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Subject Index

A - b a s e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

A - c l a u s e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

A - i n s t a n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

A - i n s t a n t i a t i o n . . . . . . . . . . . . . . . . . . . . . . . . 63

A - r e s o l u t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

abs t rac t c l ause . . . . . . . . . . . . . . . . . . . . . . . . . 12

A C - u n i f i c a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 86

A C l - d i s u n i f i c a t i o n . . . . . . . . . . . . . . . . . . . . 86

a n s w e r subs t i tu t ion . . . . . . . . . . . . . . . . . . . 39

ar i ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

a t o m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

ax iomat i za f ion . . . . . . . . . . . . . . . . . . . . . . . . . 22

c o n s e q u e n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

c o n s e r v a t i v e e x t e n s i o n . . . . . . . . . . . . . . . 24

c o n s i s t e n t ( t h e o r y ) . . . . . . . . . . . . . . . . . . . . 24

c o n s t a n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

c o n s t r a i n e d c l ause . . . . . . . . . . . . . . . . . 6, 53

c o n s t r a i n e d log ic p r o g r a m m i n g . . 4, 13

c o n s t r a i n e d r e s o l u t i o n p r i n c i p l e . . 7, 13

cons t r a in t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

cons t r a in t o f a c l ause . . . . . . . . . . . . . . . . . 53

cons t r a in t s y s t e m . . . . . . . . . . . . . . . . . . . . . 50

cons t r a in t t h e o r y . . . . . . . . . . . . . . . . . . . 6, 50

co r r ec t a n s w e r . . . . . . . . . . . . . . . . . . . . . . . . 39

b o d y ( o f a c l ause ) . . . . . . . . . . . . . . . . . . . . . 19

b o u n d va r i ab l e . . . . . . . . . . . . . . . . . . . . . . . . . 18

c a n o n i c a l h o m o m o r p h i s m . . . . . . . . . . . . 40

car r ie r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

c l ause . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

c l ause f o r m . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

c l o s e d ( theory) . . . . . . . . . . . . . . . . . . . . . . . . 22

c o d o m a i n o f a subs t i tu t ion . . . . . . . . . . 20

c o m b i n a t i o n o f res t r ic t ion t h e o r i e s . , 76

c o m p l e t e set o f E -un i f i e r s . . . . . . . . . . . 37

c o m p l e t e se t o f 9~ -un i f i e r s .. . . . . . . . . . 7 4

c o m p l e t e s impl i f i ca t ion . . . . . . . . . . . . . . 74

c o n c e p t de sc r ip t i on . . . . . . . . . . . . . . . . . . . 31

c o n c e p t logic . . . . . . . . . . . . . . . . . . . . . . . . . . 31

c o n c e p t s y m b o l . . . . . . . . . . . . . . . . . . . . . . . 3 1

dec la ra t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

d e f i n i t e a n s w e r . . . . . . . . . . . . . . . . . . . . . . . . 38

def in i te c l ause . . . . . . . . . . . . . . . . . . . . . . . . . 19

d e f i n i t e c l a u s e t h e o r y . . . . . . . . . . . . . . . . . 23

d e p e n d e n t p a r a m e t e r s . . . . . . . . . . . . . . . . 88

d o m a i n o f a subs t i tu t ion . . . . . . . . . . . . . 20

E - c o n s i s t e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

E -d i sun i f i ca t i on p r o b l e m . . . . . . . . . . . . 79

E - e q u a l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

E - e q u i v a l e n c e . . . . . . . . . . . . . . . . . . . . . . . . . 37

E- f r ee a lgeb ra . . . . . . . . . . . . . . . . . . . . . . . . . 40

E - in s t ance . . . . . . . . . . . . . . . . . . . . . . . . 37, 81

E - s o l u t i o n . . . . . . . . . . . . . . . . . . . . . . . . 36, 80

E-un i f i ca t ion p r o b l e m . . . . . . . . . . . . . . . . 36

E -un i f i e r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

112

E-incons is ten t . . . . . . . . . . . . . . . . . . . . . . . . . 81 E - m a t c h i n g p r o b l e m .. . . . . . . . . . . . 83, 88

empty RQ-c lause . . . . . . . . . . . . . . . . . . . . . 53

e m p t y subst i tut ion . . . . . . . . . . . . . . . . . . . . 20

e m p t y theory . . . . . . . . . . . . . . . . . . . . . . . . . . 24

equal i ty s ymbo l . . . . . . . . . . . . . . . . . . . . . . . 18 equat ional constra int . . . . . . . . . . . . . . . . . . . 6

