Autumn 2019 Ling 5201 Syntax I 3: Basic clause structure Robert - - PowerPoint PPT Presentation

Autumn 2019 Ling 5201 Syntax I 3: Basic clause structure

Robert Levine

Ohio State University levine.1@osu.edu

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Where we left off. . .

◮ What we have: (1) mary; m; NP john; j; NP criticized; criticize; (NP\S)/NP ◮ What we want. . . (2) john; j; NP criticized; criticize; (NP\S)/NP criticized • john; criticize(j); (NP\S) mary; m; NP mary • criticized • john; criticize(j)(m); S ◮ . . . So how are we going to get it?

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A first attempt: the AB gramar

◮ Here’s what I propose:

/ Elim \ Elim b; P; B/A a; α ; A b • a; P(α); B b; P; A\B a; α ; A a • b; P(α); B

◮ The logic of the types drives the whole proof:

◮ A\B and B/A are both implications: ‘give me an A and I’ll give you

back a B.

◮ The A-type term is given (i.e., either already proven or lexically

listed),

◮ and the result is a B-type object.

◮ The semantics applies the denotation labeling the implication to the

semantics of the antecedent premise (α),

◮ and the prosody is the concatenation of the implication term and

the antecedent term in an order determined by the direction of the implication.

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Applying the rules

/ E(lim) \ E(lim) b; P; B/A a; α ; A b • a; P(α); B b; P; A\B a; α ; A a • b; P(α); B (3)

john; j; NP criticized; criticize; (NP\S)/NP

/E

criticized • john; criticize(j); (NP\S) mary; m; NP

\E

mary • criticized • john; criticize(j)(m); S

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The semantic part. . .

◮ So our analysis of Mary criticized John derives a meaning we

write as criticize(j)(m).

◮ But what does this expression really denote? What is it

supposed to tell us?

◮ The most influential view of semantics for the past half

century, originating in the work of Richard Montague, is that

◮ a semantic representation of a sentence S is an explicit

statement of the truth conditions on sentences

◮ formulated in terms of a set-theoretic model ◮ that corresponds in 1-to-1 fashion with how the world is

structured.

◮ That view entails that the truth of a sentence must be

evaluated with respect to a specific set-theoretic model,

◮ since different models correspond to different possible ways

the world could be,

◮ or, for short, different ‘possible worlds’.

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More on semantics. . .

◮ To see how these general ideas can be used as a tool to match

form and meaning,

◮ let’s take something a little simpler to start with:

(4) John walks.

◮ This will be true just in case

◮ there is some object in our mathematical analogue of the

world—call it j—

◮ who is a member of a certain set, whose name is walk.

◮ Or, in more compact form, j ∈ walk. ◮ Now, in terms of our inference rules, this analysis appears to

present a problem: (5) walks; walk; NP\S john; j; NP john • walks; walk(j); S

◮ What is the problem here??

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Still more on semantics. . .

◮ The problem is that a set is a set, not a function. ◮ It doesn’t take arguments. ◮ This looks like a big problem for our analysis, ◮ because, for reasons of generality, we need the semantics to

correspond in general to a function applied to an argument.

◮ So are we in trouble here? Is there a way out?

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And still more on semantics. . .

◮ We can model a set as a function. ◮ So we have

(6) {j, m, a}

◮ Suppose we have a function which returns 1 for j,m, and a

and 0 for everything else. j → 1 s → b → r → a → 1 k → m → 1 . . . . . .

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And still more on semantics. . .

◮ There is a 1-to-1 relationship between such a function and the

values that the set whose members are mapped to 0 by that function,

◮ which means that we can in effect interpret the meaning of

walks to be either ‘static’ (as a set) or ‘dynamic’ (as a function) depending on the work we need this meaning to do.

◮ The two ways of interpreting this meaning are in effect the

two sides of a single semantic coin.

◮ With much in hand, we can work out the interpretations

required for more complex syntactic objects.

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Transitive verbs

◮ For example: our transitive verb criticize. ◮ We know that criticized John corresopnds to a function which,

exactly like walks, picks up an NP on its left to yield an S.

