... t h e r e l a t i o n i s p a r t i a l . T h e c o n v e r s e r e l a t i o n i s " w h o i s ' i n ' ? " .... 6.5 Comparison with the Modeling of Other Domains and Integration of.
SPECIFICATIONS FOR INTEROPERABILITY: FORMALIZING IMAGE SCHEMATA FOR GEOGRAPHIC SPACE Andrew U. Frank and Martin Raubal Department of Geoinformation Technical University Vienna Gusshausstrasse 27-29/1271 A-1040 Vienna, Austria Phone: +43-1-58801/3786 Fax: +43-1-504 35 35 {frank, raubal}@geoinfo.tuwien.ac.at
Abstract !! " " # # $% # & '( *),+-/.0-1 2 # 34 3 5 647 #8# 46 9 # ' 4 :04 77 64 ; `_ , ) + ^ - 4 , ? 6 ; 9
7 , L
4 L D . # a. @ : 7
^' ^ + @ a_ b ^ c F . , X d
# 7 Buehler 7 , and , McKee (1996) e e f g ' h 5 e e (1997) 4 4 g ' 4 ji h ^ , ? " %$ # L K E K \ , ) + /- . /- ji k 3 9
< l m 7
K
< 4 4 " '
n d d
7 o p o
4 q ' 5 rO H d 5 r?, r 7 p 4 %. 4 j 5 d
7 ji K4>' 4
= * L KK L
\ # 7 # L r s 7 @ ] n # 0 , d
, , # / d
7 4 >' 4 d
u t , ? ' ( 4 ( K
O 4 >' 4 d
u t , ? ( r 4 0
0 4 >' 4
v. 2 w
9 7 f f , ) + x - 7 # ^
^
d
7 4 >' 4 y
4 ji ; . 7 o d O z p 7 d r rr d r n 0
J 0
4 7 d
7 h # 7 # 4 l :
{
4 | }
# d
4 >' 4
4 : K L K5
\ d
7 K?, K # , ' 4 >' 4
4 . 9
' d
;4 ' # # s 7 4 ( d ( 4 d
# O , ) + - d r
o O d p , ? :% d 4 r r~4
v
a. C B / * /
/ ~ & S c , * = \: ~ , , d p: 8 7 # ~ ; Q q w l
~ a: G , Q E , ? u G @ W E 5 x a. " :
? u u
#
7 H , ? r 4 >' 4
4 `. ] 5 ] 4 4 7 d
J ] ~ 4 ] @ ] 4 ] @ ] 4 D , ) 7 h/- F 5 7 4 ' ! ( { " 4 d
# # ( r
7 ' 7 >' H : f #
(Chevallier . 1981; Mark 1993; Kuhn 1994)
+ # 4 !4 ! # C 5 :d 4 q4 77 & C47 4:
42H G$A 44 # = . +
# ; 4
; D Johnson F 7 (Johnson $A 1987) ?,{ 1987 Lakoff 1987
# ]4 7:74^ @ # 4 5 44^ 4 4. & ij C7 d &6 # k4 k d ;x # # $%qDMON,P*Q,+N=R;:dS/Q,T,:]U*V),+N=R;:] kW@N,X=R;Y,Q,U*Z,F.]654 # k4: :/ *,^s74* , 5^ , 44r'>4 (Hayes 1978; Hayes K~ ; R 5 L , ) # >' . (Egenhofer and Mark 1995) 1985; Hobbs and Moore 1985) %$ z 4 & # 7 9 , ? ' 3
ji 6 H 2
9 # # d o 7 p O 7 O 5 o ] 4 ji 9 ' 0 , ) + /- . , Y # 4 e w 4
h 4
ji w u t x 7 # u t H
7 # 4 3 , m
6 # @ . #
m
ji
# " 4
" ! 5 l ' 7
! ! ] g d
g'> r . + /- C C ! C
# ! 4
! & 4 7 4 4 C C-/ C # 5 6 d
4 5
^& 4 5 * &
( ' 4
# 4
O. /- & A$ r # # ( (
# ( 4
( D a. a. z : OM , N * P , Q += N ; R 2 : /S , Q T,2 : * U V , ) + = N ; R : KW@, N = X ; R , Y , Q * U , Z F 4 K * 4 =
ji 4 . 2 Formalizing Spatial Meaning tu?,),+- 47 tu!7 ^7
5 # m' 4
D . # a. : 4 F %. OM # 7 4 o 5 d
d4 >' 4
d o r q ' d
# o ` (Frank 4 1996a) ] D F.T,?,5 : , ^ 1987 s74? dHerskovits 4 1986; 4 Lakoff # 47 ^?," 7 }4'>4 } " ', 4'>4 ',K $% d 4. 9 ;2 LL # 4O(K ] 0s7 '3 # 7 # ]7 d # 774 ' r7 ` 4 ^ " d { 4{s7 ' # 7 # CC74 4C7 4C q '(&D?,&q 4 * 4 & q6-/[,MOF . ;
/ K ; , 4 ( d s 7 & '
ji z . +
# (Egenhofer 1992) 4
r r 4 # ] ] r 7 o r
0 4 J. , 7 ; ;7 9 d
9 2
# 9 4
9 L K O 7 K~ 7 L D a. a. : # 5 , ' 4 7 F7 4 O o O , ) + (Kuhn and Frank 1991; . Kuhn 1993)
3 Specification of Image Schemata 4 ; 6 7 4 6 7 # * :
# 5 u t 4 E Johnson (1987) u t £ d
£ £ 4 7 7 C A $ x , ?
