Unification. Two Routes to Deep Structure. Unification. Unification Grammar. Martin Kay. Stanford University University of the Saarland

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1 Two Routes to Deep Structure Derivational! Transformational! Procedural Deep Unidirectional Transformations Surface Stanford University University of the Saarland Constraint-based! Declarative Deep Surface 1 2 Grammar Functional Grammar FUG Lexical Functional Grammar LFG Generalized Phrase Structure Grammar GPSG PATR II Attribute Report 1 Report 2 Combined Report eyes blue blue blue hair black or brown brown or red brown accent Italian Italian wife see below see below see below children Ahemed & Angela Rebecca & Angela Ahmed, Angela & Rebecca age middle 48 Middle Categorial Grammar CUG Head Driven Phrase Structure Grammar HPSG Wife eyes brown brown weight 247 lbs 112 Kg 247 lbs disposition surly surly 3 4

2 ?- p(a, Q, b) = p(a, A, A). no?- p(a, Q, R) = p(a, A, A). A = a, Q = a, R = a yes?- p(q(a, a), r(x, X), s(y, Y))=p(X, Y, Z). Basic Attribute-Value X = q(a,a), Y = r(q(a,a),q(a,a)), Z = s(r(q(a,a),q(a,a)),r(q(a,a),q(a,a)))? 5 6 Path Graph < PHON > = Antonio < SYN > = noun < SYN NUM > = sg < SEM > = 'antonio PHON SYN SEM Antonio NUM 'antonio' sg noun 7 8

3 Attribute-value Matrix (AVM) phon Antonio num sg cat noun sem antonio Atomic Values number sg Complex Values agr number sg person 3 Coreference of Values number sg agr 1 person 3 subj age PHON SUBJ PRED Tigger meows PHON Tigger AGR NUMBER sing PHON meows AGR NUMBER sing Unified Values PHON SUBJ PRED Tigger meows PHON Tigger AGR 1 NUMBER sing PHON meows AGR 1 NUMBER sing PHON AGR vp AGR sg Tigger meows NUMBER sing!! AGR PHON AGR PHON AGR vp 3sg Tigger meows PERSON 3rd Tigger meows NUMBER sing PERSON 3rd 11 12

4 English Agreement The dog sleeps The dogs sleep Agreement and Subcategoriztion The dog slept The dogs slept The sheep sleeps The sheep sleep The sheep slept Not head driven! The sheep that was in the barn slept The sheep that were in the barn slept The sheep that was in the barn sleeps The sheep that were in the barn sleep German Case Head Percolation Der Junge sah den Lehrer Den Lehrer sah der Junge Das Mädchen sah der Junge der Junge sah das Mädchen Die Lehrerin sah den Lehrer Die Lehrerin sah das Mädchen VP[TENSE = t, NUM= n]! V[SUB=0, TENSE= t, NUM= n] VP[TENSE= t, NUM= n]! V[SUB=1, TENSE= t, NUM= n] NP VP[TENSE= t t, NUM= n]! V[SUB=2, TENSE= t, NUM= n] Sbar V[SUB=0, TENSE=pres, NUM=sg]! 'disappears' 'walks' V[SUB=1, TENSE=pres, NUM=sg]! 'sees' 'likes' V[SUB=2, TENSE=pres, NUM=sg]! 'says' 'claims' 15 16

