Logiki modalne i temporalne; część 2.pdf

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F:/stary_dysk/Studia/_zaj07-08/notatki/modal_logic_2.dvi
2 n ×2 n
2
2
2
2
GF
GF 2
2
GF GF k
GF
2
2 <
<
2
A ′ A
t i
T i T i
'
A A ′
'
. . . , t 1 , t 2 , . . . t k , t 1 , . . . t k , . . .
2
2
2 E
E
•8xy '(x, y)
•8x(Ax!9y(Exy^'(x, y)))
•8x(Ax!9y(¬Exy^'(x, y)))
A ' A A ′
C t C
A ′′ t
C C ′
t A ′′ A ′′
'
2
2
D = (D, R H , R V ) D
R H
R V
D t N×N
D (t(p, q), t(p + 1, q))2R H (t(p, q), t(p, q + 1))2R V
p, q
D D
2
n, m2N} V ={(n, m), (n, m + 1) : n, m2N}
L 2 GF 2
G N N×N
' L
G N = (N 2 , H, V ) H ={(n, m), (n+1, m) :
G N
'
A|= ' G N A
'^' D ' D
L
D ' D D
2
A 8x(9yHxy^9yV xy) 8xyzt((V yx^Hyz^V zt)!Hxt)
A ′′ A ′
C C ′
2 T 1
T 2
V 1
V 0
T 2
V 1
T 1
V 0
H 0
H 1
H 2
H 3
H 0
9x (H 0 x^V 0 x),
'
8x (9yHxy^9yV xy).
H
8xy (Hxy!(' 1 _' 2 _. . ._' 8 )),
' i
' 1 T 1 xy^T 2 xy^H 0 x^V 0 x^H 1 y^V 0 y,
' 2 T 1 yx^T 2 yx^H 1 x^V 0 x^H 2 y^V 0 y.
V
H
8xy ((T 1 xy^H 0 x^V 1 x^H 1 y^V 1 y)!Hxy),
8xy ((T 2 xy^H 2 x^V 0 x^H 1 y^V 0 y)!Hyx).
' '
2
2
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