B\u1ea1n \u0111\u00e3 t\u1eebng nghe n\u00f3i “m\u00e1y t\u00ednh c\u0169ng c\u00f3 tri th\u1ee9c ph\u1ea3i kh\u00f4ng” Tri th\u1ee9c trong m\u00e1y t\u00ednh bi\u1ec3u th\u1ecb nh\u01b0 th\u1ebf n\u00e0o?<\/p>\n\n\n\n
B\u1edfi v\u00ec qu\u00e1 tr\u00ecnh ho\u1ea1t \u0111\u1ed9ng tr\u00ed n\u0103ng ch\u1ee7 y\u1ebfu l\u00e0 m\u1ed9t qu\u00e1 tr\u00ecnh c\u00f3 \u0111\u01b0\u1ee3c v\u00e0 \u1ee9ng d\u1ee5ng tri th\u1ee9c, cho n\u00ean ph\u1ea1m vi nghi\u00ean c\u1ee9u ho\u1ea1t \u0111\u1ed9ng tr\u00ed n\u0103ng bao g\u1ed3m: nh\u1eadn \u0111\u01b0\u1ee3c tri th\u1ee9c, bi\u1ec3u th\u1ecb tri th\u1ee9c, \u1ee9ng d\u1ee5ng tri th\u1ee9c. V\u00e0 tri th\u1ee9c l\u1ea1i c\u1ea7n c\u00f3 h\u00ecnh th\u1ee9c bi\u1ec3u th\u1ecb th\u00edch \u0111\u00e1ng th\u00ec m\u1edbi ti\u1ec7n cho vi\u1ec7c l\u01b0u tr\u1eef trong m\u00e1y t\u00ednh, ki\u1ec3m tra t\u00ecm ki\u1ebfm, s\u1eed d\u1ee5ng v\u00e0 s\u1eeda \u0111\u1ed5i.<\/p>\n\n\n\n
Bi\u1ec3u th\u1ecb nh\u1eefng tri th\u1ee9c m\u00e0 con ng\u01b0\u1eddi \u0111\u00e3 t\u00edch l\u0169y v\u1ec1 nh\u1eadn th\u1ee9c \u0111\u1ed1i v\u1edbi th\u1ebf gi\u1edbi kh\u00e1ch quan b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p h\u1ec7 th\u1ed1ng, \u0111\u00f3 ch\u00ednh l\u00e0 v\u1ea5n \u0111\u1ec1 “bi\u1ec3u th\u1ecb tri th\u1ee9c” m\u00e0 ng\u01b0\u1eddi ta th\u01b0\u1eddng n\u00f3i t\u1edbi, t\u1ee9c l\u00e0 “bi\u1ec3u th\u1ecb tri th\u1ee9c nh\u01b0 th\u1ebf n\u00e0o”, ho\u1eb7c l\u00e0m sao \u0111\u1ec3 m\u00e1y t\u00ednh hi\u1ec3u \u0111\u01b0\u1ee3c v\u00e0 x\u1eed l\u00ed tri th\u1ee9c, v\u00e0 m\u00e1ch b\u1ea3o cho ch\u00fang ta k\u1ebft qu\u1ea3 x\u1eed l\u00fd theo ph\u01b0\u01a1ng ph\u00e1p m\u00e0 con ng\u01b0\u1eddi c\u00f3 th\u1ec3 hi\u1ec3u \u0111\u01b0\u1ee3c.<\/p>\n\n\n\n
Qua nhi\u1ec1u n\u0103m nghi\u00ean c\u1ee9u, c\u00e1c nh\u00e0 khoa h\u1ecdc m\u00e1y t\u00ednh \u0111\u00e3 c\u00f3 \u0111\u01b0\u1ee3c r\u1ea5t nhi\u1ec1u ph\u01b0\u01a1ng ph\u00e1p bi\u1ec3u th\u1ecb tri th\u1ee9c kh\u00e1c nhau. \u0110\u1eb7c bi\u1ec7t n\u1ed5i b\u1eadt trong \u0111\u00f3 l\u00e0 ph\u01b0\u01a1ng ph\u00e1p bi\u1ec3u th\u1ecb c\u00f4ng th\u1ee9c l\u00f4gic. L\u00f4gic ch\u00fang ta b\u00e0n t\u1edbi \u1edf \u0111\u00e2y l\u00e0 l\u00f4gic to\u00e1n l\u00ed. N\u00f3 bao g\u1ed3m hai b\u1ed9 ph\u1eadn t\u00ednh to\u00e1n m\u1ec7nh \u0111\u1ec1 v\u00e0 t\u00ednh to\u00e1n v\u1ecb t\u1eeb.<\/p>\n\n\n\n