◮ The semantics are exactly parallel too: criticized John denotes

a set,

◮ and Mary criticized John is true just in case Mary is a member

• f that set.

◮ So once we have criticized John, we know we have a function

from individuals to the truth values 1 or 0.

◮ But how did we get criticized John?

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More on transitive verbs

◮ Since, by our proof, criticized combines with John to get criticized John, ◮ and since criticized John denotes a property (a set, or the function

corresponding to that set),

◮ it follows that criticized corresponds to a function which

◮ semantically combines with an individual (corresponding to

e.g. j),

◮ returns a pronunciation criticized • john, and ◮ and a matching interpretation as a property, criticize(j).

◮ Thus the semantic difference between an intransitive verb such as walks

and an intransitive verb like criticized is the difference between

◮ a property on the one hand ◮ and a function from an individual to a property on the other. Robert Levine 2019 5201 11 / 30

Summing up

Expression kind Syntactic type Semantic kind Semantic type sentence S truth value ({1, 0}) t noun phrase NP individual (m, j, b, a . . .) e intransitive verb NP\S property (walks, slept, eating . . .) e, t transitive verb (NP\S)/NP relation (sees, criticizes, eating . . .) e, e, t ◮ This table can be extended considerably; so we have verbs that

combine

◮ with two NPs to yield a VP (sent Mary a book, ◮ with an NP and a PP (sent a book to Mary), ◮ with two NPs and a PP (bet John ten dollars on the outcome) ◮ and so on and on.

◮ The key point is that the syntactic type and the semantic type

match perfectly, in that

◮ given a syntactic type, we can identify the corresponding semantic

type uniquely.

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◮ This outcome makes complete sense in terms of the higher order logic we

are assuming as the compositional ‘engine’ of our framework,

◮ in that, in HOL, logical connectives such as implication, conjunction,

negation etc. are considered to be functions.

◮ Thus, the logical formula p ⊃ q is regarded as a function which takes the

truth values of propositiona p, q to a third truth value,

◮ so of type t, t, t. ◮ We aren’t thinking of implication in terms of truth, of course. . . ◮ but rather, syntactic composition. ◮ So the implicational connectives /, \ for us are functions which take

syntactic types to other syntactic types;

◮ e.g., criticize is a function of syntactic type NP, NP, S ◮ and semantic type e, e, t. ◮ which is just what you get replacing NP with its semantic type e and S

with its syntactic type t,

◮ illustrating why we refer to types of the form X\Y or Y/X as

functional types.

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Adjuncts vs. complements

◮ Some parts of sentences depend on lexical properties: (7)

• a. I told John to leave
• b. I told John that he had to leave.

(8)

• a. told; tell; ((NP\S)/VP[inf])/NP
• b. told; tell; ((NP\S)/S[that])/NP

(9)

• a. *I informed John to leave.
• b. I informed John that he had to leave.

(10) informed; inform; (NP\S)/S[that] (11)

• a. I ordered John to leave.
• b. *I ordered John that he had to leave.

(12)

• rdered; order; ((NP\S)/VP[inf])/NP

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◮ . . . and some DON’T:

(13)

Mary quietly 8 > > > > > > > > > > > > > < > > > > > > > > > > > > > : reflected read the book showed the evidence to John showed John the evidence told John to leave told John that he had to leave

• rdered John to leave

informed John that he had to leave . . . 9 > > > > > > > > > > > > > = > > > > > > > > > > > > > ; ◮ What do we want to say about quietly here? ◮ How shall we say it? ◮ Suppose we say (14) quietly; quietly; (NP\S)/(NP\S)

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◮ Then the following proof is legal:

read; read; (NP\S)/NP the • book; the-book; NP

/E

read • the • book; read(the-book); NP\S quietly; quietly; (NP\S)/(NP\S)

/E

quietly • read • the • book; quietly(read(the-book)); NP\S mary; m; NP

\E

mary • quietly • read • the • book; quietly(read(the-book))(m); S

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◮ Since (NP\S)/(NP\S) is a functional type taking NP\S as

argument,

◮ its semantics is a function taking the semantics of read the

book as argument.