equat ional const ra in t theory . . . . . . . . . 79

equat ional RQS . . . . . . . . . . . . . . . . . . . . . . . 79

equat ional theory . . . . . . . . . . . . . . . . . . . . . 23

except ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

exhaus t ive refuta t ion strategies . . . . . 67

e x i s t r e s t r i c t i o n . . . . . . . . . . . . . . . . . . . . . . . . 32

e x p a n s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

ex tens ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

F-va l id . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

fact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

feature agreement . . . . . . . . . . . . . . . . . . . . . 29 feature d i sagreement . . . . . . . . . . . . . . . . . 29

feature logic . . . . . . . . . . . . . . . . . . . . . . 12, 28

feature select ions . . . . . . . . . . . . . . . . . . . . . 29

fea ture s ymbo l . . . . . . . . . . . . . . . . . . . . . . . . 28

f e a t u r e t e r m . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

feature theory . . . . . . . . . . . . . . . . . . . . . . . . . 28

feature unif ica t ion . . . . . . . . . . . . . . . . . 4, 47

f ini tary theory . . . . . . . . . . . . . . . . . . . . . . . . . 38

f i r s t o r d e r t h e o r y . . . . . . . . . . . . . . . . . . . . . . 22 fo rmula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

free ( funct ion symbol ) . . . . . . . . . . . . . . . 24

free variable . . . . . . . . . . . . . . . . . . . . . . . . . . . t 9

func t ion symbo l . . . . . . . . . . . . . . . . . . . . . . 18

general equal i ty handl ing . . . . . . . . . 4, 11

general equat ional p rob lem . . . . . . . . . . 88

generic mode l . . . . . . . . . . . . . . . . . . . . . . . . . 40 generic m o d e l o f an RQS . . . . . . . . . . . . 70

g o a l c l a u s e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 g round (object) . . . . . . . . . . . . . . . . . . . . . . . 18 g round s a lgebra . . . . . . . . . . . . . . . 20

h e a d (o f a c l a u s e ) . . . . . . . . . . . . . . . . . . . . . . 19 He r b r a n d base . . . . . . . . . . . . . . . . . . . . . . . . 20

Herb rand m o d e l . . . . . . . . . . . . . . . . . . . . . . 22 Herb rand T h e o r e m for R Q - c l a u s e s . 63

H e r b r a n d u n i v e r s e . . . . . . . . . . . . . . . . . . . . 20

Incons i s tency L e m m a . . . . . . . . . . . . . . . . 82 independent parameters . . . . . . . . . . . . . . 88

inheri tance h ierarchy . . . . . . . . . . . . . . . . . 29

initial algebra . . . . . . . . . . . . . . . . . . . . . . . . . . 43

in t roduced variables . . . . . . . . . . . . . . . . . . 20

kernel o f a c lause . . . . . . . . . . . . . . . . . . . . . 53

K L - O N E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

least Herb rand m o d e l . . . . . . . . . . . . . . . . 39

Lif t ing L e m m a . . . . . . . . . . . . . . . . . . . . . . . . 66

literal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

logic p rog ram . . . . . . . . . . . . . . . . . . . . . . . . . 23

logic p r o g r a m m i n g . . . . . . . . . . . . . . . . 4, 12

logical symbo l . . . . . . . . . . . . . . . . . . . . . . . . 18

logical ly equivalent . . . . . . . . . . . . . . . . . . . 22

M-va l id . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 matr ix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

mos t general E-uni f ie r . . . . . . . . . . . . . . . 37

m u l t i e q u a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . 21

non- logica l s y mb o l . . . . . . . . . . . . . . . . . . . 18

n u m b e r restr ict ion . . . . . . . . . . . . . . . . . . . . 32

open fo rmula . . . . . . . . . . . . . . . . . . . . . . . . . . 19

o p e r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

paramodula t ion . . . . . . . . . . . . . . . . . . . . 4, 11

p r e d i c a t e s y m b o l . . . . . . . . . . . . . . . . . . . . . . 18

p r o g r a m c l a u s e . . . . . . . . . . . . . . . . . . . . . . . . 12

query . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 quot ient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

