APPENDIX A

INTERPRETATION OF TYPES

Syntax

There are sorts gender, agree­ment, tense and verb form;

For each sort there is a denumer­ably infinite set of feature vari­ables;

There are feature constants m and f of sort gender, 1 and 2 of sort agreement, and + and - of sort verb form; there is a l-ary feature functor 3 of rank gender-+agreement;

There is a set of feature terms for each sort defined as follows;

If v is a feature variable of sort (1,

v is a feature term of sort (1;

If k is a feature constant of sort (1, k is a feature term of sort (1;

Semantics

for each sort (1 there is a set Va of feature values.

a feature assignment G is a func­tion mapping each feature vari­able of sort (1 into a value in Va.

a feature valuation F is a func­tion mapping each feature con­stant of sort (1 into a value in Va and each feature functor of rank (11, •.. ) (1 n -+ (1 into a value in "va, x",xVan V a .

relative to F and G each feature term t of sort (1 has a feature value E(t) in Va defined as fol­lows.

263

264 APPENDIX A

If I is a feature functor of rank 0"1 x ... x 0" n ~ 0"

and tlo"" tn are feature terms of sort 0"1, .•. , O"n respectively, I(tl' ... ,tn ) is a feature term of sort 0";

There is a set of category formu­las defined as follows in terms of the feature terms and unary cate­gory predicates Nand VP of rank agreement, Sand CP ofrank verb form, and CN of rank gender;

EG (I(tl' ... ,tn)) IS

F(I)( (EG (tt), ... ,EG(tn»)).

There IS a prosodic algebra (L,+,(.,.),W,[.],L') where L is a set closed under binary opera­tions +, (.,.) and W such that + is associative and (SI' S3) W S2 = SI +S2+S3, [.J is a permutation on L, and L' ~ L is such that Vs E L,s' E L',s'+s = s+s'.

There are basic semantic do­mains A (non-empty set of in­dividuals) and {a, I} (truth val­ues) and a set I of indices. A basic type map t associates cate­gory predicates with semantic do­mains thus: t(PP) = teN) = A, t(CP) = {a, IV, t(S) = {a, I}, t(VP) = t(CN) = {a, I}A.

Relative to F, G, i E I, and a category predicate interpretation function di mapping each cate-gory predicate P of rank 0"1 X ... X

O"n to a function from Vu , x ... X

VU n into a subset of L x t(P) for each i E I, each category formula A has an associated semantic do­main T(A) and receives an inter­pretation DG,i(A) ~ Lx T(A) as follows.

INTERPRETATION OF TYPES 265

If P is a category predicate of rank crl x ... x cr nand t 1 , ... , tn are fea­t ure terms of sorts crl, ... , cr n re­spectively, P(tl, ... ,tn) is a cat­egory formula;

If A and B are formulas, A· B is a formula;

If A and B are formulas, B/A is a formula;

If A and B are formulas, A \B is a formula;

If A and B are formulas, A()B is a formula;

If A and B are formulas, B<A is a formula;

If A and B are formulas, A>B is a formula;

T(P(tl, ... ,tn» is t(P) and DG,i(p(tl,"" tn» is di(P)«(EG(td, ... , EG(tn»)).

T(A·B) is T(A) x T(B) and DG,i(A·B) is {(Sl+s2,(ml,m2))1 (sl,mt) E DG,i(A) /\ (S2' m2) E DG,i(B)}.

T(B/A) is T(Bf(A) and DG,i(B/A) is {(s,m)1 V(s',m') E DG,i(A), (s+s', m(m'» E DG,i(B)}.

T(A\B) is T(B)TCA) and DG,i(A\B) is ({s, m)1 V(s', m') E DG,i(A), (s' +s, m(m'») E DG,i(B)}.

T(A()B) ~

T(A) x T(B) and DG,i(A()B) is {(Sl,s2),(m1,m2)1 (sl,m1) E DG,i(A) /\ (S2' m2) E DG,i(B)}.

T(B<A) is T(B)TCA) and DG,i(B<A) IS

{(s,m)1 V(s',m') E DG,i(A), (s, s'), m(m'») E DG,i(B)}.

T(A>B) is T(B)T(A) and DG,i(A>B) IS

{(s,m)1 V(s',m') E DG,i(A), (s', s), m(m'» E DG,i(B)}.

266 APPENDIX A

If A and B are formulas, A0B is a formula;

If A and B are formulas, Bj A is a formula;

If A and B are formulas, AlB is a formula;

If A is a formula, OA is a formula;

If A and B are formulas, AI\B is a formula;

If A and B are formulas, Av B is a formula;

If A and B are formulas, AnB is a formula;

If A and B are formulas, AuB is a formula;

T(A0B) is T(A) x T(B) and D G,i(A0B) is {«SlWs 2 ),(ml,m2}}1 (sl,mt) E DG,i(A) 1\ (S2, m2) E DG,i(B)}.