5 Head Percolation Head Percolation VP[TENSE = t, NUM= n]! V[SUB=0, TENSE= t, NUM= n] VP[TENSE= t, NUM= n]! V[SUB=1, TENSE= t, NUM= n] NP VP[TENSE= t t, NUM= n]! V[SUB=2, TENSE= t, NUM= n] Sbar VP[TENSE = t, NUM= n]! V[SUB=0, TENSE= t, NUM= n] VP[TENSE= t, NUM= n]! V[SUB=1, TENSE= t, NUM= n] NP VP[TENSE= t t, NUM= n]! V[SUB=2, TENSE= t, NUM= n] Sbar V[SUB=0, TENSE=pres, NUM=pl]! 'disappear' 'walk' V[SUB=1, TENSE=pres, NUM=pl]! 'see' 'like' V[SUB=2, TENSE=pres, NUM=pl]! 'say' 'claim' V[SUB=0, TENSE=past, NUM= x]! 'disappeared' 'walked' V[SUB=1, TENSE=past, NUM= x]! 'saw' 'liked' V[SUB=2, TENSE=past, NUM= x]! 'said' 'claimed' PHON sleeps v LEVEL 2 SC2 AGR NP PERS 3 NUM sg CASE nom Lexicalization Agreement Subcategorization Head driven! PHON sleeps v LEVEL 2 SC2 AGR SC1 AGR NP PERS 3 NUM sg CASE nom NP PERS 3 CASE nom v SC3 1! 1 SC2 v SC2 1 v! SC1 1 v

6 Disjunction as Conjunction P I you she they sleeps _ X X sleep _ slept X X 2 was nom acc gen dat masc neut fem plur der das die die den das die die des des der der dem dem der den German Noun Morphology Disjunction as Conjunction nom acc gen dat masc neut fem plur P I you she they sleeps _ X X sleep _ slept X X 2 was Strong Weak Nom Acc Gen Dat Nom Acc Gen Dat M F N P M F N P M F N P M F N P M F N P M F N P M F N P M F N P A A A A A A A A A B B B B 2 2 der 1 C C C C D D D D E E E E F F F F G G G G H H H H I I I I 2 2 Frau I I I I 2 2 der Frau A A B B B B ein 1 1 C C C C D D E E F F F F F F F F G G G G H H I I großes 1 1 I I I I J J J J K K K K K K K K L L L L M M M M Haus 1 1 N N N N ein Großes Haus 23 24

7 What about this? Typed Feature Structures PERS v NUM 3 CASE indic Type Hierarchy case-type A particular attribute admits values of a particular type, and AVM's of a particular type admit attributes drawn from a particular set. gen-dat acc-dat nom-gen nom-acc dat gen acc nom 27 28

8 Types Type Definition 3rd sg. not 3rd sg. Specifies what features are allowable for objects of the given type. Specifies what types may unify. 1st sg. 2nd sg. 1st pl. 2nd pl. 3rd pl Typed Feature Structures Feature Structures are given sort or type names Type names correspond to classes of linguistic objects, which are, in addition, described by feature structures Certain features are appropriate for certain types Types constitute a hierarchy of Typed FS s Two feature structures f 1 and f 2, with types t 1 and t 2, unify iff The (untyped) feature structures unify, and The greatest lower bound of t 1 and t 2 is non empty 3sgmas-agr AGR 3sgmas NUMBER sg PERSON 3 GENDER MAS nom-acc CASE cval OBL -! nom-acc CASE nom-gen cval CASE OBL - cval OBL +,

9 Type Inheritance verb +subj+3sg+obj +subj+obj+that +subj+that +subj +subj+iobj+obj +subj+obj finite 3sg 1args 2args active passive +subj-3sg-obj +passive +subj +that +obj +iobj loves loved loved Trans+3sg Trans-3sg Intrans-3sg Intrans+3sg Type Definitions The child sleeps The children sleep The child slept The children slept The child finds the ball The children find the ball The child found the ball The children found the ball The child hands the ball to the teacher The children hand the ball to the teacher The child handed the ball to the teacher The children handed the ball to the teacher 35 finite: 3rd-sg: finite SYN SYN AGR 1 SUBJ np agr SYN AGR 1 AGR 1 NUM sg PERSON 3 36

10 Type Inheritance 2arg: SEM REL atom ARG1 ARG2 arg arg sem intransitive: SYN SUBJ np CASE nom transitive: intransitive 2arg SYN OBJ CASE acc np

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

The Formal Architecture of. Lexical-Functional Grammar. Ronald M. Kaplan and Mary Dalrymple 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 Architectural Issues Representation: