\u547d\u9898\u903b\u8f91\u4e2d\u7684\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf – \u5b8c\u6574\u6307\u5357<\/title><\/head><body> <\/p>\n<div style=\"background-color:#F3F3F3; padding:20px;\">\n<h1 style=\"text-align:center;\">\u547d\u9898\u903b\u8f91\u4e2d\u7684\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf<\/h1>\n\u6458\u8981\uff1a<\/strong><\/br>\u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\u3002\u89e3\u91ca\u8fd9\u4e9b\u7cfb\u7edf\u5982\u4f55\u7528\u4e8e\u89e3\u5bc6\u903b\u8f91\u8868\u8fbe\u5f0f\u4e4b\u95f4\u53ef\u80fd\u5b58\u5728\u7684\u5173\u7cfb\uff0c\u4ee5\u53ca\u6784\u5efa\u8fd9\u4e9b\u8bc1\u660e\u7684\u57fa\u672c\u5143\u7d20\uff1a\u8bed\u8a00\u3001\u516c\u7406\u548c\u63a8\u7406\u89c4\u5219\u3002\u8fd9\u91cc\u63d0\u5230\u4e86\u0141ukasiewicz\u7684\u516c\u7406\uff0c\u5e76\u89e3\u91ca\u4e86\u547d\u9898\u6f14\u7b97\u7684\u6f14\u7ece\u5f15\u64ce modus ponens\u3002\u6b64\u5916\uff0c\u8fd8\u8ba8\u8bba\u4e86\u63a8\u7406\u3001\u5b9a\u7406\u548c\u524d\u63d0\uff0c\u5e76\u89e3\u91ca\u4e86\u5728\u6f14\u7ece\u7cfb\u7edf\u4e2d\u5982\u4f55\u6267\u884c\u63a8\u7406\u3002<\/em><\/p>\n\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><\/p>\n<ol>\n<li>\u7406\u89e3<\/strong>\u547d\u9898\u903b\u8f91\u4e2d\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\u7684\u6982\u5ff5\u3002<\/li>\n<li>\u8bc6\u522b<\/strong>\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\u7684\u57fa\u672c\u7ec4\u6210\u90e8\u5206\u3002<\/li>\n<li>\u4e86\u89e3<\/strong>\u547d\u9898\u6f14\u7b97\u4e2d\u0141ukasiewicz\u7684\u516c\u7406\u3002<\/li>\n<li>\u7406\u89e3<\/strong>modus ponens\u4f5c\u4e3a\u547d\u9898\u6f14\u7b97\u7684\u6f14\u7ece\u5f15\u64ce\u3002<\/li>\n<li>\u7406\u89e3<\/strong>\u6f14\u7ece\u7cfb\u7edf\u4e2d\u5982\u4f55\u6267\u884c\u63a8\u7406\u4ee5\u53ca\u524d\u63d0\u3001\u63a8\u7406\u548c\u5b9a\u7406\u4e4b\u95f4\u7684\u533a\u522b\u3002<\/li>\n<li>\u7406\u89e3<\/strong>\u5982\u4f55\u901a\u8fc7\u516c\u7406\u6a21\u5f0f\u548c\u63a8\u7406\u89c4\u5219\u751f\u6210\u63a8\u7406\u3002<\/li>\n<li>\u8ba4\u8bc6<\/strong>\u903b\u8f91\u8fde\u63a5\u8868\u8fbe\u5f0f\u5e76\u7528\u5e38\u7528\u8bed\u8a00\u66ff\u6362\u5b83\u4eec\u7684\u80fd\u529b\u3002<\/li>\n<\/ol>\n\u5185\u5bb9\u76ee\u5f55<\/u>:<\/strong> \n<a href=\"#1\">\u4ec0\u4e48\u662f\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\uff1f<\/a> \n<a