Chapter 4: Valence & Agreement
Reminder: Where We Are Simple CFG doesn t allow us to cross-classify categories, e.g., verbs can be grouped by transitivity (deny vs. disappear) or by number (deny vs. denies). So we broke categories down into feature structures and began constructing a hierarchy of types of feature structures. This allows us to schematize rules and state crosscategorial generalizations, while still making fine distinctions.
Generalizing Transitivity: Valence (1) a. Pat relies on Kim. b. *Pat relies. c. The child put the toy on the table. d. *The child put the toy. e. The teacher became angry with the students. f. *The teacher became. g.the jury believed the witness lied. (2) The guests ate (the cheese).
Valence is not entirely semantic (3) a. The guests devoured the meal. b. *The guests devoured. c. *The guests dined the meal. d. The guests dined. e. The guests ate the meal. f. The guests ate.
Complements Head-Complement Rule: phrase COMPS word H COMPS 1,..., n 1,..., n This allows for arbitrary numbers of complements, but only applies when there is at least one. Heads in English probably never have more than 3 or 4 complements
phrase verb word verb COMPS 1, 2 1 NP 2 PP put the flowers in a vase
Adjective Valence (10) a. The children are happy. b. The children are happy with the ice cream. c. The children are happy that they have ice cream. d. *The children are happy of ice cream. e. *The children are fond. f. *The children are fond with the ice cream. g. *The children are fond that they have ice cream. h. The children are fond of ice cream.
Noun Valence (11) a. A magazine appeared on the newsstands. b. A magazine about crime appeared on the newsstands. c. Newsweek appeared on the newsstands. d. *Newsweek about crime appeared on the newsstands. e. The report surprised many people. f. The report that crime was declining surprised many people. e. The book surprised many people. f. *The book that crime was declining surprised many people.
Preposition Valence (12) a. The storm arrived after the picnic. b. The storm arrived after we ate lunch. c. The storm arrived during the picnic. d. *The storm arrived during we ate lunch. e. *The storm arrived while the picnic. f. The storm arrived while we ate lunch.
phrase adj word adj COMPS 1 1 phrase prep fond of ice cream
The Parallelism between S and NP Motivation: pairs like Chris lectured about syntax and Chris s lecture about syntax. both S and NP exhibit agreement The bird sings/*sing vs. The birds sing/*sings this/*these bird vs. these/*this birds So we treat NP as the saturated category of type noun and S as the saturated category of type verb.
Specifiers Head-Specifier Rule: phrase 1 H SPR SPR 1 Combines the rules expanding S and NP. In principle also generalizes to other categories.
Different Types SPR Values For Verbs: For Nouns: SPR NP SPR det
Some Abbreviations NOM = noun VP = SPR X verb SPR X NP = noun S = SPR verb SPR
Getting SPR Information Up the Tree How does the head s SPR value get to NOM and VP? We could revise the Head Complement Rule: phrase word SPR A H SPR A 1... n COMPS 1,..., n
A More General Solution The Valence Principle Unless the rule says otherwise, the mother s values for the features (SPR and COMPS) are identical to those of the head daughter.
More on the Valence Principle Intuitively, the features list the contextual requirements that haven t yet been found. This way of thinking about it (like talk of cancellation ) is bottom-up and procedural. But formally, the Valence Principle (like most of the rest of our grammar) is just a well-formedness constraint on trees, without inherent directionality.
phrase verb SPR 1 word noun SPR phrase verb SPR 1 Alex word verb SPR 1 COMPS 2 2 phrase noun SPR likes 3 word det SPR word noun SPR 3 the opera
Specifiers of Other Categories (31) a. They want/preferred them arrested. b. We want/preferred them on our team. c. With them on our team, we'll be sure to win. d. With my parents as supportive as they are, I'll be in fine shape.
Modifiers Not all elements following the head of a phrase are complements. Modifiers are not listed in The Head Modifier Rule (early version): phrase H PP
Coordination Rule (Chapter 4 version) 1 1 + word 1 conj
Agreement Two kinds so far: subject-verb and determiner-noun: diamonds sparkle(*s) these/*this diamonds This could be handled via stipulation in the Head-Specifier Rule But if we want to use this rule for categories that don t have the AGR feature (such as PPs and APs, in English), we can t build it into the rule.
