Ver 1.21 10 5 7 0 1 I 3 1 / 3 1.1... 3 1.2... 5 1.3... 5 1.4... 6 1.5... 7 1.6... 7 1.7... 7 2 9 2.1... 9 2.2 ( ). 10 2.3 :... 10 2.4... 11 2.5... 12 2.6... 13 II 16 3.2.1... 17 3.2.2... 19 3.2.3.. 22 3.2.4... 23 3.2.5 24 3.2.6... 25 3.3... 26 3.3.1... 26 3.3.2... 26 3.3.3... 27 4 : 28 4.1... 28 4.2... 29 4.3... 29 4.4... 30 4.5 :... 30 4.6... 31 4.7... 32 4.7.1... 32 4.7.2... 34 4.8... 36 3 16 3.1... 16 3.2... 17 1
Ver 1.21 Page 2 0 ( ) 1 2 1 [35] : 2
Ver 1.21 Page 3 I 1 / 3 1.1 45 [18] 3 1994 8 * 4 5 * 6 6 [37]
Ver 1.21 Page 4 7 89 10 11 7 * 8 9 * 10 * 11 dynamical system 12 13 14 12 * 13 * X S F : X S X s S F s : X X s 14 *
Ver 1.21 Page 5 15 16 1.2 17 18 19 15 * 16 *. 17 * 18 19 [27, ] 1.3 20 21 20 21 * [10, p188] ( )
Ver 1.21 Page 6 22 23 [37] 24 22 * 23 24 1.4 25 25 [22] : folk psychology
Ver 1.21 Page 7 1.5 26 1.6 26 [1] [3, ] 27 : 28 1.7 27 28 *
Ver 1.21 Page 8 [41] [38] 29 30 31 32 [42] 33 29 30 31 32 33
Ver 1.21 Page 9 2 2.1 34 34 [43] 35 35
Ver 1.21 Page 10 2.2 ( ) 36 2.3 : [31].. (AP1) 36
Ver 1.21 Page 11 (AP2) [21] π- [28] [29], [24] 2.4
Ver 1.21 Page 12 Chemical abstract machine [4] 37 2.5 37 38 39 T T ( T - ) T T T T T T T T T T 2.6 T 38 ([9, 1994.9p154]) 39
Ver 1.21 Page 13 T [21] 2.6 ([14]) 40 Moore 41 [12] (1) a 1,a 2,,a n b a 1,,a n,b a 1,,a n b a 1,,a n b a 1,,a n b 40 41 *
Ver 1.21 Page 14 a 1,,a n b a 1,,a n b X (1) (1) a 1,,a n b (1) (1) Γ a 1,,a n Γ b Γ 3 a, b, c b, c a a b b, c a a b c a, b (H1) a (H2) a 1,,a n b a a, a 1,,a n b (H3) : Γ i b i i =1,,n b 1,,b n c Γ 1, Γ 2,, Γ n c X C pow (X) : X A CA (Cl1) A CA (A 42 ) (Cl2) A B CA CB ( ) (Cl3) CCA = CA A A. C(A B) =CA CB X A B 43 Moore A A A Moore Moore A meet a b b c a c a b b a a = b 42 43
Ver 1.21 Page 15 a, b a b a b a b a, b a, b c a b a, b a b 2 a, b c, d, e c d a, b e, c e = a b X X 5 a, b, c 186 [12]. [12] 6 7 [14] a b V L l l A l V Moore L Moore V L A l l l 3 4 4 b d a { c, d, b } a a { a, c }
Ver 1.21 Page 16 II [9] 44 45 44 [9, 1994.9 p142] 45 [9, 1994.11p368 381] [48] 3 46 : 3.1 46 ( [9, 1995.4 p310]). ( [9, 1994.11 p359])
Ver 1.21 Page 17 P P A P B P [33, p152] 3.2 (cf. 3.2.1) 47 (cf. 3.2.2) 3.2.1 :: 47 [13] active system
Ver 1.21 Page 18 48 48 (impredicative) [8, p69] ([38]). [6] 49 [8] [8, p68] 49
Ver 1.21 Page 19 50 51 incompletability( ) inexhaustibility() [7] incompletablility inexhaustibility 50 ( ) 51 1995 p86 52 [ ] [ ] [ ] 3.2.2 52
Ver 1.21 Page 20 [48, 201] 57 68 57 68 57 [23, p40] 53 68 57 125 5 125 x, y 57 x y = x + y x y =5 68 57 125 53 [45, 1998.3.4] (a) (b) 57 5 0 54 68 57 125 [23, p108] 55 54 [13, Ch1] 55 [45, 1998.1.30] [11, 1998.3.11]
Ver 1.21 Page 21 56 57 56 ( 3.2.4) 57 [ ]. [ ].