113

R-sat is f iabi l i ty . . . . . . . . . . . . . . . . . . . . . . . . 51

R-va l id i ty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

9 l - r educ t ion ca lcu lus . . . . . . . . . . . . . . . . . 73

5R-reduction s y s t e m . . . . . . . . . . . . . . . . . . 73

9~-simplif icat ion ca lcu lus . . . . . . . . . . . . 73

9 l - s impl i f i ca t ion s y s t e m . . . . . . . . . . . . . 73

9 l -un i f i ca t ion ca lcu lus . . . . . . . . . . . . . . . 74

~R-un i f i ca t i on s y s t e m . . . . . . . . . . . . . . . . . 74

9 t -un i f i e r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

r e d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

R e d u n d a n c y L e m m a . . . . . . . . . . . . . . . . . 85

re la t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

r e l a t i v i z a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

r e n a m i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Repre sen t a t i on T h e o r e m . . . . . . . . . . . . . 84

R e s o l u t i o n P r i n c i p l e . . . . . . . . . . . . . . . . . . . . 5

res t r ic ted quan t i f i ca t ion sys t em . . . . . 50

res t r ic ted quan t i f i e r . . . . . . . . . . . . . . 26, 53

r e s t r i c t i o n (o f a quan t i f i e r ) ........... 50

res t r i c t ion (o f a subst i tu t ion) . . . . . . . 21

r e s t r i c t i o n t h e o r y . . . . . . . . . . . . . . . . . . . . . . 50

r o l e s y m b o l . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

ro le va lue m a p . . . . . . . . . . . . . . . . . . . . . . . . . 32

R Q - c l a u s e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

R Q - c l a u s e f o r m . . . . . . . . . . . . . . . . . . . . . . . 58

RQ -de r iva t i on . . . . . . . . . . . . . . . . . . . . . . . . . 61

R Q - f o r m u l a e . . . . . . . . . . . . . . . . . . . . . . . . . . 53

RQ-re fu ta t ion . . . . . . . . . . . . . . . . . . . . . . . . . 61

R Q - r e s o l u t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 61

R Q - s a t i s f i a b l e . . . . . . . . . . . . . . . . . . . . . . . . . 55

R Q - s i g n a t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . 52

RQ-s t ruc tu re . . . . . . . . . . . . . . . . . . . . . . . . . . 54

R Q - t a u t o l o g y . . . . . . . . . . . . . . . . . . . . . . . . . . 55

RQ-unsa t i s f i ab le . . . . . . . . . . . . . . . . . . . . . . 55

RQ -va l i d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

R Q S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

ru le (c lause) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Z - a l g e b r a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Z - a s s i g n m e n t . . . . . . . . . . . . . . . . . . . . . . . . . 20

Z - c o n g r u e n c e . . . . . . . . . . . . . . . . . . . . . . . . . 19

Z - d i s e q u a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 21

X - e n d o m o r p h i s m . . . . . . . . . . . . . . . . . . . . . 19

Z - e q u a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Z - h o m o m o r p h i s m . . . . . . . . . . . . . . . . . . . . 19

Z - i n s t a n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Z - s t ruc tu re . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Z- subs t i t u t ion . . . . . . . . . . . . . . . . . . . . . . . . . 20