The Specifier-Head Agreement Constraint (SHAC) Verbs and nouns must be specified as: AGR 1 SPR AGR 1
Subject-Verb Agreement walks: verb PER 3rd AGR 1 NUM sg NP SPR AGR 1 Kim: noun AGR SPR PER NUM 3rd sg we: noun AGR SPR PER NUM 1st pl (36) a. Kim walks b. *We walks.
3sing : PER NUM 3rd sg 1sing non 3sing non 1sing 1sing : 2sing : PER NUM PER NUM 1st sg 2nd sg 2sing plural plural : NUM pl
Possible AGR Values 1sing PER 1st NUM sg 2sing PER 2nd NUM sg plural PER 1st NUM pl plural PER 2nd NUM pl plural PER 3rd NUM pl 3sing PER 3rd NUM sg GEND fem 3sing PER 3rd NUM sg GEND masc 3sing PER 3rd NUM sg GEND neut
Determiner-Noun Agreement (45) a. This dog barked. b. *This dogs barked. (46) a. *These dog barked. b. These dogs barked. c. *Few dog barked. d. Few dogs barked. (47) a. The dog barked. b. The dogs barked.
SPR det person, boat, a, this: AGR 3sing people, boats, few, these: AGR PER NUM 3rd pl the: AGR PER 3rd
The Count/Mass Distinction Partially semantically motivated mass terms tend to refer to undifferentiated substances (air, butter, courtesy, information) count nouns tend to refer to individuatable entities (bird, cookie, insult, fact) But there are exceptions: succotash (mass) denotes a mix of corn & lima beans, so it s not undifferentiated. furniture, footwear, cutlery, etc. refer to individuatable artifacts with mass terms cabbage can be either count or mass, but many speakers get lettuce only as mass. borderline case: data
Our Formalization of the Count/Mass Distinction Determiners are: COUNT (much and, in some dialects, less), COUNT + (a, six, many, etc.), or lexically underspecified (the, all, some, no, etc.) Nouns select appropriate determiners count nouns say SPR <COUNT +> mass nouns say SPR <COUNT > Nouns themselves aren t marked for the feature COUNT So the SHAC plays no role in count/mass marking.
dog, word noun AGR 1 SPR det AGR 1 3sing COUNT + SPR
walks, word verb AGR 1 SPR noun AGR 1 3sing SPR
word the, det SPR
phrase 0 SPR word phrase 4 verb 1 0 AGR 3 SPR SPR 1 word word det noun AGR 3 3sing 4 AGR 3 COUNT + PER 3rd walks NUM sg SPR SPR 2 2 T he dog
The Type Hierarchy (so far) feat struc expression, agr-cat PER,NUM val-cat pos SPR,COMPS word phrase 3sing GEND non 3sing adj agr-pos AGR prep conj non 1sing 1sing verb noun det AUX CASE COUNT 2sing plural
TYPE FEATURES/CONSTRAINTS IST feat-struc expression feat-struc pos val-cat word expression phrase expression val-cat feat-struc SPR list(expression) 1 COMPS list(expression) pos agr-pos AGR verb AUX feat-struc pos agr-cat { } agr-pos +, noun CASE { } agr-pos nom, acc det COUNT { } agr-pos +, adj,prep,conj agr-cat PER NUM { } 1st, 2nd, 3rd { } sg, pl pos feat-struc 3sing PER NUM GEND non-3sing 1sing PER NUM non-1sing 2sing PER NUM plural NUM 3rd sg { } fem, masc, neut agr-cat agr-cat non-3sing 1st sg non-3sing non-1sing 2nd sg non-1sing pl
Abbreviations S = verb SPR NP = noun SPR VP = verb NOM = SPR X noun SPR X V = D = word word verb det SPR N = word noun
The Grammar Rules Head-Specifier Rule phrase 1 H SPR SPR 1 Head-Complement Rule phrase H word 1... n COMPS 1,..., n Head-Modifier Rule phrase H PP Coordination Rule 1 1 + word conj 1
The Principles Head Feature Principle (HFP): In any headed phrase, the value of the mother and the value of the head daughter must be identical. Valence Principle: Unless the rule says otherwise, the mother s values for the features (SPR and COMPS) are identical to those of the head daughter. Specifier-Head Agreement Constraint (SHAC): Verbs and common nouns must be specified as: AGR 1 SPR AGR 1
I, word noun AGR 1sing SPR word dog, Sample Lexicon noun AGR 3sing SPR D COUNT + word furniture, noun AGR SPR 3sing D COUNT
a, word det AGR 3sing COUNT + SPR word much, More Lexicon det AGR 3sing COUNT SPR barks, word verb AGR 3sing SPR NP like, word verb AGR non-3sing SPR NP COMPS NP
Chapter 5: Semantics
Building a precise model Some of our statements are statements about how the model works: prep and AGR 3sing can t be combined because AGR is not a feature of the type prep. Some of our statements are statements about how (we think) English or language in general works. The determiners a and many only occur with count nouns, the determiner much only occurs with mass nouns, and the determiner the occurs with either. Some are statements about how we code a particular linguistic fact within the model. All count nouns are SPR < COUNT +>.