◮ What work does this function do? ◮ Mary read the book must be true if Mary quietly read the

book is true; i.e.,

◮ if m ∈ quietly(read(the-book)) then necessarily

m ∈ (read(the-book)). . .

◮ but the converse does not hold. ◮ So what is the relationship between the two sets?

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◮ quietly(read(the-book)) ⊆ read(the-book) ◮ So quietly’s semantic action is to map a set to one of its subsets. ◮ Compare this kind of example with (15) Mary allegedly read the book. ◮ Is it the case that if m ∈ allegedly(read(the-book)) then necessarily m ∈ (read(the-book))? ◮ Clearly not; the semantic action of allegedly is fundamentally different from the ‘intersective’ modification contributed by quietly. ◮ Instead, allegedly changes the evaluation conditions on the set denoted by read the book. . . ◮ . . . to the set of individuals who have been claimed to belong to read(the-book). . . ◮ . . . making allegedly’s denotation one containing crucial reference to a speech act which itself refers to the denotation of the modified VP.

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Auxiliaries

◮ There is a class of forms in English with several specific and somewhat idiosyncratic properties. N(egation) (16)

• a. *John

8 > > < > > : took passed designed postponed 9 > > = > > ; not the exam.

• b. Mary

8 > > < > > : should must may will 9 > > = > > ; not take the exam. I(nversion) (17)

• a. *

8 > > < > > : Took Passed Designed Postponed 9 > > = > > ; John the exam? b. 8 > > < > > : Should Must May Will 9 > > = > > ; Mary take the exam?

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C(ontraction) (18)

• a. *John

8 > > < > > : tookn’t passedn’t designedn’t postponedn’t 9 > > = > > ; the exam.

• b. Mary

8 > > < > > : shouldn’t mustn’t ?mayn’t won’t 9 > > = > > ; take the exam. E(llipsis) (19)

• a. *John likes listening to Bach and Handel, and Mary likes too.
• b. *Sue attempted to solve the problem, and Bill attempted too.

(20)

• a. John will listen to Bach and Handel,and Mary

8 > > > < > > > : should might will . . . 9 > > > = > > > ; too

• b. John is listening to Bach and Handel, and Mary is too.
• c. John had listened to Bach and Handel, and Mary had too.

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What syntactic type should be assigned to auxiliaries?

(21) Mary should read that book.

◮ read is (NP\S)/NP; ∴ read that book is NP\S ◮ ∴ two possibilities:

◮ should is (NP\S)/(NP\S) (. . . because?) ◮ should is some mystery category XP and read that book is

XP\(NP\S) (. . . because?)

◮ We’re looking for coverage and economy of description ◮ Which story is preferable on those grounds?

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◮ Start with read that book as XP\(NP\S). ◮ Q: What will the lexical type for read be? ◮ A: Necessarily, (XP\((NP\S)))/NP ◮ Q: What are the implications for the rest of the English lexicon?

(22) Mary should 8 > > > > > > > > > > > > > < > > > > > > > > > > > > > : relax write a note to Bill write Bill a note talk to Bill discuss John with Bill realize that John is a spy tell Bill that John is a spy admit to Bill that John is a spy . . . 9 > > > > > > > > > > > > > = > > > > > > > > > > > > > ; .

◮ Q: What do we have to say?

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◮ A: We have to add a final syntactic argument XP\ to every

verb type in English!

◮ We have the choice between

◮ on the one hand, assuming that a huge range of semantically

and syntactically diverse and often eccentric lexical items all just happen to want to combine with the very small number of exponents of the category XP; or,

◮ on the other hand, positing a single pattern of selection for the

fifteen or so members of a highly unified set of elements with a number of quite idiosyncratic lexical properties in common.

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◮ But it doesn’t stop there. ◮ What further happens based on e.g.

(23)

• a. Mary should have relaxed
• b. Mary should be relaxing.
• c. Mary should have been relaxing.

◮ In terms of coverage and economy of description, which

makes more sense?

◮ But this is a strictly syntactic argument. What about the

semantics?

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What work do auxiliaries actually DO?