href=\"#2\">\u547d\u9898\u903b\u8f91\u4e2d\u7684\u0141ukasiewicz\u516c\u7406<\/a> \n<a href=\"#3\">Modus Ponens\uff1a\u547d\u9898\u6f14\u7b97\u7684\u6f14\u7ece\u5f15\u64ce<\/a> \n<a href=\"#4\">\u63a8\u7406\u3001\u5b9a\u7406\u548c\u524d\u63d0<\/a> \n<a href=\"#5\">\u5982\u4f55\u5728\u547d\u9898\u903b\u8f91\u4e2d\u8fdb\u884c\u8bc1\u660e\uff1f<\/a> \n<a href=\"#6\">\u8bc1\u660e\u7b49\u4ef7\u6027\u7684\u6982\u5ff5<\/a> \n<a href=\"#7\">\u6f14\u7ece(Meta)\u5b9a\u7406<\/a> \n<a href=\"#8\">\u6f14\u7ece\u5b9a\u7406\u7684\u9006\u5b9a\u7406<\/a> \n<a href=\"#9\">\u5173\u4e8e\u8868\u8fbe\u5f0f\u7684\u63a8\u7406\u548c\u5173\u4e8e\u63a8\u7406\u7684\u63a8\u7406<\/a> \n<a href=\"#10\">\u5355\u8c03\u6027\u89c4\u5219<\/a> \n<a href=\"#11\">\u5bf9\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\u548c\u547d\u9898\u903b\u8f91\u7684\u7efc\u5408\u601d\u8003<\/a>\n<\/p>\n <center> \n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/OvoEDefcSZg\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n <\/div>\n\u5728\u6211\u4eec\u5bf9\u903b\u8f91\u7684\u7814\u7a76\u4e2d\uff0c\u6211\u4eec\u5df2\u7ecf\u5230\u8fbe\u4e86\u4e00\u4e2a\u8f6c\u6298\u70b9\uff0c\u56e0\u4e3a\u6211\u4eec\u5f00\u59cb\u56de\u987e\u547d\u9898\u903b\u8f91\u7684\u6f14\u7ece\u7cfb\u7edf\u3002\u8fd9\u662f\u6211\u4eec\u6240\u89c1\u7684\u4e00\u5207\u5f00\u59cb\u53d8\u5f97\u64cd\u4f5c\u6027\u5e76\u4e14\u771f\u6b63\u7684\u903b\u8f91\u7cbe\u795e\u5f00\u59cb\u663e\u73b0\u7684\u5730\u65b9\uff0c\u56e0\u4e3a\u6211\u4eec\u5c06\u7814\u7a76\u8bc1\u660e\u7684\u672c\u8d28\u3002\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u6211\u4eec\u5047\u8bbe\u4f60\u5df2\u7ecf\u4e86\u89e3\u5982\u4f55\u7f16\u5199\u8868\u8fbe\u5f0f\u5e76\u7406\u89e3\u547d\u9898\u903b\u8f91\u7684\u5185\u5bb9\uff1b\u5982\u679c\u4f60\u8fd8\u4e0d\u662f\u5f88\u6e05\u695a\uff0c\u5efa\u8bae\u4f60\u590d\u4e60\u4e4b\u524d\u7684\u8bfe\u7a0b\u3002<\/span><\/p>\n\u505a\u5b8c\u8fd9\u4e9b\uff0c\u63a5\u4e0b\u6765\u7684\u662f\u5ba1\u89c6\u547d\u9898\u903b\u8f91\u4e2d\u7684\u8868\u8fbe\u5f0f\u5982\u4f55\u76f8\u4e92\u5173\u8054\u4ee5\u5f62\u6210\u6f14\u7ece\u3002\u6784\u5efa\u8fd9\u4e9b\u5173\u7cfb\u7684\u673a\u5236\u662f\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\u3002<\/strong><\/span><\/p>\n<a