Semantics: Where s the Beef? So far, our grammar has no semantic representations. We have, however, been relying on semantic intuitions in our argumentation, and discussing semantic contrasts where they line up (or don't) with syntactic ones. Examples? structural ambiguity S/NP parallelism count/mass distinction complements vs. modifiers
Our Slice of a World of Meanings Aspects of meaning we won t account for Pragmatics Fine-grained lexical semantics: The meaning of life is life, or, in our case, RELN INST life i
Our Slice of a World of Meanings MODE INDEX RESTR prop s RELN SIT SAVER SAVED save s i, j RELN NAME NAMED name Chris, i RELN NAME NAMED name Pat j... the linguistic meaning of Chris saved Pat is a proposition that will be true just in case there is an actual situation that involves the saving of someone named Pat by someone named Chris. (p. 140)
Our Slice of a World of Meanings What we are accounting for is the compositionality of sentence meaning. How the pieces fit together Semantic arguments and indices How the meanings of the parts add up to the meaning of the whole. Appending RESTR lists up the tree
Semantics in Constraint-Based Grammar Constraints as (generalized) truth conditions proposition: what must be the case for a proposition to be true directive: what must happen for a directive to be fulfilled question: the kind of situation the asker is asking about reference: the kind of entity the speaker is referring to Syntax/semantics interface: Constraints on how syntactic arguments are related to semantic ones, and on how semantic information is compiled from different parts of the sentence.
Feature Geometry SYN SEM MODE INDEX RESTR pos SPR COMPS list(expression) list(expression) { prop, ques, dir, ref, none} { i, j, k,... s 1, s 2,... } list(pred)
How the Pieces Fit Together Dana, word SYN noun AGR 3sing SPR SEM INDEX i MODE ref RESTR RELN name NAME Dana NAMED i
How the Pieces Fit Together slept, word SYN SEM verb SPR NPj INDEX s 1 MODE prop RELN sleep RESTR SIT s 1,... SLEEPER j
The Pieces Together S 1 NP SEM INDEX i VP SYN SPR 1 SEM RESTR RELN SIT s 1 SLEEPER i sleep,... Dana slept
A More Detailed View of the Same Tree SEM S INDEX MODE RESTR SEM INDEX RESTR 1 NP i name RELN NAME Dana NAMED i VP SYN SPR 1 SEM RESTR RELN SIT s 1 SLEEPER i sleep,...
To Fill in Semantics for the S-node We need the Semantics Principles The Semantic Inheritance Principle: In any headed phrase, the mother's MODE and INDEX are identical to those of the head daughter. The Semantic Compositionality Principle:
Semantic Inheritance Illustrated SEM S INDEX s 1 MODE RESTR prop SEM INDEX RESTR 1 NP i name RELN NAME Dana NAMED i VP SYN SPR 1 SEM RESTR RELN SIT s 1 SLEEPER i sleep,...
To Fill in Semantics for the S-node We need the Semantics Principles The Semantic Inheritance Principle: In any headed phrase, the mother's MODE and INDEX are identical to those of the head daughter. The Semantic Compositionality Principle: In any well-formed phrase structure, the mother's RESTR value is the sum of the RESTR values of the daughter.
Semantic Compositionality Illustrated SEM INDEX s 1 MODE RESTR prop RELN NAME NAMED i S name Dana, RELN SIT s 1 SLEEPER i sleep,... SEM INDEX RESTR 1 NP i name RELN NAME Dana NAMED i VP SYN SPR 1 SEM RESTR RELN SIT s 1 SLEEPER i sleep,...