◮ We can best answer this question somewhat indirectly, by examining

cases of meaningless sentence subjects. (24)

• a. There is a crowd in front of the theatre.
• b. A crowd is in front of the theatre.

(25)

• a. There were three demonstrators arrested at the rally.
• b. Three demonstrators were arrested at the rally.

◮ Q: What contribution does there make to the truth conditions on the

sentence?

◮ A: None whatever. For any conceivable situation where the a. examples

are true, the b. examples are true and vice versa.

◮ Since sentences with there are invariably equivalent in their semantics to

their analogues without there, there cannot possibly have any truth conditional meaning of its own. . .

◮ . . . and hence is semantically empty.

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◮ Now we examine cases of meaningful sentential subjects. (26)

• a. John slept.
• b. Mary phoned Bill.
• c. Anne sent a letter to Steve.

◮ Sentence a. predicates a property of John; sentence b. asserts that the ‘phone’ relation held between Mary and Bill; sentence c. asserts that there is some letter such that the ‘send’ relation held between Anne, that letter and Bill. ◮ In all cases, the subject is mapped to membership in a set of individuals, ◮ with admission to that set determined by specific cognitive criteria imposed by the verb in each case. (27) *There 8 < : slept phoned Bill sent a letter to Steve 9 = ;. ◮ Q: Is this what we expect? ◮ A: We would expect nothing else, because since there is semantically empty, it cannot denote an individual, hence cannot be a member of a set of individuals.

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◮ Q: So then what should we make of (28)?

(28)

• a. There will be an investigation held.
• b. There might be a car in the garage.
• c. There must be quite a crowd gathering.

◮ Will etc. clearly cannot be ‘about’ there on the one hand and some

set on the other.

◮ b. tells us rather that it may be true that there is a car in the garage;

• c. tells us that it must be true that there is a crowd gathering.

◮ In all these cases, what the auxiliary is ‘about’ is not one or more

individuals and the relationship between them

◮ but about the status of a certain proposition: that it is possibly

true, or necessarily true, or will be true in the future.

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◮ In the same way, in (29), the auxiliary says nothing about the particular

transaction between Mary and Sue: (29) Mary 8 < :

• a. will
• b. could
• c. should

9 = ; write to Sue.

◮ What it’s doing rather is telling us something about how to evaluate the

truth of the proposition positing communication by writing with Mary transmitting and Sue receiving.

◮ Let’s call this proposition ψ. ◮ Then the meaning of

◮ (29a): ψ is true at some point in the future; ◮ (29b): ψ is possibly true; ◮ (29c): ψ is ethically or practically desirable.

◮ Q: How do these semantic conclusions play against the syntax-based

conclusion we came to making the syntactic type of auxiliaries functions from VPs to VPs?

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◮ A: By the rules we’ve stated, implicational syntactic types invariably

correspond to semantic functions. . .

◮ which take the semantics of the corresponding syntatic arguments as

their semantic arguments.

◮ On our analysis, auxiliaries take the combination of (i) the VP they

combine with and (ii) their own subjects as their arguments: (30) John might apologize. (31)

apologize; apologize; VP might; ♦; VP/VP might • apologize; ♦apologize; VP john; j; NP . . . . . . john • might • apologize; ♦(apologize(j)); S

◮ On the other hand, suppose that a VP such as apologize took might as

its argument.

◮ How could might possibly wind up taking the combination of John and

apologize as its own argument, given that it itself is the argument of apologize ??

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Taking stock

◮ We can draw a couple of general conclusion at this point. ◮ The most important one: even in very basic clause structure, we have

evidence of higher-order kinds of expressions. . .

◮ . . . not just functions which take individuals as arguments (the way VPs

such as apologize do). . .

◮ . . . but functions which themselves take other functions as their own

arguments.

◮ But we also can see that in some cases the semantic action of these

functions seems a bit wonky.

◮ Auxiliaries apparently take two arguments, so the last line of the proof on

the preceding slide should be ♦(apologize)(j). . .

◮ . . . whereas what we want to wind up with is ♦(apologize(j)). ◮ We have a syntax-semantics mismatch and we’re going to need

something extra to handle it.

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