Z - t e r m a lgebra . . . . . . . . . . . . . . . . . . . . . . . . 20

Z - m o d e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

sat isf iabil i ty . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

sat isf iable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

semant ic n e t w o r k . . . . . . . . . . . . . . . . . . . . . 31

s igna ture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

s ignature wi th

res t r ic ted quant i f ie rs . . . . . . . . . . 52

s i m p l e c o n s t r a i n t . . . . . . . . . . . . . . . . . . . . . . 73

s imple res t r ic t ion . . . . . . . . . . . . . . . . . . . . . 73

s k o l e m f u n c t i o n . . . . . . . . . . . . . . . . . . . . . . . 20

so r t d e c l a r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . 25

sort h i e r a r ch y . . . . . . . . . . . . . . . . . . . . . . . . . 12

so r t s i g n a t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . 25

sort s t ruc ture . . . . . . . . . . . . . . . . . . . . . . . . . . 25

s o r t s y m b o l . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

sor t t h e o r y . . . . . . . . . . . . . . . . . . . . . . . . 12, 25

sor t un i f i ca t ion . . . . . . . . . . . . . . . . . . . . . 4, 12

sor t un i f ica t ion p r o b l e m . . . . . . . . . . . . . 45

s o r t e d l o g i c . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

sor ted r e so lu t i on . . . . . . . . . . . . . . . . . . . . . . 12

sou n d n es s and c o m p l e t e n e s s

o f R Q - r e s o l u t i o n . . . . . . . . . . . . . . 66

special equat iona l p r o b l e m . . . . . . . . . . 88

s tandard equa l i ty t h e o r y . . . . . . . . . . . . . 23

s t rongly c o m p l e t e s impl i f ica t ion

ca lculus . . . . . . . . . . . . . . . . . . . . . . . . . 74

s t r u c t u r e d so r t . . . . . . . . . . . . . . . . . . . . . . . . . 28

subsor t dec la ra t ion . . . . . . . . . . . . . . . . . . . 25

subs t i tu t ion c o m p o n e n t . . . . . . . . . . . . . . 20

su b s t i t u t i o n w i th e x c e p t i o n s ......... 80

subs t i tu t ion wi th sor t res t r ic t ions . . . 4 6

subs t ruc tu re . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

114

T - B o x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

t a u t o l o g y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

t a x o n o m i c a l k n o w l e d g e ... . . . . . . . . 3, 31

t e rm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

t e rm declara t ion . . . . . . . . . . . . . . . . . . . . . . . 25

t e rmino log ica l a x iom . . . . . . . . . . . . . . . . . 32

t e r m i n o l o g y . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

t h e o r e m o f a t h e o r y . . . . . . . . . . . . . . . . . . . 22

t h e o r y r e s o l u t i o n . . . . . . . . . . . . . . 4, 10, 12

theory uni f ica t ion . . . . . . . . . . . . . . . . . . 4, 11

total t he o ry re so lu t ion . . . . . . . . . . . . . . . . 13

uni f ica t ion a lgor i thm . . . . . . . . . . . . . . . . . 11

Uni f i ca t ion H i e r a r c h y . . . . . . . . . . . 11, 38

Uni f i ca t ion T h e o r y . . . . . . . . . . . . . . . . . . . 11

un i ta ry t h eo ry . . . . . . . . . . . . . . . . . . . . . . . . . 38

u n i v e r s e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

u n k n o w n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

unsa t i s f iable . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

va l id . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

va lue res t r ic t ion . . . . . . . . . . . . . . . . . . . . . . . 32

var iable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

v a r i e t y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

we l l - so r t ed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

X- res t r i c t ed E-un i f i ca t ion p r o b l e m . 88

Symbol Index

V F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

V x F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

V - x F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

V X : R F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

g ' x : s F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

VR F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

V R /2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

V R : C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3 F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

~ x ' F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 _ x F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3X:R F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3 x : s F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 __~ [ o ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3 R F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

. _ ~ : C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3<_nR:C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3 > n R . ' C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

C//R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3

~ / / R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

S - < S ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

A := C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

A - = C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

C m D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

C u D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

-~C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

R, I .S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

~ s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

s n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

s t a t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

r Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

( A , a ) 1= F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

( A , oO ~ VX:R F . . . . . . . . . . . . . . . . . . . . . . 55

( A , a ) / = J x : R F . . . . . . . . . . . . . . . . . . . . . . . 55

( A , a , C ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

A ~ F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

M ~ F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

T g F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

F /= G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

F -~ G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

M o d ( F ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

T h ( ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

T ( V ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

FE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 JE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

~z+fl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

ICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

[ 0 ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

[ a ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

a - T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

D o i n G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

116

C o d f f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

V C o d c r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

s =E t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 cr =E ~" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Cr=E 7:/V1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

S >-E cr [W] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

~, >-E a - ~ [ W ] . . . . . . . . . . . . . . . . . . . . . . . . 81

~ >-E ~ [W] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 S U B ( V , W ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

UE(F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

UE(I~ / i ~ l ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

c U E ( F ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

I.tUE( F) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Se( l" , A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

( F ) E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

(( ri )e: i ~ 0 . . . . . . . . . . . . . . . . . . . . . . . . . 38

( F , A ) E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 ( Q .O )E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 ( V u B x V y . O )E . . . . . . . . . . . . . . . . . . . . 89

( V y a x . 1-')E . . . . . . . . . . . . . . . . . . . . . . . . . 89 ( v v 3x v r . r )e . . . . . . . . . . . . . . . . . . . . 89

( V u ---3x V y . r U A )E . . . . . . . . . . . . . . 89

( t/U . S = t )E . . . . . . . . . . . . . . . . . . . . . . . . . . 89 ( V u si = ti (l_~i~_n))E . . . . . . . . . . 89

( 3 x . F ) e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

( 3 x . F U A )E . . . . . . . . . . . . . . . . . . . . . . . . 89 ( 3 x . A )E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Lecture Notes in Artificial Intelligence (LNAI)

Vol. 345: R.T. Nossmr~ (Ed.), Advanced Topics in Artificial Intelligence. VII, 233 pages. 1988.