What Identifies Indices? S 1 NP i VPSPR 1 D NOM i SPR 1 RESTR VP RELN SIT s 3 SLEEPER i sleep PP the cat slept on the mat
Other Aspects of Semantics Tense, Quantification (only touched on here) Modification Coordination Structural Ambiguity
Quantifiers (44) A dog saved every family (45) a. There was some particular dog who saved every family. b. Every family was saved by some dog or other (not necessarily the same dog). (46) a. (Exist i: dog(i))(all j: family(j))save(i,j) b. (All j: family(j))(exist i: dog(i))save(i,j) (47) save(i,j) (48) (All j: family(j))save(i,j)
predication RELN BV QRESTR QSCOPE exist i predication predication
RELN exist RESTR BV i QRESTR 1, RELN dog 1 INST i QSCOPE 2 RELN save RELN family 3, 4SAVER i INST j SAVED j, 2 RELN all BV j QRESTR 3, QSCOPE 4
RELN exist RESTR BV i 2 QRESTR 1, RELN dog 1, INST i QSCOPE 4 RELN save RELN family 3, 4SAVER i INST j SAVED j RELN all BV j QRESTR 3, QSCOPE 2
Evolution of a Phrase Structure Rule Ch. 2: NOM NOM PP VP VP PP Ch. 3: Ch. 4: Ch. 5: phrase COMPS itr H phrase SPR phrase H phrase H 1 SYN SPR PP PP SYN MOD 1 Ch. 5 (abbreviated): phrase H 1 MOD 1
Evolution of Another Phrase Structure Rule Ch. 2: X X + CONJ X Ch. 3: Ch. 4: Ch. 5: 1 1 + word 1 SYN 0 SEM IND s 0 conj 1 + SYN 0 SYN 0... SEM IND s 1 SEM IND s n 1 Ch. 5 (abbreviated): 0 IND s 0 1 word SYN SEM conj 1 conj IND s 0 RESTR ARGS s 1...s n conj 0 0... IND s 0 IND s 1 IND s n 1 RESTR ARGS s 1...s n SYN 0 SEM IND s n 0 IND s n
Combining Constraints and Coordination Coordination Rule 0 IND s 0 conj 0 0... IND s 0 IND s 1 IND s n 1 RESTR ARGS s 1...s n 0 IND s n Lexical Entry for a Conjunction and, SYN SEM INDEX MODE RESTR conj s none RELN SIT and s
Combining S IND s 0 Constraints and Coordination Lexical Entry for and SYN conj INDEX s and, MODE none SEM RELN and RESTR SIT s S IND s 1 conj IND s 0 RESTR RELN and SIT s 0 ARGS s 1, s 2 S IND s 2 Coordination Rule 0 IND s 0 0... IND s 1 Pat sings conj 0 IND s 0 IND s n 1 RESTR ARGS s 1...s n and 0 IND s n Lee dances
S IND s 0 Structural Ambiguity, 1 S IND s 0 ADV MOD 1 Tree I S IND s 1 CONJ S IND s 2 frequently NP V P and NP V P P at sings Lee dances IND s 0 MODE prop RELN name RELN sing RELN and NAME Pat, SIT s 1, SIT s 0, NAMED k SINGER k ARGS s 1, s 2 RESTR RELN name RELN win RELN frequently NAME Lee, SIT s 2, ARG s 0 NAMED j WINNER j
S IND s 0 Structural Ambiguity, S IND s 1 CONJ S IND s 2 Tree II NP V P and 1 S IND s 2 ADV MOD 1 P at sings NP V P frequently IND s 0 MODE prop RELN NAME NAMED RESTR RELN NAME NAMED Lee dances name RELN sing RELN and Pat, SIT s 1, SIT s 0, k SINGER k ARGS s 1, s 2 name RELN win RELN frequently Lee, SIT s 2, ARG s 2 j WINNER j
Question About Structural Ambiguity Why isn t this a possible semantic representation for the string Pat sings and Lee dances frequently? IND s 0 MODE prop RELN NAME NAMED RESTR RELN NAME NAMED name RELN sing RELN and Pat, SIT s 1, SIT s 0, k SINGER k ARGS s 1, s 2 name RELN win RELN frequently Lee, SIT s 2, ARG s 1 j WINNER j
Semantic Compositionality IND s 0 MODE prop RELN NAME NAMED RESTR RELN NAME NAMED IND s 0 MODE prop RELN NAME NAMED RESTR RELN NAME NAMED name RELN sing RELN and Pat, SIT s 1, SIT s 0, k SINGER k ARGS s 1, s 2 name RELN win RELN frequently Lee, SIT s 2, ARG s 0 j WINNER j name RELN sing RELN and Pat, SIT s 1, SIT s 0, k SINGER k ARGS s 1, s 2 name RELN win RELN frequently Lee, SIT s 2, ARG s 2 j WINNER j
Semantic Compositionality The meaning of a phrase is determined by the meaning of its parts and how they are put together.
