. -, , . , , :
(p q) ( p q).
. .
. à , . . ( , ).
W; . R W. R(t, w) 1, w t.
. (W, R), W , RÍW´W W, . R .
1
W = {1, 2, 3, 4, 5}, R = {(1, 1), (1, 2), (2, 3), (1, 5), (5, 4), (4, 4), (4, 3)}. (W, R) , W, , R. , 1 1, 2 5, (1, 1), (1, 2) (1, 5) R.
2
(, £) , £. , N = (w, £), (Z, £), (Q, £), (R, £) , , , .
3
, , W = {1, 2, 3, 4} R = {(1, 2), (2, 3), (3, 4), (4, 1)}.
, , (w, R), R (m, n), m £ n + 1.
, ( P). . h: P P(W), W. p w, w Î h(p), .
(W, R, h) . h.
= (W, R, h) . t Î W M, t |= A :
1) , M, t |= , t Î h(p);
2) M, t |= 1 ();
3) M, t |= Ø , M, t |= ;
4) M, t |= & , M, t |= M, t |= ;
5) M, t |= , , u |= u Î W, tRu.
|
|
: tRu , (t, u) Î R. M, t |= : t , t ̻. : |= (t), |=t , .
, , 1 5:
6) M, t |= Ú , M, t |= M, t |= ;
7) M, t |= ( ) M, t |= , M, t |= ;
8) M, t |= à, M, t |= u Î W , tRu.
1
:
9) M, t |= Ø( Ú ), M, t |= Ø & Ø;
10) M, t |= Ø , M, t |= àØ;
11) M, t |= Øà, M, t |= Ø.
2
p, q Î P. M = (W, R, h), W = {1, 2, 3, 4, 5},
R = {(1, 1), (1, 2), (2, 3), (1, 5), (5, 4), (4, 4), (4, 3)}, h(p) = {1, 2, 5}, h(q) = {1, 3, 4}
h(r) = Æ r Ï {p, q}.
( 1, 2 5; q 1, 3 4). :
1) 1 3, 4;
2) Ø 3, 0 3;
3) àq & àØq 1, q 1;
4) àq, q 2, 3 2;
5) à1 àq , .. .