Questions and Answers in a Context-Dependent ... - Semantic Scholar

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TEXTS AND STUDIES LINGUISTICS AND

Managing

PHILOSOPHY

Editors:

J A A K K O H I N T I K K A , A c a d e m y of ¥ Inland STANLEY

IN

and Stanford

University

P E T E R S , T h e U n i v e r s i t y of T e x a s at A u s t i n

Editorial

Board:

E M M O N B A C H , U n i v e r s i t y of M a s s a c h u s e t t s at A m h e r s t J O A N B R E S N A N , M a s s a c h u s e t t s I n s t i t u t e of T e c h n o l o g y J O H N L Y O N S , U n i v e r s i t y of J U L I U S M . E . M O R A V C S I K , Stanford PATRICK

S U P P E S , Stanford

University University

D A N A S C O T T , Oxford

V O L U M E

Sussex

University

4

FORMAL SEMANTICS AND PRAGMATICS FOR NATURAL LANGUAGES Edited b y F.

G U E N T H N E R

Universität Tübingen, Seminar

für Englische

P h i l o l o g i e , Tübingen, B . R . D .

and S. J . S C H M I D T Universität Bielefeld,

D.

R E I D E L

DORDRECHT

B.R.D.

P U B L I S H I N G

C O M P A N Y

: HOLLAND /BOSTON

L O N D O N : E N G L A N D

: U.S.A.

Library of Congress Cataloging in Publication Data

M a i n entry under title:

UP

Formal semantics and pragmatics for natural languages. (Synthese language library; v. 4) "Essays in this collection are the outgrowth of a Workshop held in June 1976." Includes bibliographies and index. 1. Languages — Philosophy. 2. Semantics. 3. Pragmatics. 4. Predicate calculus. 5. Tense (Logic). 6. Grammar, Comparative and general. I. Guenthner, Franz. II. Schmidt, S. J., 1941III. Series. P106.F66 401 78-13180 I S B N 90-277-0778-2 I S B N 90-277-0930-0 pbk.

Published by D. Reidel Publishing Company, P.O. Box 17, Dordrecht, Holland Sold and distributed in the U.S.A., Canada, and Mexico by D. Reidel Publishing Company, Inc. Lincoln Building, 160 O l d Derby Street, Hingham, Mass. 02043, U.S.A.

f Bayerische j I Staatsbibliothek 1 l Müncnen J

A l l Rights Reserved Copyright © 1979 by D. Reidel Publishing Company, Dordrecht, Holland N o part of the material protected by this Copyright notice may be reproduced or utilized in any form by or any means, electronic or mechanical, including photocopying, recording or by any informational storage and retrieval System, without written permission from the Copyright owner Printed in The Netherlands

C O N T E N T S

P R E F A C E

J A A K K O

Vll H I N T I K K A

and

L A U R I

C A R L S O N

/ Conditionals,

G e n e r i c Quantifiers, a n d O t h e r A p p l i c a t i o n s of Subgames R I C H A R D M . S M A B Y / A m b i g u o u s Coreference W i t h Quantifiers EDWARD K E E N A N /' N e g a t i v e Coreference: Generalizing Q u a n t i f i c a t i o n for N a t u r a l L a n g u a g e T A N Y A R E I N H A R T / Syntactic D o m a i n s for Semantic Rules R O B I N C O O P E R / V a r i a b l e B i n d i n g a n d Relative Clauses M . J . C R E S S W E L L / A d v e r b s o f Space a n d T i m e F R A N Z G U E N T H N E R / T i m e Schemes, Tense L o g i c a n d the A n a l y s i s of E n g l i s h Tenses LENNARTÄQVIST/A System o f C h r o n o l o g i c a l Tense L o g i c H A N S K A M P / Semantics versus P r a g m a t i c s G I L L E S F A U C O N N I E R / I m p l i c a t i o n Reversal i n a N a t u r a l Language J Ä N O S S . P E T Ö F I / Structure a n d F u n c t i o n of the G r a m m a t i c a l C o m p o n e n t o f the Text-Structure W o r l d - S t r u c t u r e T h e o r y R O L A N D