5 # , 4 ¡ , ¢ 7 # f f # , ? f d 5
z . +
# ( 4
4 7 4 ; 5 4 5 O: , ? E :0 67 2
H 4 7 2 2
4 7 7 3 6 4 ` a_ 7 4 # m 4 # @ . ' 6
6 4 L m
7 ; m 4 4 3 g # ;
4 7 7 ^ 7 4 k ' k 4 ' # " ` a_
3, ? r & & A$ # & , ? @ . , Q m
# (Kuhn and Frank 1991) 4
C r : H : k 4 x m k 5 ' # :
4' k 7 5 4 : x 4 4 7 7 L \ / L r 4 4 r d H , ? r p A$ o 5 C 4
k 7 # 4 7 7 k x
. h # 5 m k 4 5 k 4 ; . ¤F # L4 . Johnson’s (1987 ¥J¦¨§ª©«¬ §8®°¯ ±/«² «°§8³® ¥J¦¨´2µ ¶8² ·¸¬ ¦¨§ ±/² ¦ ³°¹8«ºª® ¥J¦¨¶ª§ª©®°¯ »¼¦¨¯ ³® ½J®·¾© ¯ «¬ §ª©`½J®°´]¦¨¿8«² ÂO© © ¯ «³°©¬ ¦¨§ Ã9«·¸·¸Ä¼¥J¦¨¶ª§ª© À §8«°Á² ®°´]®°§ª© Ǭ §ª¹ ¥J®°§ª©®°¯ Ä Å ®°¯ ¬ µ Æ8®°¯È Å «°© Æ ¥>È1³² ® ÉH®«°¯ ļÊË«°¯ Ì˳«² ® Ã9®°¯ ºª¬ §8º Ìε² ¬ © ©¬ §8º Å «°¯©Ä¼Í]Æ8¦ ² ® Êζ8² ² Ä À ´2µ © È Ã9«°©³°Æ8¬ §8º Ì檵®°¯ ¬ ´2µ¦ ·¸¬ ©¬ ¦¨§ ¥J¦¨§ª©«³°© Ï ©®°¯ «°©¬ ¦¨§ Å ¯ ¦ ³®·¸· Ìζª¯ »¼«³® Ð`Á Ѹ®³°© ¥J¦ ² ² ®³°©¬ ¦¨§ Table 1: Selective list of image schemata (Johnson 1987 p.126).
3.1 Previous Formal Description of Image Schemata Y,6 4:@474;m'> # d # ' : ( # o
r 4 3& ' V # d 5 (Wierzbicka K 7 4 KK 1996) = , ? , ' K L
L d
r $ # p . (Mark et al. 1995) 6 5 7 ; , , ? m # 7 # ; 6 < d
z d < 7 7 9 Ý
@
7 4 ] , ) + 7 8# # 5 *, ' # \ (Campari = , ? K and L Frank 7# # . 1995) 3.4 Methods to Formalize Image Schemata 3.4.1 Predicate Calculus MO nCDª bcF # 5g GkP*N=R;Q,+ R;VUÞ4 74 # 7 74.\+3 '>:Ë q 7 7H H vq$A 445o?, z44 '>:Ë7vv '9 L'9] 2 :`?, n*47/ # d44 (Hayes 1977; McCarthy 1985)
3.4.2 Relations Calculus 2 5 00 # J @DV # H bb S/ * -/ K bbF:j7 4; L ; $% 94 q (Frank 1992; Frank 1996b) . /S K >' ji 674 # ; K 7 7 (Schroeder 1895; Maddux 1991) 9 3 4 < K ; 7
; L ; d
} D ; Û r Û L F L , ? 4 p. q 4 3 4 H , ? r ' 9 5 7 L ;D ; d
4 ; ; ( 7 7 4 d F # 5 r ( 4 d
( # ( 5 d 4 2 . 4 7 K 4 >' E E K 4 : = # = L d
K , ' l ? = = 4 . a (R;S) c = aRb and bSc for example: North;NorthEast = {North or NorthEast} meet;inside = {inside, covered, overlap}
3.4.3 Functions IJ7f e 7 4 f( # 4 ?, 0 4:a.vU* d4] 9'37 d4D ÛÜ.aÛ F.9+ 74 $% '>:9 ~7 ß7 ?, # 74jL74KD F. Bird and Wadler 1988; Bird and Moor 1997
IJ7& d4& r 4 r'( q q?, :%7z4 # ?56 4 d4^ 4.Q,$% 4 ^ , # d 7\ 4K L7 \K . f . g (x) = f (g (x)).
3.4.4 Model Based Q 4,4 7^ ^74^ @ 4 # D ,4 5 gg 4£C g7 g ' . Q (Knauff et al. 1995)) 7
q
4 q & C 4 7 9 6 ' 4 4 4 3 6
9
k 4 7 6 7 d
m 4 5 x l u x ' m 4 x 4 l
5.=+! := ^ d $ (&4 774 # # 5 4. e4 d 4 "744 7 " 4 'x 4K l4m