T(BjA) is T(B)T(A) and DG,i(BTA) is {(s,m}1 V(sl,m/) E DG,i(A), (sWs1), m(m/)} E DG,i(B)}.

T(A1B) is T(Bf(A) and DG,i(A1B) is {(s, m}1 V(SI, m/) E DG,i(A), (SIWS), m(m/)} E DG,i(B)}.

T(OA) is T(A)l and DG,i(OA) is {(s,m}1 Vj E I,(s,m(j») E DG,j(A)}.

T(AI\B) is T(A) x T(B) and DG,i(A 1\

B) is {(s,(ml,m2))1 (s,ml) E DG,i(A) and (s, m2) E DG,i(B)}.

T(AVB) is ({I} x T(A» U ({2} x T(B» and DG,i(A V

B) is {(s,(n,m))1 either n = 1 and (s, m) E DG,i(A), or n = 2 and (s, m) E DG,i(B)}

T(AnB) is T(A) n T(B) and DG,i(AnB) is DG,i(A)nDG,i(B).

T(A)UT(B) is T(A) U T(B) and DG,i(AUB) is DG,i(A)UDG,i(B).

INTERPRETATION OF TYPES 267

If A is a formula and v is a fea­ture variable of sort (T, /\vA is a formula;

If A is a formula and v is a fea­t ure variable of sort (T, V v A is a formula;

If A is a formula and v is a fea­ture variable of sort (T, nvA is a formula;

If A is a formula and v is a fea­ture variable of sort (l, UvA is a formula;

If A is a formula, ~A is a for­mula;

If A is a formula, []A is a for­mula;

If A is a formula, []-1 A is a for­mula;

T(/\vA) is T(At" and DG,i(/\vA) is {(s, m)1 "Ie E V"' (s,m(e») E DG[v:=e),i(A)}

T(VvA) is V" x T(A) and DG,i(VvA) is {(s,{e,m))1 (s,m) E DG[v:=e),i(A)}

T(nvA) is T(A) and DG,i(nvA) is {(s, m)1 "Ie E V"' (s, m) E DG[v :=e],i (A)}

T(VvA) is T(A) and DG,i(VvA) is {(s, m) I .3e E Vo, (s, m) E DG[v:=e),i(A)}

T(~A) is T(A) and DG,i(~A) is {(s, m)1 (s, m) E DG,i(A) and s E L'}.

T([ ]A) is T(A) and DG,i([ ]A) is {([s],m)1 (s,m) E DG,i(A)}.

T([ ]-1 A) is T(A) and DG,i([ ]-1 A) IS

{(s,m)1 ([s]'m) E DG,i(A)}.

APPENDIX B

GENTZEN SEQUENT RULES

------id a - x: A => a - x: A

r,a - x:A,b - y:B => i[a+b] - X[x,y]:C -------------·L

r, e - z: A·B => i[e] - X[lI"lZ, 1I"2Z]: C

r => a - t/J: A .6. => f3 - l/;: B ----------·R

r,.6. => a+f3 - (t/J, l/;): A·B

r => a - t/J:A .6.,b - y: B => 'Y[b]- X[y]:C ----------------/L

.6., r, e - z: B/A => i[c+a) - X[(z ¢»): C

r,a - x:A => i+a -l/;:B --------------/R

r => i - >.xl/;: B/A

r => a - t/J:A .6.,b - y: B => i[b] - X[y]:C ---------------\L

6.,r,e- z:A\B => i[a+e] - X[(z ¢)]:C

r, a - x: A => a+y - l/;: B ---------\R

r => '/ - >.xl/;: A\B

269

270 APPENDIX B

r,a - x:A,b - y:B ~ ,[(a,b)] - X[x,y):C --------------------------·oL

r, e - z: AoB ~ ,[e] - X[1I'1Z, 1I'2Z): C

r ~ 0'- ¢: A Ll ~ j3 - 'Ij!: B ------------------~oR

r, Ll ~ (a, (3) - (¢, 'Ij!): AoB

r ~ 0'- ¢: A Ll, b - y: B ~ ,[b] - X[y]: C ----------------------------<L Ll,r,e- z:B<A ~ ,[(e,O'»)- X[(z ¢)]:C

r, a - x: A ~ (" a) - 'Ij!: B ----------------<R

r ~ a - ¢:A Ll,b - y: B ~ ,[b)- X[y]:C ---------------------------->L

Ll, r, e - z: A>B ~ ,[(a, e)] - X[(z ¢»): C

r,a - x:A ~ (a,,) - 'Ij!:B ---------------->R

r ~,- >'x1jJ:A>B

r, a - x: A, b - y: B ~ ,[(aWb») - X[x, y]: C ---------------------------0L

r,e- z:A0B ~ ,[e)- X[1I'1Z,1I'2Z]:C

r ~ a - ¢: A ~ ~ j3 - 1jJ: B -------------------'0R r, Ll ~ (O'Wj3) - (¢, 1jJ): A0B