The Type Hierarchy feat struc predication agr-cat PER NUM expression SYN SEM syn-cat sem-cat MODE INDEX RESTR val-cat SPR COMPS MOD 3sing GEND non 3sing word phrase pos 1sing non 1sing agr-pos AGR adj prep adv conj 2sing plural verb noun det AUX CASE COUNT
Feature Declarations & Type Constraints TYPE FEATURES/CONSTRAINTS IST feat-struc expression feat-struc SYN syn-cat SEM sem-cat syn-cat sem-cat predication word, phrase val-cat MODE INDEX RESTR feat-struc pos val-cat { } prop, ques, dir, ref, none { } 1 i, j, k,..., s 1, s 2,... list(predication) { } RELN love, walk,...... SPR COMPS MOD pos agr-pos AGR verb AUX list(expression) list(expression) list(expression) feat-struc feat-struc expression feat-struc feat-struc pos agr-cat { } agr-pos +, TYPE FEATURES/CONSTRAINTS IST noun CASE { nom, acc } agr-pos det COUNT adj, prep, adv, conj agr-cat 3sing PER NUM PER NUM GEND non-3sing 1sing PER NUM non-1sing 2sing PER NUM plural NUM { } agr-pos +, { } 1st, 2nd, 3rd { } sg, pl 3rd sg { } fem, masc, neut pos feat-struc agr-cat agr-cat non-3sing 1st sg non-3sing non-1sing 2nd sg non-1sing pl
Abbreviations S = VP = V = SYN SYN word SYN PP = SYN P = DP = word SYN SYN verb SYN SPR NPi = SEM verb NOM = SYN SPR X N = verb word SYN prep AP = SYN A = prep det SPR word SYN noun SPR INDEX i noun SPR X noun adj adj
The Grammar Rules Head-Specifier Rule phrase 1 HSYN SYN SPR SPR 1 Head-Complement Rule phrase word H SYN SYN COMPS 1,..., n 1... n Head-Modifier Rule phrase H 1 SYN SYN MOD 1 Coordination Rule SYN 0 SEM IND s 0 SYN 0 SEM IND s 1... SYN 0 SEM IND s n 1
Old Principles Head Feature Principle (HFP) In any headed phrase, the value of the mother and the value of the head daughter must be identical. Valence Principle Unless the rule says otherwise, the mother's values for the features (SPR, COMPS, and MOD) are identical to those of the head daughter. Specifier-Head Agreement Constraint (SHAC) Verbs and common nouns must be specified as: SYN AGR 1 SPR AGR 1
New Principles Semantic Inheritance Principle In any headed phrase, the mother's MODE and INDEX values are identical to those of the head daughter. Semantic Compositionality Principle In any well-formed phrase structure, the mother's RESTR value is the sum of the RESTR values of the daughters.
Sample Lexicon dog, SYN noun AGR 3sing SPR DP i MOD SEM MODE ref INDEX i RESTR RELN dog INST i Kim, SYN noun AGR 3sing SPR MOD SEM MODE ref INDEX i RESTR RELN name NAME Kim NAMED i love, SYN verb SPR NP i COMPS NPacc j MOD SEM MODE prop INDEX s RESTR RELN love SIT s LOVER i LOVED j
Sample Lexicon, Continued today, SYN adv SPR MOD VP INDEX s SEM MODE none RESTR RELN today ARG s and, SYN conj SEM INDEX s MODE none RESTR RELN and SIT s a, word SYN det AGR 3sing COUNT + SPR MOD SEM MODE none INDEX i RESTR RELN exist BV i