H A U S S E R

and

D I E T M A R

Z A E F F E R E R

O F P A R T I C I P A N T S

77 107 131 171 201 223 255 289 303

/ Questions

and A n s w e r s i n a Context-dependent M o n t a g u e G r a m m a r W A L T H E R K I N D T / T h e I n t r o d u c t i o n o f T r u t h Predicates into F i r s t - O r d e r Languages LIST

1 37

339 359 373

I N D E X

375

V

ROLAND

HAUSSER A N D DIETMAR

Q U E S T I O N S

A N D A N S W E R S IN A

C O N T E X T - D E P E N D E N T

0.

ZAEFFERER

M O N T A G U E

G R A M M A R

INTRODUCTION

A successful f o r m a l reconstruction of a fragment of a n a t u r a l language like the one presented i n M o n t a g u e (1973) calls for extensions i n various directions. T w o of the most challenging ones a m o n g t h e m are the i n c l u s i o n of non-declarative sentence m o o d s a n d a treatment o f context-dependency b e y o n d the interpretation of tense. T h e present paper advances some Steps in b o t h directions since we believe that d e a l i n g w i t h context-dependency is a prerequisite for a satisfactory treatment of interrogatives. W h i l e transformationalists tend to regard interrogatives i n i s o l a t i o n , scholars interested i n the semantics of n a t u r a l language, b o t h outside the M o n t a g u e s c h o o l (e.g., K e e n a n a n d H u l l , 1973) a n d inside (e.g., H a m b l i n , 1973), have noted the r e l a t i o n that l i n k s u p questions w i t h their possible answers. M o n t a g u e himself suggests that a syntax a n d semantics of interrogatives s h o u l d p r o v i d e a c h a r a c t e r i z a t i o n of the semantic content of a correct answer. W h e t h e r a certain expression counts as a correct answer, however, depends o n the context i n w h i c h it is uttered. A n a p p r o p r i a t e context has t o c o n t a i n a n utterance of a c o r r e s p o n d i n g i n t e r r o g a t i v e expression. Therefore we shall tackle the p r o b l e m from the rear. F i r s t we ask: W h a t are the expressions that m a y serve as answers w h e n uttered i n a n appropriate context a n d h o w are they interpreted? A n d then: H o w are interrogatives to be analysed i n order t o m a k e sure that each c o r r e s p o n d i n g answer is assigned a correct interpretation? O u r attempt m a y thus be regarded as a first step t o w a r d a f o r m a l g r a m m a r of discourse. 1

2

3

1. T Y P E S O F Q U E S T I O N S A N D A N S W E R S

G r a m m a r i a n s usually classify interrogatives i n t o the f o l l o w i n g three m a i n categories: (A) (B) (Q

Y e s - n o questions A l t e r n a t i v e questions WH-questions. 339

F . Guenthner and S. J. Schmidt {eds.), Formal Semantics and Pragmatics for N a t u r a l Languages, 339-358. A l l Rights Reserued. Copyright © 1978 by D . Reidel Publishing Company, Dordrecht. Holtand.

ROLAND

340

HAUSSER AND DIETMAR

ZAEFFERER

C a t e g o r y (C) may be subclassified a c c o r d i n g to what element of the sentence is asked for: (Cl) (C2) (C3) (C4)

the subject the direct object a subject complement a n object complement

(C5)

an adverbial,

Category. (C5) comprises again a n u m b e r of subcategories we shall not enumerate here. In the following, we shall restrict ourselves to the most i m p o r t a n t types, namely (A) (yes-no questions), ( C l ) a n d (C2) (which we shall c a l l term questions), a n d those subcategories of (C5) (adverbial questions) that use the question w o r d s how, where, when, a n d why. Let us examine n o w the expressions that m a y serve as answers to these types of questions. C o n s i d e r for example (1), an instance of a y e s - n o question: (1)

D o e s J o h n love M a r y ?

W i t h respect to a context created by a n utterance of (1), or, as we shall also say, i n the context of (1), the f o l l o w i n g expressions m a y be used i n g i v i n g a n answer: (la) (lb) (lc) (ld) (le)

Yes. H e does. H e does so. H e loves her. H e loves M a r y .

(10 (lg) (1h)

J o h n loves her. J o h n loves M a r y . Yes, (lb).

(Im)

Yes, (lg).

N e g l e c t i n g the different degrees of acceptability of ( l a ) - ( l ) > ^ that they a l l have two fealures i n c o m m o n : m

w

m

a

Y State

(i)

they c o m m i t the Speaker (disregarding i r o n y , etc.) to the t r u t h of (lg), a n d

(ii)

they supply just the i n f o r m a t i o n required by the utterance of (1).

T h i s contrasts them w i t h answers like (In) a n d (lo):

CONTEXT-DEPENDENT

(In)

Yes, certainly.

(lo)

Yes, p r o b a b l y .

M O N T A G U E G R A M M AR

341

w h i c h give m o r e a n d less, respectively, Information t h a n required a n d w h i c h m a y therefore be called over- a n d under-answers, respectively. Since these w i l l presumably have to be analysed o n the basis of exact answers, we feel entitled not to treat them here. L o o k i n g t h r o u g h o u r list of possible answers to (1) one c a n notice that there is an increase of r e d u n d a n c y a n d explicitness f r o m (la) to (lg) a n d again f r o m (lh) to (Im). W e m a y call therefore (la) a m i n i m a l or n o n r e d u n d a n t answer a n d (lg) a redundant answer. (lb)—(lf) are then partially r e d u n d a n t answers, a n d ( l h ) - ( l n i ) c o m b i n e each a n o n - r e d u n d a n t answer w i t h a (partially) redundant one. R e g a r d i n g the semantics of (la) t h r o u g h (Im), it is clear that they are equivalent o n l y w i t h respect to certain contexts, namely those p r o d u c e d by an utterance of (1). If we replace (1) by (2), (2)

D o e s B i l l love M a r y ?

( l a ) - ( l e ) a n d (lh)—(lk) are still equivalent to each other, but not to (lf), (lg), (11), a n d (Im). T h e former two still express the same p r o p o s i t i o n as they d i d w i t h respect to the first context, but they have n o w a different i l l o c u t i o n a r y force insofar as they c a n n o t c o u n t as answers a n y m o r e . T h e latter two b e c o m e somewhat o d d i n the new context. 4

T h i n g s are very similar w i t h respect to term questions a n d their answers. C o n s i d e r the f o l l o w i n g examples: (3) (3a)

W h o dates M a r y ? Bill.

(3b) (3c) (3d) (3e)

Bill Bill Bill Bill

does. does so. dates her. dates M a r y .

A g a i n we may distinguish between a m i n i m a l , n o n - r e d u n d a n t answer l i k e (3a), p a r t i a l l y redundant answers l i k e (3b)-(3d) a n d a (fully) redundant answer like (3e). There are, however, no answers to term questions c o r r e s p o n d i n g to the ( h ) - ( ) cases of example (1). C o n c e r n i n g adverbial questions, the k i n d s of expressions that may play the r o l e of an a p p r o p r i a t e answer are demonstrated by the f o l l o w i n g example: m

342

(4) (4a) (4b) (4c) (4d) (4e) (4f) (4g)

ROLAND HAUSSER AND DIETMAR

ZAEFFERER

W h e n w i l l M a r y meet J o h n ? A t seven p.m. She w i l l d o so at seven p.m. She w i l l meet h i m at seven p.m. She w i l l meet J o h n at seven p.m. M a r y w i l l d o so at seven p.m. M a r y w i l l meet h i m at seven p.m. M a r y w i l l meet J o h n at seven p.m.

A g a i n , there is a scale of increasing r e d u n d a n c y f r o m (4a) to (4g). A n d again the t r u t h value of the answer expression w i l l depend o n the question i n the context of w h i c h it is uttered, except for (4g). In this respect (4g) behaves l i k e (3e) a n d (lg). T h i s shows that redundant answers are not very interesting from a semantical point of view since their semantic representation is identical to that of o r d i n a r y declarative sentences. In fact, they are o r d i n a r y declarative sentences a n d the question w i t h respect to w h i c h they are interpreted determines o n l y the i l l o c u t i o n a r y force that they carry. T h e i r a n s w e r h o o d depends o n the relation between their intension a n d that of the question expression, a n d b o t h can be established independently. T h e Situation is different, as we have seen, w i t h the other k i n d s of answers, where not o n l y the i l l o c u t i o n a r y force depends o n the m e a n i n g of the question expression but also the respective m e a n i n g the answer expression has. Since b o t h , redundant a n d n o n - r e d u n d a n t answers are possible, a n d since n o n redundant answers are generally m u c h m o r e n a t u r a l , we h o l d that no serious theory of questions a n d answers s h o u l d restrict itself to a treatment of redundant answers alone, a n d that it s h o u l d be able to handle both. A s s h o w n above, redundant answers represent no p r o b l e m w i t h respect to semantic interpretation; the problems they pose concern o n l y the theory of speech acts. T h e r e m a i n i n g answer-types, o n the other h a n d , do present interesting p r o b l e m s c o n c e r n i n g s e m a n t i c i n t e r p r e t a t i o n . W e m a y distinguish between the (a)-cases, w h i c h we called m i n i m a l answers, a n d the r e m a i n i n g ones, w h i c h share the feature of c o n t a i n i n g one o r more u n b o u n d or e x o p h o r i c pro-forms. B u t the p r o b l e m of e x o p h o r i c pro-forms is not l i m i t e d to answer-expressions alone, it m a y be viewed as a n instance of the general p r o b l e m of determinirig the reference for pro-forms. W e shall not go deeper into this matter here (cf. Hausser, 1977), but it seems that once this p r o b l e m is solved, a l l p a r t i a l l y redundant answers may be reduced to redundant ones. Therefore it is the p h e n o m e n o n of m i n i m a l answers that represents the basic a n d c r u c i a l p r o b l e m to be solved by a semantic theory of questions a n d answers. A final l o o k at alternative questions a n d their

CONTEXT-DEPENDENT

M O N T A G U E G R A M M A R

343

answers m a y demonstrate n o w o u r reason for neglecting t h e m i n this context. C o n s i d e r (5)-(5f)

:

(5) (5a) (5b) (5c) (5d)

D o e s M a r y sleep or is J o h n sick? M a r y sleeps. J o h n is sick. T h e former. T h e latter.

(5e) (5f)

Yes. No.

T h e e x a m p l e shows that w i t h respect to alternative questions, o n l y r e d u n d a n t answers (5a, b) or answers w i t h e x o p h o r i c proforms (5c, d) are possible, but not m i n i m a l answers of the y e s - n o type. 2. E X T E N D I N G T H E P T Q - L O G I C

INTO

A CONTEXT-DEPENDENT SYSTEM

W h i l e the fragment of E n g l i s h presented i n ' E n g l i s h as a f o r m a l language' ( M o n t a g u e , 1974, C h a p t e r 6) is given a direct semantic interpretation, the fragments contained i n ' U n i v e r s a l g r a m m a r ' ( M o n t a g u e , 1974, C h a p t e r 7) a n d i n P T Q are (for the sake of perspicuity) interpreted indirectly v i a a u x i l i a r y languages of typed intensional logic. T h e ' p r a g m a t i c ' aspect of the n o t i o n of truth defined i n P T Q lies i n the fact that it is made relative not o n l y to a given m o d e l or interpretation, as usual i n m o d e l theoretical semantics, but also to a so-called p o i n t of reference , consisting of a possible w o r i d a n d a moment of time. T h i s w i l l not suffice, however, for the i n t e r p r e t a t i o n of m i n i m a l answers, since, as we have p o i n t e d out i n the preceding section, their truth value depends o n the m e a n i n g of a previously uttered interrogative expression. Therefore we have to extend the P T Q logic i n t o a context-dependent System w h i c h specifies for each point of reference the m e a n i n g of the preceding utterance. W e c o u l d do that, f o l l o w i n g a Suggestion by D . L e w i s (1970), by s i m p l y a d d i n g a further c o o r d i n a t e , a 'previous discourse c o o r d i n a t e \ to the point of reference, but this a p p r o a c h w o u l d be exposed to M . J . CressweH's objection that it leads to a n i n f l a t i o n of coordinates: " w h y not a c o u n t r y , climate, religion, o r 'previous d r i n k s ' c o o r d i n a t e ? " (Cresswell, 1973, p. 111). W e therefore prefer another way of extending the P T Q - l o g i c w h i c h comprises the following three steps. 5

6

F i r s t we replace the interpretation or intensional m o d e l by a context-

344

ROLAND

HAUSSER A N DDIETMAR

ZAEFFERER

m o d e l W e define a c o n t e x t - m o d e l as an ordered triple ]).

If we interpret (15a') w i t h respect to (15'), we m a y read it r o u g h l y as follows: T h e set of properties of the p r o p o s i t i o n that J o h n w i l l leave contains the p r o p e r t y of not being the case. T h e r e d u c t i o n shows the desired equivalence w i t h the redundant answer (19): (19) J o h n won't leave. (19') - i W leave' ( j ) (15a'/15') - i W leave' (j) 5. A D V E R B I A L Q U E S T I O N S A N D T H E I R MINIMAL

ANSWERS

O u r general a p p r o a c h w o r k s for a d v e r b i a l questions as well as for term a n d y e s - n o questions. W e shall therefore restrict o u r discussion to two special points. F i r s t it is o b v i o u s that an adverbial question determines not only the

CONTEXT-DEPENDENT

M O N T A G U E G R A M M A R

351

syntactic category of the expression w h i c h , together w i t h the füll stop, makes u p a m i n i m a l answer, but also part of its semantic content. T h e f o l l o w i n g examples m a y serve as a n i l l u s t r a t i o n : (20)

H o w does B i l l w a l k ?

(20a)

Rapidly.

(20b)

Slowly.

(20c)

A t seven p.m.

(20d)

A t the corner.

(20e)

Into the park.

(20f)

Because of M a r y .

O n l y (20a) a n d (20b) m a k e sense i n the context of (20), (20c)-(20f) don't. T h e d a t a are s i m i l a r to those w h i c h c o n c e r n the difference between w h a t , w h o , and

which

plus a c o m m o n n o u n phrase, a n d therefore we account for t h e m

in a n a n a l o g o u s way: W e i n t r o d u c e a feature i n t o the t r a n s l a t i o n of the a d v e r b i a l question w o r d (e.g., M A N N E R i n the case of how — we use u p p e r case letters i n order to a v o i d confusion w i t h the c o m m o n n o u n t r a n s l a t i o n m a n n e r ' ) a n d we ensure by a m e a n i n g postulate that this feature turns o u t to be r e d u n d a n t if the answer is suitable. B u t there is another p h e n o m e n o n to be noticed w h i c h has n o counterpart a m o n g the term questions. C o m p a r e (21), (22), a n d the answers (21a)-(22a): (21)

W h e r e does J o h n w a l k ?

(22)

W h e r e w i l l J o h n meet the blonde?

(21a)

In the p a r k .

(21b)

Into the p a r k .

(22a)

A t the party.

(21a)-(22a) d o a l l m a k e sense i n the context of (21), but o n l y (21a) a n d (22a) d o so i n the context of (22). T h e consequence is clear: (21) has to be assigned two readings, due to the lexical a m b i g u i t y of the question w o r d where. following

translations, derived

The

a c c o r d i n g to the rules stated i n the

A p p e n d i x , show o u r p r o p o s a l for d e a l i n g w i t h that p h e n o m e n o n : (21') (21")

> U ^ * f A P x C P L A C E ^ ) A a { x , P}]fwalk')). Xa j*(kPx[DIRECTIONSJ) A a { x , P}]fwalk')). v

1

x

U s i n g M P ( 1 4 ) a n d M P ( 1 5 ) (cf. the a p p e n d i x , 8.4) we get the f o l l o w i n g translations for (21a) a n d (21b) i n the context of the place- a n d the d i r e c t i o n r e a d i n g of (21), respectively:

352

ROLAND

HAUSSER AND

DIETMAR

ZAEFFERER

(21a'/21') in'O'/walk', P V y [ A (21b'/21")

u[park'

(K)«-*K =

I?]

A

into'O,^walk', P V t ' [ A « [ p a r k ' ^ w ) « - ^ * ; ] A P{y}]). A g a i n , we have equivalence w i t h the redundant answers (23) a n d (24): (23) (24)

J o h n w a l k s i n the park. J o h n walks into the park. 6. M U L T I P L E

QUESTIONS

T h u s far we have been considering o n l y questions that ask for one a n d only one item. W i t h respect to them, a m i n i m a l answer consists i n the declarative utterance of one expression of the c o r r e s p o n d i n g category. There are, however, interrogative sentences like (25) w h i c h ask for m o r e t h a n one item: (25)

W h o kisses w h o m ?

A suitable m i n i m a l answer is, e.g., (25a): (25a)

M a r y Bill.

W e may call questions like (25) two-term questions. A somewhat different example is the following: (26) (26a)

W h e n w i l l J o h n meet M a r y where? A t seven p.m. at the corner.

Questions of this k i n d may be called two-adverbial questions. B u t the items asked for i n a m u l t i p l e question need not be of the same category, as the following example demonstrates: (27) (27a)

W h o seeks the d r a g o n where? M a r y i n the park.

N o t e , however, that the degree of acceptability of the question and especially of the m i n i m a l answer diminishes as the n u m b e r of questioned items increases: (28) (28a)

W h o kisses w h o m where when h o w ? M a r y B i l l at the corner in the evening r a p i d l y .

But since, apart from acceptability, there is no p r i n c i p l e d reason against a question-answer pair like (28), (28a), o u r rules account also for cases like this.

CONTEXT-DEPENDENT

M O N T A G U E

G R A M M A R

353

T h e Situation is different w i t h expressions l i k e the f o l l o w i n g : (29)

* D o e s J o h n leave when?

(29a)

* Y e s i n the evening.

T h e reason for rejecting (29) is not a l o w degree of acceptability but sheer u n g r a m m a t i c a l i t y : A yes-no question c a n n o t c o n t a i n any a d d i t i o n a l questioned item. W e therefore restrict the possibility of generating m u l t i p l e questions to term a n d adverbial questions (cf. rule S19.(d) i n the A p p e n d i x ) . 7. C O N C L U D I N G R E M A R K S

In c o n c l u s i o n we shall point out briefly some of the most i m p o r t a n t respects in w h i c h o u r a p p r o a c h differs f r o m other recent proposals c o n c e r n i n g the f o r m a l semantics of questions. W e differ from K e e n a n a n d H u l l (1973) m a i n l y i n three points: (a) W e provide explicit a n d separate rules for translating question a n d answer expressions f r o m n a t u r a l i n t o logical language, (b) we d o not restrict ourselves to w h i c h a n d yes-no questions, and (c) we d o not exclude answers of the n o b o d y / n o t h i n g type from the class of n a t u r a l answers. W e differ f r o m H a m b l i n (1973) i n that o u r a p p r o a c h does not m a k e it necessary to 'lift' the whole semantics i n type, letting, e.g., the intension of a f o r m u l a be the unit set of a p r o p o s i t i o n instead of the p r o p o s i t i o n itself. W h i l e H a m b l i n proposes to let questions denote u n i f o r m l y sets of p r o p o s i t i o n s , we propose to let questions denote different types of sets a c c o r d i n g to the type of that expression w h i c h is the c r i t i c a l one i n any k i n d of answer. F i n a l l y , i n contrast to K a r t t u n e n ( 1 9 7 6 ) , we d o not believe that a n adequate analysis of direct questions c a n be given by supplementing a g r a m m a r of embedded questions w i t h the remark that direct questions c a n be derived f r o m a deleted performative I ask y o u to teil me' plus the c o r r e s p o n d i n g embedded questions. A p a r t from other problems c o n c e r n i n g the performative analysis we see no way such a p r o p o s a l c o u l d be amended i n order to account for the p h e n o m e n o n of m i n i m a l answers w h i c h we showed to be the c r u c i a l semantic p r o b l e m i n c o n n e c t i o n w i t h direct questions. 4

8.

A n e x t e n s i o n of the minimal answers 8.1.

APPENDIX

P T Q - j r a g m e n t of E n g l i s h i n c l u d i n g d i r e c t q u e s t i o n s and

Additional categories

(a) C a t e g o r i e s f o r d i r e c t q u e s t i o n s t/(t//t)

is the category of direct y e s - n o questions.

354

ROLAND

HAUSSER

AND DIETMAR

ZAEFFERER

t/T

is the category o f direct one-term questions.

t/IA V

is the category o f direct o n e - a d v e r b i a l questions.

If A , B e { T ,

IAV),

then (... { t / A ) / . . .)/B

are the categories

o f direct

m u l t i p l e questions, i n p a r t i c u l a r (t/T)/T

is the category o f direct two-term questions, a n d

(t/IAVyiAV

is the category of direct t w o - a d v e r b i a l questions.

(b) F r i m e d

categories

If A is a category, then ( A ) is also a category (parentheses w i l l be o m i t t e d if f

n o a m b i g u i t y can arise). I n p a r t i c u l a r , t' is the category o f open sentences. 8.2.

Additional basic

ß , = B,J = B jl l

T

u {sleep, leave}

Q

/v

B

expressions

u {seven p.m., n o b o d y , nothing}

Q

B , = {who, what} T

= B ^ P u {meet, kiss, imagine}

B

T

B

I A V

, = { h o w , when, w h e r e

ß

C N

=ß^ u

V

]

Q

where ,

p

why}

2

{blonde, g i r l , d r u m - m a j o r , h u m a n , d r a g o n , evening, corner,

party} BiAv/T B iAv/T {i ß, = {yes, no}. =

f

u

nt0

> > because of} at

//r

8.3.

A d d i t i o n a l S- and T - r u l e s

Let s be an a d d i t i o n a l distinct member of C o n , M A N N E R , T I M E , P L A C E , e

DIRECTION,

and R E A S O N

be p a r t i c u l a r

C o n « ^ ; ^ » , , ) , a n d a be the variable v ^ Q

(a) B a s i c T 1 .(d)'

distinct

members

of

S J { 1 A V ) y

rules J o h n , M a r y , B i l l , n i n e t y , seven

p . m . translate into j * , m * , b * , n * , s*

respectively. (f)

n o b o d y a n d n o t h i n g translate into P ~ ) V x [ h u m a n ' ( x ) A P{.x}] and

(g)

P ~ i V x [ — i h u m a n ' ( x ) A P { x } ] respectively.

who a n d what

translate into P ^ { x [ h u m a n ' ( x ) A P ( x } ] j a n d

P ^ { x [ n h u m a n ' ( x ) A P{x}]} respectively. (h)

h o w , when,

w h e r e , w h e r e , why translate into {

2

k P x [ M A N N E R ( a ) A ,/{x, P } ] , k P x [ T I M E ( a ) A a \ x , P } ] , kP

x[PLACE

{ a ) A «{x,

P}],

k P x[DIRECTION

( a ) A a { x , P}], k P x [ R E A S O N ( a ) A *{x, P } ] respectively.

CONTEXT-DEPENDENT

(i)

M O N T A G U E

355

GRAM MAR

y e s , n o translate into p [ p ] , p [ - T p ] respectively.

S2a.

If c e P ,

T2a.

If

then F ( ^ ) e P - , where F ( c ) = w h i c h 2a

CN

€ P

C

2 a

7

a n d ^ translates i n t o

N

then F

2 a

( Q translates into

P^(X[C'(X)AP{X}]}.

(b) R u l e s of f u n c t i o n a l

application

S 4 . - S 1 0 . a p p l y to n o r m a l categories as well as to their p r i m e d variants. If one of the i n p u t expressions is of a p r i m e d category, the category of the O u t p u t expression has to be replaced by its p r i m e d variant. S5'.

If S e P

a n d ß e P , then F (ö, R

IVIT

where F (ö,

ß) e P ,

5

lv

5

if ß does not have the f o r m h e or who a n d F (ö, n

5

ß) = 5ß

he ) = 6 him n

n

and

who)= S whom.

F (ö, 5

(c) F o r m a t i o n r u l e s f o r d i r e c t

questions

(Since o u r m a i n concern here is not syntax a n d for the sake of brevity we give o n l y a r o u g h outline of rule S19, a n explicit Statement of w h i c h w o u l d require the definition of several a u x i l i a r y notions.) 518.

If < x e P

a n d öeP ,

T

then F (a,
a n d a, a',...,ß,

members of P

R

and P

I A V

>

/ ? ' , . . . are the first, second,

...

respectively that o c c u r in , then

either: (a)

there is no such a o r ß a n d F where

1 9

( $ ) e P,/, F () = $ \ , R

19

v

comes f r o m by first r e p l a c i n g the first verb i n

by its d o - s u p p o r t e d f o r m (the d o - s u p p o r t e d form of is being is, of course, etc.) a n d then s u b s t i t u t i n g the a u x i l i a r y for the initial w h e t h e r ; (b)

or

there is exactly one a e P > as r e q u i r e d a n d F () e

P ,

where either a = w h o a n d F ( ) = ?, o r a = w h o m

and

20

T

2 0

t/T

F ( < l ) ) = w h o m ' ?, where (j)' comes from , replacing the first verb i n b y its d o -

whom

s u p p o r t e d f o r m , a n d p r e p o s i n g the a u x i l i a r y ; o r (c)

there

is

exactly

one

as

ßeP . lAV

required

and

F2i()=ß' ?» where 4>* comes f r o m , by

F i ( ( t > ) G Pt/iAv* 2

deleting ß i n 1) a o r ß as required a n d Fi2,n()^Pi.., /Ay...y^B€{T t

T19.

F ,„() = ?.

1AV}\

9

22

If (j) e P,., (j) translates into ,' a n d a , . . . , a , i n that order, are 1

n

the free occurrences, from left to right, of variables i n (/>', then F i9()> 2 o ( < t > l 2i( a n d 22,«() translate into /i.v ... l v 4 > " where v - { i ^ i ^ r i ) is the i-th variable of the same type as a' a n d 0 " comes f r o m $ ' by r e p l a c i n g each a ' i n ' by the i-th variable of the same type. F

F

n

l

(d) F o r m a t i o n S20a.

F

y

rules for minimal If A e {t//t,

answers

T, I A V ] and a e P

then F ( a ) e P „ where F ( a ) 2 3

A9

2 3

= a.. T20a.

( A G {*//*, T , 7/1K}) a n d