Autumn 2020 Ling 5201 Syntax I 3: Basic clause structure Robert - - PowerPoint PPT Presentation

Autumn 2020 Ling 5201 Syntax I 3: Basic clause structure

Robert Levine

Ohio State University levine.1@osu.edu

Robert Levine 2020 5201 1 / 29

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?

Robert Levine 2020 5201 2 / 29

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 and the result is a B-type object.

◮ This is the critical aspect of the proof: the combinatorics are entirely

determined by the form of the types.

◮ The semantics applies the denotation labeling the implication (the

functor, P) to the semantics of the antecedent premise (α), yielding the semantics of the sign typed by the ‘consequent’ (which is what you get when you calculate P(α))

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

the antecedent term prosody in an order determined by the direction of the implication, as expressed by \ or /.

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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 this 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 corresponds 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,/ ◮ along with 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 2020 5201 11 / 29

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, 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 whose syntactic type is NP, NP, S ◮ and whose 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)/Sthat)/NP

(9)

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

(10) informed; inform; (NP\S)/Sthat (11)

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

(12)

• rdered; order; ((NP\S)/VP

inf )/NP Robert Levine 2020 5201 14 / 29

◮ . . . 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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