Vol. 346: M. Reinfrank, J. de Kleer, M. L. Ginsberg, E. Sande- wall (Eds.), Non-Monotonic Reasoning. Proceedings, 1988. XIV, 237 pages. 1989.

Vol. 347: K. Morik (Ed.), Knowledge Representation and Organization in Machine Learning. XV, 319 pages. 1989.

Vol. 353: S. H611dobler, Foundations of Equational Logic Programming. X, 250 pages, i989.

Vol. 383: K. Furukawa, H. Tanaka, T. Fujisaki (Eds.), Logic Programming '88. Proceedings, 1988. IX, 251 pages. 1989.

VoI. 390: J.P. Martins, E.M. Morgado (Eds.), EPIA 89. Proceedings. 1989. XII, 400 pages. 1989.

Vol. 395: M. Schmidt-Schaug, Computational Aspects of an Order-Sorted Logic with Term Declarations. VIII, 171 pages. t 989.

Vol. 397: K.P. Jantke (Ed.), Analogical and Inductive Inference. Proceedings, 1989. IX, 338 pages. 1989.

Vol. 406: C.J. Barter, M.J. Brooks (Eds.), A1 '88. Proceedings, 1988. VIII, 463 pages. 1990.

Vol. 418: K.H. BIS.sius, U. Hedtsttick, C.-R. Rollinger (Eds.), Sorts and Types in Artificial Intelligence. Proceedings, 1989. VIII, 307 pages. 1990.

Vol. 419: K. Weichselberger, S. POhlmann, A Methodology for Uncertainty in Knowledge-Based Systems. VIII, 132 pages. !990.

Vol. 422: B. Nebel, Reasoning and Revision in Hybr id Representation Systems. XII, 270 pages. 1990.

Vol. 437: D. Kumar (Ed.), Current Trends in SNePS - Semantic Network Processing System. Proceedings, 1989. VII, 162 pages. 1990.

Vol. 444: S. Ramani, R. Chandrasekar, K.S.R. Anjaneyulu (Eds.), Knowledge Based Computer Systems. Proceedings, 1989. X, 546 pages. 1990.

Vnl. 446: L. Pliimer, Termination Proofs for Logic Programs. VIII, 142 pages. 1990.

Vol. 449: M.E. Stickel (Ed.), 10th International Conference on Automated Deduction. Proceedings, 1990. XV1, 688 pages. [990.

Vol. 451 : V. Mar~, O. Step~inkov~i, Z. Zdr~ihal (Eds.), Artificial Intelligence in Higher Education. Proceedings, 1989. IX, 247 pages. 1990.

Vol. 459: R. Studer (Ed.), Natural Language and Logic. Proceedings, 1989. VII, 252 pages. 1990.

Voi. 462: G. Gottlob, W. Nejdl (Eds.), Expert Systems in Engineering. Proceedings, i990. IX, 260 pages, t990.

Vol. 465: A. Fuhrmann, M. Morreau (Eds.), The Logic of Theory Change. Proceedings, 1989. X, 334 pages. 1991.

Vol. 475: P. Schroeder-Heister (Ed.), Extensions of Logic Programming. Proceedings, 1989. VIII, 364 pages. 1991.

VoL 470: M. Filgaeiras, L. Damas, N. Moreira, A.P. Tom,~s rEds.). Natural Language Processing. Proceedings, 1990. Vtl, 253 pages. 1991.

Vol. 478: J. van Eijck (Ed.), Logics in A1. Proceedings. 1990. IX, 562 pages. 1991.

Vol. 481: E. Lang, K.-U. Carstensen, G~ Simmons, Modelling Spatial Knowledge on a Linguistic Basis. IX, 138 pages. 199i.

Vol. 482: Y. Kodratoff (Ed.), Machine Learning - EWSL-91. Proceedings, 1991. XI, 537 pages. 1991.

Vol. 513: N. M. Mattos, An Approach to Knowledge Base Management. IX, 247 pages. 1991.

Vol. 515: J. P. Martins, M. Reinfrank (Eds.), Truth Maintenance Systems. Proceedings, 1990. VII, 177 pages. 1991.

Vol. 517: K. NBkel, Temporally Distributed Symptoms in Technical Diagnosis. IX, 164 pages. 1991.

VoI. 518: J. G. Williams, lnstantiation Them'y. VIII, 133 pages. 1991.

Vol. 522: J. Hertzberg (Ed.), European Workshop on Planning. Proceedings, 1991. VII, 121 pages. !991.

Vol. 535: P. Jorrand, J. Kelemen (Eds.), Fundamentals of Ar- tificial Intelligence Research. Proceedings, 1991. VII1, 255 pages. 1991.

Vol. 541 : P. Barahona, L. Moniz Pereira, A. Porto (Eds.), EPIA '91. Proceedings, 1991. VIII, 292 pages. 1991.

Vol. 542: Z. W. Ras, M. Zemankova (Eds.), Methodologies for Intelligent Systems. Proceedings, 1991. X, 644 pages. 1991.

Vol. 543: J. Dix, K. P. Jantke, P. H. Schmitt (Eds.), Non- monotonic and Inductive Logic. Proceedings, 1990. X, 243 pages. 1991.

Vol. 546: O. Herzog, C.-R. Rollinger (Eds.), Text Understand- ing in LILOG. XI, 738 pages, t991.

VoI. 549: E. Ardizzone, S. Gaglio, F. Sorbello (Eds.), Trends in Artificial Intelligence. Proceedings, i991. XIV, 479 pages. 1991.

VoI. 565: J. D. Becker, I. Eisele, F. W. Mtindemann (Eds.), Par- allelism, Learning, Evolution. Proceedings, 1989. VIII, 525 pages. 1991.

Vol. 567: H. Boley, M. M. Richter (Eds.), Processing Declara- tive Kowtedge. Proceedings, 1991. XII, 427 pages. 1991.

Vol. 568: H.-J. B0rckert, A Resolution Principle for a Logic with Restricted Quantifiers. X, 116 pages. 1991.

Lecture Notes in Computer Science

Vol. 509: A. Endres, H. Weber (Eds.), Software Development Environments and CASE Technology. Proceedings, 1991. VIII, 286 pages. 1991.

Vol. 510: J. Leach Albert, B. Monien, M. Rodrfguez (Eds.), Automata, Languages and Programming. Proceedings, 1991. XII, 763 pages. 1991~

Vol. 511 : A. C. F. Colchester, D.J. Hawkes (Eds.), Information Processing in Medical Imaging. Proceedings, 1991. XI, 512 pages. 1991.

Vol. 512: P. America (Ed.), ECOOP '91. European Conference on Object-Oriented Programming. Proceedings, 1991. X, 396 pages. 1991.

Vol. 513: N. M. Mattos, An Approach to Knowledge Base Management. IX, 247 pages. 1991. (Subseries LNAI).

Vol. 514: G, Cohen, P. Charpin (Eds.), EUROCODE '90. Pro- ceedings, 1990. XI, 392 pages. 1991.

Vol. 515: J. P. Martins, M. Reinfrank (Eds.), Truth Maintenance Systems. Proceedings, 1990. VII, 177 pages. 1991. (Subseries LNAI).

Vol. 516: S. Kaplan, M. Okada (Eds.), Conditional and Typed Rewriting Systems. Proceedings, 1990. IX, 461 pages. 1991.

Vol. 517: K. N/Skel, Temporally Distributed Symptoms in Technical Diagnosis. IX, 164 pages. 1991. (Subseries LNAI).

Vol. 518: J. G. Williams, Instantiation Theory. VIII, 133 pages. 1991. (Subseries LNAt).

Vol. 519: F. Dehne, J.-R. Sack, N. Santoro (Eds.), Algorithms and Data Structures. Proceedings, 1991. X, 496 pages. 1991.

Vol. 520: A. Tarlecki (Ed.), Mathematical Foundations of Computer Science 1991. Proceedings, 1991. XI, 435 pages. 199l.

Vol. 521 : B. Bouchon-Meunier, R. R. Yager, L. A. Zadek (Eds.), Uncertainty in Knowledge-Bases. Proceedings, 1990. X, 609 pages. 1991.