Ver 1.21 Page 22 [17,. ] 58 3.2.3 59 58 24 21 59 60 60 p107
Ver 1.21 Page 23 [32, p111 112] 61 62 63 61 62 63 a b (a = b) a = b b = c a = c 3.2.4 [23]
Ver 1.21 Page 24 [23, p117] [23, p151] 68 + 57 125 [23, p188-9] 3.2.5 64 64 ( 3.3.3)
Ver 1.21 Page 25 65 65 [44] ( 4.5) 3.2.6 : m m 1 1 m m
Ver 1.21 Page 26 66 3.3 3.3.1 66 3.3.2
Ver 1.21 Page 27 3.3.3 [20] [8] 4.5 ([19])
Ver 1.21 Page 28 4 : 67 [10, p108] 4.1 [25, p45]. 67 [39] 68 [16] 68
Ver 1.21 Page 29 [34, p58] [26, p81] 4.2 69 [10, p160] B C B C [15, p160] 4.3 [20, p8] 69 [46]
Ver 1.21 Page 30 [40, p188] 4.4 DNA 70 70 4.5 : 71 72 73 [9, 1995.4 p309] 3.2.4 71 72 73
Ver 1.21 Page 31 (cf. 4.7.2) 74 [9] [9, 1995 p313] 8 A B B A C 75 74 75 76 4.6 77 76 77 [36]
Ver 1.21 Page 32 78 X S 79 R X x S s R- x, s R x = s cf. 9 X S x = s x s x s 4.7 4.7.1 80 x S x Y 78 M. Barr Chu autonomous category *-autonomous category *-autohomous category Pratt http://boole.stanford.edu/chuguide.html. Wille (Formal Concept analysis) [5] Barwise [2] 79 X S = { (x, s) x X, s S } 3.2.1 80
Ver 1.21 Page 33 S Y 8182 s X s T X T ( 9 ) F y F y F F F F F F F T s T s T T T T T T T T T T 2.6 F F F F F = F T T 81 S Y S y (y Y ) Y 82 F, G F G 83 X 2.6 X X 84 S F S F T X T S P Q def P Q 1. P Q X P X Q 2. P Q X P X Q 3. P Q X P X Q 85 83 F G F, G F, G F G F G F G F G 84 i F i = { F F Fi i }. 85 P Q = P Q X P X Q = X P X Q P Q = P Q X P X Q = X P X Q
Ver 1.21 Page 34 X S X, S 4.7.2 : a, b, c d a, b, c d a, b, c d a, b, c d a b a b a b X a X b X a X b = X F F a b a b = S a, b X a a a a X b X a b b a b a S b a a b 86 X o X (X, S, =) (X, S) (X o,s, =) (X o, S o X o X o S o x x S x S o x S o 86
Ver 1.21 Page 35 x S x S x z z S z z 87 S o X S S o (X, S o, =) (X o, S o ) s X s 87 F S F x, y x y = X o T x y T x, y S o x, y s x, y s x, y s x, y s x, y s s x, y s X s x, y
Ver 1.21 Page 36 X s S o E (X, S, =) S E C =(X, S) X o (X o,s, =) 88 C o C ( ) C o C E X o X s X o X o E ( ) X o E C o C (*) 88 ( ) X, S = = = (X 1,S 1, = 1 ) (X 2,S 2, = 2 ) 4.8 1. 2.
Ver 1.21 Page 37 3. 4. PQ1 PQ2 PQ3 5.. [PQ1] [PQ2-3] 6. 7. 8. 9. 10. 89 [9, 10] 90 89 X X ([10, p110]) 90 [9] [47]
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Ver 1.21 Page 39 (cf.[49]) ( )
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