GENTZEN SEQUENT RULES

r ~ a - ¢: A ~,b - y: B ~ ,[b] - X[y]: C ----------------------------TL ~,r,e- z:BTA ~ ,[(eWa)] - X[(z ¢)]:C

r,a - x:A ~ (,Wa) - tfJ:B -----------------TR

r ~ , - AXtfJ: BT A

r ~ a - ¢:A ~,b - y: B ~ ,[b] - X[y]:C -----------------------------lL ~,r,e- z:A1B ~ ,[(aWe)] - X[(z ¢)]:C

r,a - x:A ~ (aW,) - tfJ:B ------------------!R

r ~ , - AXtfJ: ALB

r,a - x:A ~ f3 - tfJ[x]:B ------------------OL r,a - z:OA ~ f3 - tfJ[-z]:B

or ~ a - ¢: A ------------IOR or ~ a - '¢:OA

r,a - x:A ~ r - x[x]:C --------------------ALa r,a - w:AAB ~,- X[1I"1W]:C

r, b - y: B ~ r - x[y]: C --------------------ALb r,b - w:AAB ~,- X[1I"2W]:C

271

272 A P PEN D I X B

r:::} cr - ¢:A r:::} cr -1jJ:B --------------------AR

r:::} cr - (¢,1jJ):AAB

r, d - x: A :::} "I - ¢: C r, d - y: B :::} "I - 1jJ: C ---------------------------------VL

r, d - w: AvB :::} "I - (w ---+ x.¢; y.1jJ): C

r :::} cr - ¢: A ---------VRa r:::} cr - tl¢:AVB

r :::} f3 - 1jJ: B -------VRb r:::} f3 - t21jJ:AVB

r,a - x:A:::} "I - X:C ----------------~nLa r, a - x: AnB :::} "I - x: C

r, b - y: B :::} "I - x: C ----------------~nLb r,b - y:AnB:::} "I - X:C

r :::} cr - ¢: A r :::} cr' - ¢': B ---------------------·1 nR, cr = cr', ¢ = ¢'

r :::} cr - ¢: AnB

r, d - w: A :::} "I - ¢: C r, d - w: B :::} "I' - ¢': C ---------------------------------UL, cr = cr', ¢ = ¢'

r, d - w: AUB :::} "I - ¢: C

GENTZEN SEQUENT RULES

r ~ Q - ¢:A ------URa r ~ Q - ¢:AUB

r ~ j3 - .,p: B

r,a - x:A[v +- t] ~ j3 - .,p[x]:B ----------AL r, a - y: AvA ~ j3 - .,p[(y t)): B

r ~ Q - ¢:A -------AR, v not free in r r ~ Q - ).v¢: AvA

r, a - x:A ~ j3 - .,p[x]:B ----------VL, v not free in r, B r, a - z: VvA ~ j3 - .,p[7I"2z): B

r ~ Q - ¢: A[v +- t) ------VR r ~ Q - (t,¢):VvA

r, a - x: A[v +- t] ~, - x: C ---------nL

r,a - x: nvA ~ ,- X:c

r ~ Q - ¢:A ------In R, v not free in r r ~ Q - ¢:nvA

273

274 APPENDIX B

r,a - x:A:::} f3 -1jJ: B --------UL, v not free in r, B r, a - x: UvA :::} f3 - 1jJ: B

r => 0 - q'J: A[v +- t] -------UR

r :::} 0 - q'J: UvA

r, a - x: A => f3 - 1jJ: B ---------6L r, a - x: 6A => f3 -1jJ: B

6r => 0 - q'J:A ------6R 6r => 0 - q'J:6A

r, a - x: 6A => 1[01 + 02] - 1jJ: C ------------6P, a = 01 or 02 r, a - x: 6A => 1[02 + od - 1jJ: C

r,a - x:A => f3[a] -1jJ:B ---------[]L r, a - x: []A => f3[[a]-I] -1jJ: B

r => 0 - q'J: A -----[]R r:::} [0] -q'J:[]A

r, a - x:A :::} fJ[a] -1jJ: B ---------:..~---[ ]-1 L r,a - x:[ ]-IA:::} f3[[a)) -1jJ:C

GENTZEN SEQUENT RULES

r::::} a - ¢:A -------[ ]-1 R r::::} [a]-1 - ¢:[]-1A

275

APPENDIX C

SUMMARY GRAMMAR

Main Clause Declaration

S( + )VUa(N(a).(S( +)/ .6. ON (a)))

Lexical Assignments

a

about

alleged

am

and

annoys

are

believes

'AxAy3z[(x z)l\(y 'z)] Ong( nr( (8(1) i ON (3(g))) L8(1)) /CN (g))

about OnanJ(((N(a)\8(1))\(N(a)\8(1)))/O(((N(a)\8(1))/

UaN (a) )\(N (a )\8(1))))

alleged Ong( CN (g) / (OCN (g)))

'.,\xAy(X ......... z.[y = z]; w.((w AU[U = y]) y)) O((N(1 )\8( + ))/(UaN(a )Vng(CN(g)/CN(g))))

, Ax AY[Y 1\ x] Onr((8(1)\[ ]-18(1))/8(1))

annoy D(([ ]CP\8)/N)

'.,\xAy(X ......... z.[y = z]; w.((w AU[U = yn y)) O((N(1)\8( + ))/(UaN(a)Vng(CN(g)/CN(g))))

believe O((UgN(3(g))\S( + ))/(DS( + ))VCP(t)))

277

278 A P PEN D I X C

cook ' AXAY[C cook y) II (x y)] O/\gCN(g)

deaf 'AXAY[(X y) II C- deaf y)] Ong(CN(g)jCN(g»

(either, or) , AX AY[ x V y] Onf«[ ]-lS(J)jS(J»)TS(J)

every 'AXAY'v'Z[(X z) II (y 'z)] Ong(nf( (S(J)T ON (3(g» )lS(J» JCN (g»

find - find O««N(1)UN(2))\S( + »n(UaN(a)\S( - )))jUaN(a))

fin~ - find O«UgN(3(g»\S( + »jUaN(a»

from 'Ax«-fromadn x), Cfromadv x» O«ng(CN(g)\CN(g»l\nanf «N(a)\S(/»\

(N (a )\S(J») )jUaN( a»

gIVes - gIve O«UgN (g )\S( + »j(UgN(g ).UgN (g»)

herself 'AXAY«X y) y) OnJ( «N (3(f» \S(J» T N (3(f») 1 (N (3(f» \S(J»)

herself 'AXAY«X y) y) Onfng««N(3(g»\S(J»j(N(3(f»·N(3(f»»>

«N(3(g» \S(/»)l N(3(f»»

himself ~ AXAY«X y) y) Onf«(N(3(m»\S(J»)lN(3(f»)1(N(3(m»\S(/»)

himself

I

IS

John

man

Mary

me

myself

myself

necessarily

possibly

SUMMARY GRAMMAR 279

->.x>.y«x y) y) Onfng( « (N(3(g) )\S(J»j(N(3(m»· N(3(m»»>

«N(3(g »\S(J) )jN(3(m»»

~>'x(xi)

Onf(S(J)j(N(1 )\S(J»)

In

Onanf( «N( a )\S(J»\ (N( a )\S(I» )/UaN ( a»

->.x>.y(x -+ z.[y = z]; w.«w >.u[u = y]) y» Ong«N(3(g»\S( + »j(UaN(a)V(CN(g)jCN(g»»

'j ON(3(m»

man OCN(m)

m ON(3(f»

~ >.x(x i) Onanf« (N (a )\S(J» iN(1»!(N (a )\S(J»)

'>.x>.y«x y) y) OnJ( «N( 1) \S(J) H N (1) H(N( 1 )\S(J»)

->.x>.y«x y) y) Onjng« «N(3(g) )\S(J) )/(N (1). N (1»»

«N (3(g» \S(I)i N C 1»)

~ >'xO-x OnJ(S(J)/OS(J»

->'xO-x OnjCS(J)jOS(J»

280 APPENDIX C

seeks 'AXC try T x -find» Ong«N(3(g»\S( + »/O«(N(3(g»\S( + »/UaN( a»\

(N(3(g »\S( + »»

that 'AXX

OnJ(CP(J)/OS(J»

the ')"Xty(x y) Ong(N(3(g)/CN(g»

to ')..xx

Ona(VP(a)/(N(a)\S( -»)

tries try Ong«N(3(g»\S( + »/VP(3(g»)

walk walk O«(N(1)UN(2)))\S( + »n(UaN(a)\S( -)))

walks walk O(UgN(3(g»\S( +»

who 'AX)"y)"Z[(Y z) /\ (x 'z)J Ong([ ]-l(CN(g)\ CN(g) )/(S( +)/ L':.ON (3(g»»

whom ')..W)..x)..yAZ[(y z) /\ (w (x 'z»J Ongnh(N(3(h)jN(3(g»)!([ ]-l(CN(g)\ CN(g»/

(S( +)/ L':.ON(3(h)))))

whose ')..s)..w)..x)..y)..z[(y z)/\(x (w 'd[(st)/\(poss (t,z»)))] Ongnhni«N(3(h )jN(3( i»l([ ]-l(CN(g)\ CN(g»/

(S( +)/ L':.DN(3(h»» )/CN (i»

woman woman OCN(f)

you

yourself

yourself

SUMMARY GRAMMAR

, >.x(x you) O«S(I)TN(2))lS(I))

'>.x>.y«x y) y) Onv( (N(2)\S( v ))TN(2))1(N(2)\S( v)))

->.x>.y«x y) y) Onfng« «N(3(g) )\S(I) )j(N(2)· N (2))»

«N(3(g) )\S(I))T N (2)))

281

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IN DEX

a-equality 50 ,a-equality 50-1, 53, 140 ,a-reduction 140, 142, 176, 178-

9 7J-equality 51, 140 1J-reduction 142

Abrusci 198 abstract syntax 12 accessibility relation 130, 134-5 accidental capture 50, 140 Across-the-Board Exception 241 additive 63 adjective 11, 16,24,75,89, 185

intensional 24-5, 146-9 intersective 24-5, 146-7 subsective 24

Ades 79, 251 Adjukiewicz 2, 70, 250 Adjukiewicz/Bar- Hillel calculus

2, 87, 250-251 adnominal 162 adverbial 11, 16, 26, 35, 80, 85,

162, 164 algebra 7

absolutely free 8, 44; see also algebra, term

free 7-8 prosodic 14 semantic 14 semiotic 14 term 8; see also algebra, ab­

solutely free

297

alphabetic variants 50 ambiguating relation 44-5 ambiguity 4, 8, 10, 30, 34, 36,

42,44,155,161-2,168 lexical 168, 225 local 161 quantificational9-1O, 28, 31,

34,78, 114, 116-7 analysis tree 22, 44 Anderson 61 arrow 15-7 assignment 15

lexical 16 associativity 192-3, 195, 197; see

also structural rule, as­sociation

attribute-value matrix 178 Avron 61

Bach 103, 239 backward chaining 53-4 Bar-Hillel 2, 70, 250 Barry 80,86, 192, 198,204 Barton 72, 257 basis 51 Bedeutung 11 Belnap 61 van Benthem 2-3, 60, 73, 75-6,

142,170,178,251 Berwick 72, 257 binary branching 193 binder 114, 149 Borghuis 142

298

Bouma 87 bracket operators 218-9, 221-2;

see also structural in­hibition

bracketing paradox 129 Bresnan 170 de Bruin 55 Buszkowski 70

Calder 87 Carnap 11 Carpenter 86, 178, 225, 260 case statement 167,169 case, accusative 78, 86 case, nominative 78, 86 categorematicity 22, 79 categorial grammar 1-3, 70; see

also Lambek calculus classical 70-71, 81; see also

Adjukiewicz/Bar-Hillel calculus

categorisation 15, 69 lexical 69

category form 15-6, 19 category object 15 category theory 15 Chomsky 13, 19, 191,208, 239,

255-7,259, 260-1 Church-Rosser property 51, 140-

1; see also diamond prop­erty

cliticisation 158 clitic climbing 158 clitic group 91 cohabitation condition 15-6, 69-

70, 250 combinatory grammar 87, 231-

2, 239, 251

Complex Noun Phrase Constraint 215-6, 238-9, 241,246

complementiser 168 compositionality 1-4, 137, 250,

260 composition 67,94,98, 120 compound main clause types 226-

7, 235 comprehension 12 computation rule 142 concrete syntax 12 configuration 66, 92-3 constituent structure 78, 80, 83,

118, 122, 129 construction, prosodic 13 construction, semantic 13 construction, semiotic 14-5, 21 constructive logic 3, 19 context-free grammar 15,69-70,

78, 232 contextuality 137, 158 contraction 192-3, 201, 206-7,

211; see also structural rule, contraction

contractum 141 contradiction 9 Coordinate Structure Constraint

80,215-6,222,228,238-41

coordination reduction 38, 124 coordination 38-40, 43, 76, 80,

82-84, 86 Boolean 180 constituent 124 iterated 192, 212 non-Boolean 86, 180 non-constituent 83, 85, 122 subject 77

unlike constituents 168 copula 146-7

of identification 75 of predication 75-6

Curry-Howard correspondence 3, 47-8,52,55,57,67,73, 142,162,165,171,251

Curry 3, 55 Cut-elimination 47, 62, 65, 72,

206, 250

D-structure 19, 260-1 de dicto reading 10, 30, 35-36;

see also non-specific read­zng

de re reading 10, 30-1, 35; see also specific reading

deductive system 18 deep structure 19, 259-60; see

also see also D-siructure definite clause grammar 70, 232 definite description 231, 248 dependent function 171, 181 dependent sum 181 Dekker 86 descriptive adequacy 256-7 determiner 89, 114, 185 diamond property 51, 140; see

also Church-Rosser prop­erty

differential penetrability 229, 245-6

discontinuous functor 104, 113 discontinuity 3, 92, 103 discontinuous coordination par-

ticle 114 discontinuous idiom 104, 113 disjoint union 165 ditransitive verb 84, 127-8

299

Dosen 48, 60, 165, 192 down-up cancellation 139-40, 142 Dowty 82, 84, 127,251 Dunn 65

E-Ianguage 256 embedding translation 192-3,199,

220-1 Emms 76, 116, 170 entailment 9-11, 24-5, 30, 39,

249 equivalence rule 142 expansion 206-7; see also struc­

tural modality, expan­s!on

explanatory adequacy 256-7 exponential 63 extraction site 1l0, 117, 227-8,

243 extraction, medial 80, 208, 231-

3 extraction, obligatory 228, 234 extraction, parasitic 192, 209-

11 extraction, subject 228, 244

Faltz 76 feature logic 178-179 feature percolation 118, 121-2,

251 head 175

Feys 55 field 7-8 filler 225, 229, 236, 243, 245 Fitch-style deduction 96-8, 1l0,

194-6, 198, 200, 208, 219, 222, 231,245

labelled 96 foot 91

300

formal language modell, 16,69 frame 53 freely generated set 8, 12 Fregean analysis 137, 250 Fregean intensionalisation 142 Frege 2, 4, 11,250 Friedman 140

Gabbay 92 Gaifman 2, 70 Gallier 170 Gallin 140 Gamut 1 gap 80, 104, 118, 225, 229, 238,

242 gapping 122-6

multiple 127 Gavarro 158, 225, 242 Gazdar 76, 118, 170, 258 gender 185, 187 generalisation 180 Generalised Phrase Structure Gram­

mar 170, 175, 189, 236 generation 70, 254 generative capacity 256-7

strong 69, 78 weak 69-70, 78

Gentzen sequent calculus 2, 47, 53-5,57,59,62,65,88-91,93,96,100,107,130, 149, 154, 162, 164, 166, 168, 173, 182, 194-5, 201,208,217,219

Girard 48, 61, 191-2 Government-Binding Theory 13,

19, 170,260-1 grammar equivalence 255

grammar of semantic categories 2

grammar subsumption 255 groupoid 66-7, 69-70, 73, 90,106-

7, 126, 197, 202, 204, 207

free 106-7,126 multi- 91-2, 107,221 semilattice-ordered 165, 207

Head-Driven Phrase Structure Gram-mar 170, 178, 232

headedness 89 Hendriks 42, 151,254 hereditary property 207; see also

persistence Hepple 80, 106, 143, 192, 204,

242, 254 hidden variable 140-1 Hindley 51 Hollenberg 134, 205, 254 Horn 239 Howard 55 Husserl 2, 250 hybrid logic 88; see also multi­

modal logic

I-language 256-7 identity element 103 identity rule 47, 53 IL 4, 7-8, 13, 44, 48, 138-41,

145, 255 infixation 103-4, 106, 115, 236 inhabitation 15, 17

legitimate 15 injection 167 intension 22, 28, 30, 137

intensional domain 129 intensional function application

137 intensionality 3, 11,22-4,26,34-

5,43, 137, 141 interrogativisation 225 intonation 249 intonational phrase 91 intuitionistic logic 3, 47-8, 52,

55-6, 59-63, 73, 192-3, 203

islandhood 80, 110, 192,213,215, 217, 222, 227-9, 233, 238-42, 246

Jacobson 251 Janssen 140 Johnson 178-9

Kandulski 66 Kanzawa 162 Karlgren 162 Katz 193 Kayne 76, 193, 228, 233 Keenan 76 Klein 87,118,170,251,258 knowledge oflanguage 255-6,259 Konig 254 Kripke model 59-60, 65, 192 Kurtonina 204, 207, 222

labelled deduction 92,105-7,134-5

labelled deductive system 93, 100 labelling 92-4

prosodic 92-3, 95 semantic 92-5

301

Lafont 48, 61 lambda calculus 3, 73,140, 171,

251 intensional 137-8, 140 simply typed 48-9, 137 typed 55, 73

Lambek 2-3, 15, 64-6, 162-3, 250-1

Lambek calculus 2, 60, 70, 73, 81,87,93,197,211,231-2

associative 64-5, 67, 70, 78-80, 83,87, 89, 94, 97-8,129,192-3,195-201, 203,205,209,213,218, 220-1

non-associative 66-7,70,72-3, 77-8, 80, 87-9, 93, 97,106,129,192-5,197, 202, 204-5, 208, 213, 218,220-1

Lambek/van Benthem calculus 197

language in extension 256-9; see also E-Ianguage

language in intension 256-9 see also I-language

Lasnik 19, 256 Lecomte 254 left node raising 84-5, 124 Lesniewski 2, 250 Leibniz 1 Leslie 80, 192 Lexical-Functional Grammar 170 Liberman 89 lifting 43, 78, 94-5, 97

