Bill’

C-structure accidents conceal undesired symmetry Consider fictitious English-X allowing post-verbal subjects in VP: Went Bill. VP (to) I expected Bill to go. but *I expected to go Bill. ‘expect SUBJ XCOMP OBJ’ ( OBJ) = ( XCOMP SUBJ) S NP V NP = ( SUBJ) = VP John expected NP VP to PRED ‘expect SUBJ XCOMP OBJ’ SUBJ PRED ‘John’ OBJ go NP Bill XCOMP PRED ‘Bill’ PRED ‘go SUBJ PRED ‘Bill’

Subsumption with VP subject *John expected to go Bill. ‘expect SUBJ XCOMP OBJ’ ( OBJ) << ( XCOMP SUBJ) S NP VP John expected NP VP to go NP PRED ‘expect SUBJ XCOMP OBJ’ SUBJ PRED ‘John’ OBJ XCOMP << PRED ‘go ( SUBJ) SUBJ PRED ‘Bill’ Bill Minimal model is Incomplete

Subsumption without VP subject John expected Bill to go. ‘expect SUBJ XCOMP OBJ’ ( OBJ) << ( XCOMP SUBJ) S NP VP John expected NP VP Bill to go PRED ‘expect SUBJ XCOMP OBJ’ SUBJ PRED ‘John’ OBJ XCOMP PRED ‘Bill’ PRED ‘go ( SUBJ) SUBJ PRED ‘Bill’ Minimal model is Complete <<

French is English-X • VP Subjects in Extraction Domains “Stylistic Inversion” La lettre qu’enverra à la direction le patron The letter that will-send to the management the boss S’ XP S ( TOPIC) = = = ( {COMP, XCOMP}* GF) ( LDD) = + VP V NP = ( SUBJ) = ( LDD) • Complement subject doesn’t raise to object | *Le livre que le libraire a convaincu d’offrir Jean à ma fille. The book that the bookseller convinced John to offer to my daughter. convaincre ( PRED) = ‘convaincre SUBJ, XCOMP ’ ( OBJ) << ( XCOMP SUBJ)

Equality: Atypical but still needed Subject-to-subject chains: SUBJ (not OBJ) of highest verb may appear in lowest clause le livre que le patron du labo pouvait recommander à cet étudiant le livre que pouvait recommander le patron du labo à cet étudiant the book that the head of-the lab could recommend to this student le livre que le patron du labo croyait pouvoir recommander à cet étudiant le livre que croyait pouvoir recommander le patron du labo à cet étudiant the book that the head of-the lab thought he could recommend to this student pouvoir ( PRED) = ‘pouvoir SUBJ, XCOMP ’ ( SUBJ) = ( XCOMP SUBJ) croire ( PRED) = ‘croire SUBJ, XCOMP ’ ( SUBJ) = ( XCOMP SUBJ)

Other uses of Subsumption in LFG • Earlier proposals: – Subset in feature resolution (Dalrymple & Kaplan, 2000) ( PERSON) – Implicit in feature distribution over sets (Kaplan & Maxwell, 1988) – Implicit in Restriction operator (Kaplan & Wedekind, 1993) /CASE << • Recent observation: – Can represent distinctive properties of sub-f-structures – Example: Partial VP fronting in German

Partial VP fronting in German: Problem Das Buch gegeben hat Hans dem Mädchen The book given has John the girl ‘John has given the girl the book’ S’ VP VP S ( TOPIC) = = = ( XCOMP*) NP TOPIC PRED SUBJ S V V Das Buch gegeben hat NP VP Hans (NP) ( OBJ 2) = ( OBJ) = S’ VP (NP) NP dem Mädchen (V) = hat Hans PRED geben XCOMP SUBJ OBJ Das Buch OBJ 2 dem Mädchen No record of topicalized elements

Partial VP fronting in German: Subsumption Das Buch gegeben hat Hans dem Mädchen The book given has John the girl ‘John has given the girl the book’ S’ VP VP S ( TOPIC) = = << ( XCOMP*) TOPIC VP PRED SUBJ S V V Das Buch gegeben hat NP VP Hans (NP) ( OBJ 2) = ( OBJ) = S’ NP (NP) NP dem Mädchen (V) = PRED geben OBJ Das Buch hat Hans PRED geben XCOMP SUBJ OBJ Das Buch OBJ 2 dem Mädchen <<

Completeness? • Topic substructure does not have all governed functions. • Must extend definition: E. g. An f-structure is complete if it has all governed functions or it subsumes an f-structure with all governed functions.