EL++
EL++
EL EL
EL+
EL++
+ ++
EL EL
EL++
EL++ NC
NR NI
! "
EL++ I = ∆I , ·I
∆I
·I a ∈ NI aI ∈ ∆I A ∈ NC
A : ∆I → [0, 1]
I
r ∈ NR
rI : ∆I × ∆I → [0, 1]
EL++
C $d D
r 1 ◦ . . . ◦ rk $ s
◦t
C I C
C
EL++ A
I A
A
I K = {A, C}
A C A
C
! !I (x) = 1
I
⊥ ⊥! (x) = 0
1 x = aI
{a} {a}I (x) =
0
" #
C #D (C # D)I (x) = min C I (x), DI (x)
" " ##
∃r.C (∃r.C)I (x) = sup" y∈∆I min # rI (x, y) , C I (y)
C %d D $ I min C I (x)% , d ≤ DI (x)
r1 ◦ . . . ◦ rk % s r1 ◦ . . . ◦t rkI" (x,
t I
# y) ≤ s (x, y)
I I
C(a) ≥ d C" a #≥ d
r (a, b) ≥ d r I a I , bI ≥ d
EL++
EL++
C
D C C $dC D
{o} B C! =
C ∪ {{o} $ C, D $ B} o B
BCC
RC C C
S BCC × BCC [0, 1] R RC × BCC × BCC
[0, 1]
S (C, D) = d
C $dC D R (r, C, D) = d C $dC ∃r.D
S S (C, D) := 1 D = C D =(
S (C, D) = 0 C, D ∈ BCC ∪ {⊥}
R R (r, C, D) = 0 r ∈ RC C, D ∈ BCC ∪ {⊥}
S (C, C " ) = d1 C " %d2 D ∈ C S (C, D) < min (d1 , d2 )
S (C, D) = min (d1 , d2 )
S (C, C1 ) = d1 S (C, C2 ) = d2 C1 # C2 %d3 D ∈ C
S (C, D) < min (d1 , d2 , d3 )
S (C) := min (d1 , d2 , d3 )
S (C, C " ) = d1 C " %d2 ∃r.D ∈ C R (r, C, D) < min (d1 , d2 )
R (r, C, D) := min (d1 , d2 )
R (r, C, D) = d1 S (D, C " ) = d2 ∃r.C " %d3 E ∈ C
S (C, E) < min (d1 , d2 , d3 )
S (C, E) = min (d1 , d2 , d3 )
R (r, C, D) > 0 S (D, ⊥) > 0 S (C, ⊥) = 0
S (C, ⊥) = 1
S (C, {a}) = 1 S (E, {a}) = 1 C !d E
D ∈ BCC S (C, D) < min (d, S (E, D))
S (C, D) := min (d, S (E, D))
R (r, C, D) = d r % s ∈ C R (s, C, D) < d
R (s, C, D) := d
R (r1 , C, D) = d1 R (r2 , D, E) = d2 r1 ◦ r2 % r3 ∈ C
R (r3 , C, E) < min (d1 , d2 )
(r3 , C, D) := min (d1 , d2 )
S (C, {a}) > 0 {a} S (C, {a}) < 1
S (C, {a}) := 1
!d
C !d E C, E ∈ BCC
C1 , . . . , Ck+1 ∈ BCC
r1 , . . . , rk ∈ RC min (R (r1 , C1 , C2 ) , . . . ,
R (rk , Ck , Ck+1 )) = d Ck+1 = E C1 = C C1 = {a}
{a} BCC
S
C {o} B
C {o} $dC B S ({o} , B) ≥ d
{a} ∈ BCC S ({a} , ⊥) > 0
EL++ EL++
EL+
EL+
EL++
C +D $ ⊥
{a} +{ b} $ ⊥