Nh\u00e0 to\u00e1n h\u1ecdc, tri\u1ebft h\u1ecdc \u0110\u1ee9c Gottfied Wilhelm von Leibniz \u0111\u00e3 \u0111\u01b0a ra m\u1ed9t \u00fd t\u01b0\u1edfng l\u1edbn lao v\u00e0o nh\u1eefng n\u0103m 70 c\u1ee7a th\u1ebf k\u1ef7 XVII l\u00e0: Ch\u1ebf t\u1ea1o m\u1ed9t m\u00e1y suy l\u00ed \u0111\u1ec3 c\u01a1 gi\u1edbi h\u00f3a ph\u00e9p quy n\u1ea1p v\u00e0 di\u1ec5n d\u1ecbch l\u00ed t\u00ednh c\u1ee7a con ng\u01b0\u1eddi. Leibniz su\u1ed1t \u0111\u1eddi \u0111\u00e3 \u0111\u1ed5 bao t\u00e2m huy\u1ebft v\u00e0o vi\u1ec7c \u0111\u00f3. \u00d4ng \u0111\u00e3 \u0111\u1eb7t n\u1ec1n m\u00f3ng cho l\u00f4gic to\u00e1n l\u00ed. \u00d4ng \u0111\u00e3 th\u1eed bi\u1ec3u th\u1ecb l\u00f4gic th\u00e0nh m\u1ed9t lo\u1ea1i t\u00ednh to\u00e1n, t\u1eeb \u0111\u00f3 m\u00e0 bi\u1ec3u th\u1ecb qu\u00e1 tr\u00ecnh t\u01b0 duy b\u1eb1ng qu\u00e1 tr\u00ecnh t\u00ednh to\u00e1n k\u00ed hi\u1ec7u.<\/p>\n\n\n\n
Bi\u1ec3u th\u1ecb tri th\u1ee9c b\u1eb1ng c\u00f4ng th\u1ee9c l\u00f4gic th\u00ec c\u1ea7n ph\u1ea3i k\u00ed hi\u1ec7u h\u00f3a to\u00e0n b\u1ed9 tri th\u1ee9c v\u00e0 t\u00ednh to\u00e1n l\u00f4gic. V\u00ed d\u1ee5 bi\u1ec3u th\u1ecb “tuy\u1ebft m\u00e0u \u0111\u1ecf” b\u1eb1ng P, bi\u1ec3u th\u1ecb “h\u00f4m n\u00e0y tr\u1eddi m\u01b0a” b\u1eb1ng Q, bi\u1ec3u th\u1ecb “ng\u00e0y mai tr\u1eddi m\u01b0a” b\u1eb1ng R. V\u1eady th\u00ec “tuy\u1ebft kh\u00f4ng ph\u1ea3i m\u00e0u \u0111\u1ecf” s\u1ebd bi\u1ec3u th\u1ecb l\u00e0: \u00acP. V\u00e0 “h\u00f4m nay tr\u1eddi m\u01b0a v\u00e0 ng\u00e0y mai tr\u1eddi c\u0169ng m\u01b0a” c\u00f3 th\u1ec3 bi\u1ec3u th\u1ecb l\u00e0: Q\u039bR. \u1ede \u0111\u00e2y \u00ac v\u00e0 \u039b \u0111\u1ec1u l\u00e0 t\u1eeb li\u00ean k\u1ebft c\u1ee7a t\u00ednh to\u00e1n l\u00f4gic. L\u1ea1i v\u00ed d\u1ee5 Human (x) bi\u1ec3u th\u1ecb “x l\u00e0 ng\u01b0\u1eddi”, Mortal (x) bi\u1ec3u th\u1ecb “x s\u1ebd ch\u1ebft”. V\u1eady th\u00ec “v\u1edbi m\u1ecdi x; x l\u00e0 ng\u01b0\u1eddi v\u00e0 x s\u1ebd ch\u1ebft c\u00f3 th\u1ec3 bi\u1ec3u th\u1ecb l\u00e0: \u2200 x (Human (x) \u039b Mortal (x)). \u1ede \u0111\u00e2y Human (x) v\u00e0 Mortal (x) g\u1ecdi l\u00e0 v\u1ecb t\u1eeb, \u2200 g\u1ecdi l\u00e0 l\u01b0\u1ee3ng t\u1eeb ph\u1ed5 d\u1ee5ng.<\/p>\n\n\n\n
T\u1ea7m quan tr\u1ecdng c\u1ee7a bi\u1ec3u thi l\u00f4gic l\u00e0 k\u1ebft qu\u1ea3 di\u1ec5n d\u1ecbch c\u1ee7a n\u00f3 trong ph\u1ea1m vi nh\u1ea5t \u0111\u1ecbnh \u0111\u1ea3m b\u1ea3o ch\u00ednh x\u00e1c, c\u00f2n c\u00e1c ph\u01b0\u01a1ng th\u1ee9c bi\u1ec3u th\u1ecb tri th\u1ee9c kh\u00e1c th\u00ec \u0111\u1ebfn nay v\u1eabn ch\u01b0a \u0111\u1ea1t \u0111\u01b0\u1ee3c y\u00eau c\u1ea7u n\u00e0y. \u0110\u00f3 l\u00e0 m\u1ed9t nguy\u00ean nh\u00e2n l\u00f4gic \u0111\u01b0\u1ee3c d\u00f9ng ph\u1ed5 bi\u1ebfn cho vi\u1ec7c bi\u1ec3u th\u1ecb tri th\u1ee9c. Ph\u01b0\u01a1ng ph\u00e1p bi\u1ec3u th\u1ecb l\u1ea5y l\u00f4gic l\u00e0m c\u01a1 s\u1edf trong vi\u1ec7c nghi\u00ean c\u1ee9u tr\u00ed tu\u1ec7 nh\u00e2n t\u1ea1o \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i c\u00f2n c\u00f3 m\u1ed9t nguy\u00ean nh\u00e2n kh\u00e1c l\u00e0 ph\u01b0\u01a1ng ph\u00e1p suy ra tri th\u1ee9c m\u1edbi t\u1eeb tri th\u1ee9c hi\u1ec7n c\u00f3 ta c\u00f3 th\u1ec3 c\u01a1 gi\u1edbi h\u00f3a.<\/p>\n\n\n\n