Vol. 522: J. Hertzberg (Ed.), European Workshop on Planning. Proceedings, 1991. VII, 121 pages. 1991. (Subseries LNA!).

Vol. 523: J. Hughes (Ed.), Functional Programming Languages and Computer Architecture. Proceedings, 1991. VII1, 666 pages. 1991.

Vol. 524: G. Rozenberg (Ed.), Advances in Petri Nets 1991. VIII, 572 pages. 1991.

Vol. 525: O. Gtinther, H.-J. Schek (Eds.), Large Spatial Databases. Proceedings, 1991. XI, 471 pages. 1991.

Vol. 526: T. Ito, A. R. Meyer (Eds.), Theoretical Aspects of Computer Software. Proceedings, 1991. X, 772 pages. 1991.

Vol. 527: LC.M. Baeten, J. F. Groote (Eds.), CONCUR '91. Proceedings, 1991. VIII, 541 pages. 1991.

Vol. 528: J. Maluszynski, M. Wirsing (Eds.) Programming Language Implementation and Logic Programming. Proceed- ings, 1991. XI, 433 pages. 1991.

Vol. 529: L. Budach (Ed.) Fundamentals of Computation Theory. Proceedings, 1991. XII, 426 pages. 1991.

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Vol. 531: E, M. Clarke, R. P. Kurshan (Eds.), Computer-Aided Verification. Proceedings, 1990. VIII, 372 pages. 1991.

Vol. 532: H. Ehrig, HM. Kreowski, G. Rozenberg (Eds.), Graph Grammars and Their Application to Computer Science. Pro- ceedings, [990. X, 703 pages, i991.

Vol. 533: E. BOrger, H. Kleine Brining, M M. Richter, W. SchOnfeld (Eds.), Computer Science Logic. Proceedings, 1990. VIII, 399 pages. 1991.

Vol. 534: H. Ehrig, K. P. Jantke, F. Orejas, H. Reichel (Eds.L Recent Trends in Data Type Specification. Proceedings, 1990. VIII, 379 pages. 1991.

Vol. 535: P. Jm'rand, J. Kelemen (Eds.), Fundamentals of Arti- ficial Intelligence Research. Proceedings, 1991. VIII, 255 pages. 1991. (Subseries LNAI).

Vol. 536: J. E. Tomayko, Software Engineering Education. Pro- ceedings, 1991~ VIII, 296 pages. 1991.

Vol. 539: H. F. Mattson, T. Mora, T. R. N. Ran (Eds.), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Proceedings, 1991. XI, 489 pages. 1991.

Vol. 540: A. Prieto (Ed.), Artificial Neural Networks. Proceed- ings, 1991. XIII, 476 pages. 1991.

Vol. 541: P. Barahona, L. Moniz Pereira, A. Porto (Eds.), EPIA '91. Proceedings, 1991. VIII, 292 pages. 1991. (Subseries LNAI).

Vol. 542: Z. W. Ras, M. Zemankova (Eds.), Methodologies for Intelligent Systems. Proceedings, 1991. X, 644 pages. 1991. (Subseries LNAI).

Vo]. 543: J. Dix, K. P. Jantke, P. H. Schmitt (Eds.), Non- monotonic and Inductive Logic. Proceedings, 1990. X, 243 pages. 1991. (Subseries LNAI).

Vol. 546: O. Herzog, C.-R. Rollinger (Eds.), Text Understand- ing in LILOG. XI, 738 pages. 1991. (Subseries LNAI).

Vol. 549: E. Ardizzone, S. Gaglio, F. Sm'bello (Eds.), Trends in Artificial Intelligence. Proceedings, 1991. XIV, 479 pages. 1991. (Subseries LNAI).

Vol. 565: J D. Becker, I. Eisele, F. W. Mandemann (Eds.), Par- allelism, Learning, Evolution. Proceedings, 1989. VIII, 525 pages. 1991. (Subseries LNAI).

Vol. 567: H. Boley, M. M. Richter (Eds.), Processing Declara- tive Kowledge. Proceedings, 1991. XII, 427 pages. 1991. (Subseries LNAI).

Vol. 568: H.-J. Bt~rckert, A Resolution Principle for a Logic with Restricted Quantifiers. X, 116 pages. 1991. (Subseries LNAI).