302

linear logic 61-5,67,191-3,197, 199-201, 203; see also Lambek/van Benthem cal­culus

cyclic 198 non-commutative 64, 198,203;

see also Lambek calcu­lus

linking rule 92, 107 logic of resource 3, 48; see also

linear logic and Lam­bek calculus

Logical Grammar 1, 3 logical rule 47, 53 long distance dependency 157-

8, 225, 227-8 Ludlow 259

meaning 1, 3, 12,250 meaning categories 2 meaning postulate 27,31,36,43,

139 melody 249 Merin 12 metalanguage 256 metre 249 metrical tree 89 Milward 168 Mints 134 mixed composition 231-2 modal axiom 4 135 modal axiom T 134 modal closure 140-1, 143 modal licensing 143 modal logic, K 130, 134, 142,

208

modallogic, S4 63-4,130-1,134, 143, 208

modal logic, S5 130-1, 134, 143, 148,172, 175,181,183

modal logic, T 130 modally free 140 model theoretic semantics 11-12 monoid 103, 105-6, 151 monostratality 1, 3, 227, 261 monotonicity 61; see also weak-

enmg Montague Grammar 3,137, 149,

157, 225 Montague Semantics 3, 225 Montague 1-4, 11-2, 16, 18-19,

22,27,30,37,42-4,76-9, 114, 137, 139, 141, 147, 149, 251-2, 256, 261

Moortgat 2, 87, 89, 103, 105-6, 114, 120, 149, 159, 192, 213, 232-3, 254

Morrill 80, 82, 85-9, 91,96,104, 106-7,120,123,126-7, 129, 142-3, 150, 158, 162,165,192,198,204, 211-2, 218, 221, 225, 242, 254, 260

Move-a 191, 260-1 movement 208; see also Move-a multiarrow 15 multi category 15 multimodal logic 88, 91-2, 98,

100, 106; see also hy­brid logic

multiple binding 61,179

multiplicative 62-3 Muskens 140

natural deduction sequent cal­culus 52-5, 57-9, 149, 172-3,175,181-2

natural language processing 254, 256-7; see also genera­tion, parsing and recog­nition

non-directional di vision 101, 165 non-specific reading 10, 30, 154;

see also de dicta read­mg

normal form 51, 140 normal form, {3- 54 normal form, {3ry-Iong 54

Ncspor 91 Noun Phrase Constraint 239 null plural determiners 235

object language 256 object wide scope 9, 28 Oehrle 12,87 Ono 60 opaque context creating element

11

paraphrase 9-10, 31, 35,117,155, 159, 228, 235, 238, 249

parsing 71, 254 Partee 76, 86 particle verb 104 PASCAL 161 Pentus 70 permutation 197; see also struc­

tural rule, perm utation

303

Pereira 70 persistence 203; see also heredi-

tary property person 186, 188 phonetics 12 phonological phrase 91 phonological utterance 91 phonological word 91 phonology 12 phrase structure grammar 70,85,

118,121-2; see also context­free grammar

Pickering 86 pied-piping 79, 117-8,120-2,128,

227-8, 234-8, 247-8 medial 121 nominal 122 of reflexives 121,128, 160 prepositional 122

point of view 158 Polish School 2, 250 Pollard 87, 118, 121, 158, 170,

179, 251 polymorphism 122, 161-3, 168-

9, 182-3, 187 second-order 76, 178

polynomial 7-8 possessive, subject of 238-9, 242 Postal 193 Prawitz 53 Prawitz-style deduction 57, 80,

96, 143, 151, 163, 166, 172,181,209

preposition 16,35-6,43, 162-4 preposition stranding 133 prepositional phrase 162

304

presupposition 249 Prijatelj 142 Prince 89 production 12 program synthesis 53 program verification 53 projection principle 260 PROLOG 176 proof normalisation 53, 142 proper name 29, 43, 77-8 propositional attitude verb 11,

22-3, 30-1 prosodic construction 13 Prosodic Island Constraint 240 prosodic phrasing 110, 192,213-

5,217,222 psychological reality 258 PTQ 92-3, 139 Pullum 118, 170, 258-9

quantification 3, 42, 137, 236 quantifier floating 101, 103 quantifier phrase 43, 77-8, 114-

5 medial 116

quantifier raising 28,42, 152, 154, 157

quantifier scope 30, 114, 116-7 constraints 216, 217, 224

quantifying-in 28-31, 34-5, 37, 42-3, 104

raising to the worst case 43, 137 Reape 258 re-entrancy 178 reanalysis 193 recognition 254-5 redex 140 reference 2

reflexivisation 127, 137, 158, 160, 236

object-antecedent 127-9, 160 subject-antecedent 129, 159

relational type 40 relative pronoun 104, 110, 118,

121-2 relativisation 41-2,79-80,98,110,

117, 157, 208, 227-30, 232-3, 238, 246

medial 110 peripheral 110

relevance logic 61, 203 residuation 65, 72-3, 87-8, 90-

1,103,106-7,115,202, 221-2, 250

resolution refutation 180 rewrite rule 162 rhyme 249 rhythm 249 right node raising 84-5 rigid designator 139, 145 Ristad 72, 257 Roorda 165, 254 Rooth 76, 86 Ross 80, 215, 238 rule of formation 44, 70-2, 137

axiomatic 17-8 proper 17-8

Russell 2, 250

S-structure 19,260-1 Sag 87, 118, 158, 168, 170, 179,

251, 258 de Saussure 12, 249, 256 Schroeder-Heister 48, 192 scope 7, 140, 143; see also quan­

tifier scope Seldin 51

semantic construction 13 semantically potent features 170,

189 semigroup 64, 69-70, 89-90, 103,

105, 141, 197,203-5 Abelian 61, 197, 203; see

also semigroup, commu­tative

commutative 61, 197, 203; see also semigroup, Abelian

semilattice 61, 203 semiotic construction 142 sense 2, 11 Sentential Subject Constraint 215,

217,228,238-9,241-2 sequent 47, 51 sequent calculus 72-3, 78, 92, 96,

105, 107, 130, 134; see also Gentzen sequent cal­culus and natural de­duction sequent calcu­lus

Shamir 2, 70 Sheiber 70 ~gn language 12, 249 signified 12, 249 signifier 12, 249 Sinn 11 Skolem normal form 180 small clause 76 Smith 101 Solias 106, 123, 125-7 specific reading 10, 30, 154; see

also de re reading statement of formation 16, 141 Steedman 79, 82, 84, 86-7, 118,

124-5, 211, 213, 229, 231,251

stress 89

305

strong normalisation 51 structural description 249-50, 254 structural facilitation 192, 213,

221; see also structural rule

structural inhibition 213-4, 219, 221-2

structural modality 63-4, 125, 198, 213; see also ex­ponential

association 208 association and commutation

208 contraction 200-1,211 contraction and weakening

200-1 expansion 201, 212 exchange 198; see also struc­

tural modality, permu-tation

permutation 198-9, 222; see also structural modality, exchange

structural operator 3, 204, 207; see also structural modal­ity

association and commutation 205

conjunctive 205 contraction 206 disjunctive 205 permutation 205

structural rule 19,47,53-5,59-60,62-5,100,193,218; see also structural op­erator

adjunction identity 109 association 67,89,91-2,94,

109

306

contraction 19, 47, 53, 59, 61, 63-4,93

exchange 59, 198; see also structural rule, permu­tation

monotonicity 59; see also struc­tural rule, thinning and structural rule, weaken­mg

permutation 19,47,53,59, 64-5, 67, 93; see also structural rule, exchange

split-wrap 109 thinning 59; see also struc­

tural rule, monotonic­ity and structural rule, weakening

weakening 19, 47, 53, 59-61, 63-4, 93; see also structural rule, mono­tonicity and structural rule, thinning

subjacency 208 Subject Condition 239 subject equi 24 subject pro-drop 225, 235 subject wide scope 9, 28 substitution 7 su betitution salva veri tate 11 su bstructural logic 192, 202; see

also logic of resource and relevance logic

surface structure 19, 259-60 see also S-structure

syllable 91 symbol 1, 3-4, 12, 250 syncategorematicity 22-3,38, 76 syntactic structure 249-50, 254

Szabolcsi 87, 121,211,231, 251

T-model 19, 260 Tait 55 tautology 9 Taylor 48 tense 187, 189 that-less relatives 228, 234-5 theorem of formation 19, 73 theory of formation 18, 69, 71 theta criterion 260 Thomason 139 Thompson 48 topicalisation 225-7 transformation 192-3, 260; see

also movement transformational grammar 2, 19,

34, 191, 193, 208, 255, 258-9, 261

Troelstra 61 truth-conditional semantics 9, 11,

43 truth value 4, 10-11,22,74 Ty2 140 type assignment system 51 type map 73-4, 101, 133, 151,

162, 164-5, 171, 182, 203, 207, 251

basic 141 type raising 43; see also raising

to the worst case

unification 170, 180, 192, 251 graph 178

unification grammar 87, 161, 170, 176, 178, 191,251

unique readability 8, 44 universal grammar 256,258-9

up-down cancellation 140, 142 Uszkoreit 87, 251

vacuous abstraction 61 van Eijck 34 Venema 67, 106,206-7 verb form 187-8

base 155 verb-second 226 Versmissen 105, 205 Vogel 91

Wallen 134 wanna contraction 110 Wansing 60 Warren 140 weakening 192-3, 207, 211; see

also monotonicity and structural rule, weaken­Ing

wide scope and 86 wide scope or 86 Wilson 101 Wood 76 wrapping 103-4, 106, 113, 115,

128, 232-3, 236 head- 127

Yetter 198

Zeevat 87 Zhang 87

307