name=\"1\"><\/a><\/p>\n<h2>\u4ec0\u4e48\u662f\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\uff1f<\/h2>\n\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\uff0c\u6216\u6f14\u7ece\u8ba1\u7b97\u7cfb\u7edf\uff0c\u6709\u4e09\u4e2a\u57fa\u672c\u7ec4\u6210\u90e8\u5206\uff1a<\/span><\/p>\n<ol style=\"color: #000000; text-align: justify;\">\n<li>\u4e00\u79cd\u5f62\u5f0f\u8bed\u8a00\u3002<\/strong><\/li>\n<li>\u4e00\u4e2a\u516c\u7406\u6a21\u5f0f\u3002<\/strong><\/li>\n<li>\u57fa\u672c\u63a8\u7406\u89c4\u5219\u3002<\/strong><\/li>\n<\/ol>\n\u6211\u4eec\u5df2\u7ecf\u56de\u987e\u4e86\u6240\u6709\u4e0e\u5f62\u5f0f\u8bed\u8a00\u76f8\u5173\u7684\u5185\u5bb9\u3002\u73b0\u5728\u6211\u4eec\u5c06\u4ecb\u7ecd\u516c\u7406\u6a21\u5f0f\u548c\u57fa\u672c\u63a8\u7406\u89c4\u5219\u3002<\/span><\/p>\n\u4e3a\u4e86\u6784\u5efa\u547d\u9898\u6f14\u7b97\u7684\u6f14\u7ece\u7cfb\u7edf\uff0c\u6211\u4eec\u5c06\u4ece\u0141ukasiewicz\u7684\u516c\u7406<\/strong>\u5f00\u59cb\u6784\u5efa\u6f14\u7ece\u7cfb\u7edf\uff0c\u57fa\u672c\u63a8\u7406\u89c4\u5219\u6211\u4eec\u5c06\u4f7f\u7528\u80af\u5b9a\u524d\u4ef6\u6cd5\uff08Modus Ponens\uff09\u3002<\/strong><\/span><\/p>\n<a name=\"2\"><\/a><\/p>\n<h2>\u0141ukasiewicz\u7684\u547d\u9898\u903b\u8f91\u516c\u7406<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=206s\" target=\"_blank\" rel=\"noopener\">\u5982\u679c \\alpha, \\beta<\/span> \u548c \\gamma<\/span> \u662f\u547d\u9898\u6f14\u7b97\u7684\u8868\u8fbe\u5f0f\uff0c<\/span><\/strong><\/a>\u90a3\u4e48\u4ee5\u4e0b\u662f\u547d\u9898\u6f14\u7b97\u7684\u516c\u7406\uff1a<\/span><\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td>[A1]<\/td>\n<td>(\\alpha \\rightarrow (\\beta \\rightarrow \\alpha))<\/span><\/td>\n<\/tr>\n<tr>\n<td>[A2]<\/td>\n<td>((\\alpha \\rightarrow (\\beta \\rightarrow \\gamma))\\rightarrow ((\\alpha\\rightarrow \\beta)\\rightarrow(\\alpha \\rightarrow \\gamma)))<\/span><\/td>\n<\/tr>\n<tr>\n<td>[A3]<\/td>\n<td>((\\neg\\beta \\rightarrow \\neg\\alpha)\\rightarrow(\\alpha\\rightarrow \\beta))<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<a name=\"3\"><\/a><\/p>\n<h2>\u80af\u5b9a\u524d\u4ef6\u6cd5\uff1a\u547d\u9898\u6f14\u7b97\u7684\u6f14\u7ece\u5f15\u64ce<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=392s\" target=\"_blank\" rel=\"noopener\">\u5982\u679c \\alpha<\/span> \u548c \\beta<\/span> \u662f\u547d\u9898\u6f14\u7b97\u7684\u6709\u6548\u8868\u8fbe\u5f0f\uff0c<\/span> <\/strong><\/a>\u90a3\u4e48\u80af\u5b9a\u524d\u4ef6\u6cd5\u89c4\u5b9a\uff0c\u4ece \\alpha<\/span> \u548c (\\alpha \\rightarrow \\beta)<\/span> \u53ef\u4ee5\u63a8\u5bfc\u51fa \\beta<\/span>\u3002\u4ee5\u63a8\u7406\u5f62\u5f0f\u4e66\u5199\u5982\u4e0b\uff1a<\/span><\/p>\n<table style=\"color: #000000; text-align: justify;\">\n<caption>\u80af\u5b9a\u524d\u4ef6\u6cd5\u7684\u7ed3\u6784<\/caption>\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td>\\alpha<\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td>(\\alpha \\rightarrow \\beta)<\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td>\\beta<\/span><\/td>\n<td>; MP(1,2)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u8fd9\u91cc\u4f7f\u7528\u201cMP(1,2)\u201d\u7b80\u5199\u8868\u793a\u7b2c(1)\u548c\u7b2c(2)\u6b65\u4e4b\u95f4\u7684\u80af\u5b9a\u524d\u4ef6\u6cd5\uff0c\u6574\u4e2a\u63a8\u7406\u7684\u7efc\u5408\u8868\u793a\u4e3a\uff1a<\/p>\n\u56e0\u6b64 \\{\\alpha, (\\alpha \\rightarrow \\beta)\\}\\vdash \\beta <\/span>\n\u6211\u4eec\u5f88\u5feb\u5c31\u4f1a\u770b\u5230\uff0c\u4ece\u0141ukasiewicz\u7684\u516c\u7406\u548c\u80af\u5b9a\u524d\u4ef6\u6cd5\u51fa\u53d1\uff0c\u53ef\u4ee5\u6784\u5efa\u547d\u9898\u6f14\u7b97\u7684\u6240\u6709\u6f14\u7ece\u6280\u5de7\uff0c\u8fd9\u4e9b\u6280\u5de7\u7efc\u5408\u4e86\u5e38\u89c4\u63a8\u7406\u7684\u57fa\u672c\u89c4\u5219\uff0c\u5e76\u4e3a\u7ecf\u5178\u903b\u8f91<\/strong>\u5960\u5b9a\u4e86\u57fa\u7840\u3002<\/p>\n<a name=\"4\"><\/a><\/p>\n<h2>\u63a8\u7406\u3001\u5b9a\u7406\u548c\u524d\u63d0<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=506s\" target=\"_blank\" rel=\"noopener\">\u5728\u547d\u9898\u903b\u8f91\u7684\u6f14\u7ece\u7cfb\u7edf\u4e2d\u8fdb\u884c\u7684\u63a8\u7406<\/span><\/strong><\/a>\uff08\u6216\u6f14\u7ece\uff09\u662f\u4e00\u7cfb\u5217\u8868\u8fbe\u5f0f\u7684\u5e8f\u5217\uff0c\u5176\u4e2d\u6bcf\u4e2a\u8868\u8fbe\u5f0f\u8981\u4e48\u662f\u4e00\u4e2a\u524d\u63d0\uff0c\u8981\u4e48\u662f\u4ec5\u4f7f\u7528\u0141ukasiewicz\u7684\u516c\u7406\u548c\u80af\u5b9a\u524d\u4ef6\u6cd5\u4ece\u524d\u63d0\u4e2d\u5f97\u51fa\u7684\u8868\u8fbe\u5f0f\u3002\u5b9a\u7406\u662f\u65e0\u524d\u63d0\u6f14\u7ece\u7684\u7ed3\u679c\u3002\u524d\u63d0\u53ef\u4ee5\u662f\u4efb\u4f55\u65e2\u4e0d\u662f\u516c\u7406\u4e5f\u4e0d\u662f\u4ece\u516c\u7406\u63a8\u5bfc\u51fa\u7684\u8868\u8fbe\u5f0f\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u5f53\u6211\u4eec\u6709\u4e00\u7ec4\u524d\u63d0 \\Gamma<\/span> \u548c\u901a\u8fc7\u4f7f\u7528 \\Gamma<\/span> \u4e2d\u7684\u67d0\u4e2a\u5143\u7d20\u3001\u516c\u7406\u548c\u80af\u5b9a\u524d\u4ef6\u6cd5\u5f97\u5230\u7684\u8868\u8fbe\u5f0f \\alpha<\/span> \u65f6\uff0c\u5199\u4e3a \u00ab\\Gamma \\vdash \\alpha<\/span>\u00ab\uff0c\u6211\u4eec\u8bf4<\/p>\n\u4ece \\Gamma<\/span> \u53ef\u63a8\u51fa<\/em>\\alpha<\/span>\n\u5982\u679c \\Gamma<\/span> \u662f\u4e00\u4e2a\u7a7a\u96c6\uff0c\u90a3\u4e48\u6211\u4eec\u4e0d\u5199\u4f5c \u00ab\\emptyset\\vdash \\alpha<\/span>\u00bb \u800c\u662f\u5199\u4f5c \u00ab \\vdash \\alpha <\/span>\u3002\u00bb \u8fd9\u8868\u793a \u00ab\\alpha<\/span> \u662f\u4e00\u4e2a\u5b9a\u7406\u00bb\u3002\u8fd9\u79cd\u8868\u793a\u5b9a\u7406\u7684\u65b9\u5f0f\u53ef\u4ee5\u6269\u5c55\u5230\u516c\u7406\u7684\u8868\u793a\uff0c\u6240\u4ee5\u5982\u679c \\alpha<\/span>\u3001\\beta<\/span> \u548c \\gamma<\/span> \u662f\u8868\u8fbe\u5f0f\uff0c\u90a3\u4e48\u0141ukasiewicz\u7684\u516c\u7406\u53ef\u4ee5\u5199\u6210\u4ee5\u4e0b\u5f62\u5f0f<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>[A1]<\/td>\n<td>\\vdash (\\alpha \\rightarrow (\\beta \\rightarrow \\alpha))<\/span><\/td>\n<\/tr>\n<tr>\n<td>[A2]<\/td>\n<td>\\vdash((\\alpha \\rightarrow (\\beta \\rightarrow \\gamma))\\rightarrow ((\\alpha\\rightarrow \\beta)\\rightarrow(\\alpha \\rightarrow \\gamma)))<\/span><\/td>\n<\/tr>\n<tr>\n<td>[A3]<\/td>\n<td>\\vdash((\\neg\\beta \\rightarrow \\neg\\alpha)\\rightarrow(\\alpha\\rightarrow \\alpha))<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u57fa\u4e8e\u6b64\uff0c\u6211\u4eec\u8bf4\u516c\u7406\u662f\u81ea\u660e\u7684\u9648\u8ff0\uff0c\u6216\u5b9a\u7406\u662f\u4ece\u7a7a\u767d\u63a8\u65ad\u51fa\u7684\u8868\u8fbe\u5f0f\uff0c\u6216\u8005\u516c\u7406\u548c\u5b9a\u7406\u662f\u547d\u9898\u6f14\u7b97\u7684\u6027\u8d28\u3002<\/p>\n<a name=\"5\"><\/a><\/p>\n<h2>\u547d\u9898\u903b\u8f91\u4e2d\u5982\u4f55\u6267\u884c\u8bc1\u660e\uff1f<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=783s\" target=\"_blank\" rel=\"noopener\">\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u6211\u4eec\u5c06\u505c\u6b62\u8ba8\u8bba\u7406\u8bba\u5e76\u8f6c\u5411\u5b9e\u8df5\u3002<\/span><\/strong><\/a> \u5173\u4e8e\u6267\u884c\u8bc1\u660e\u53ef\u4ee5\u8bf4\u5f88\u591a\u4e8b\u60c5\uff1b\u4f46\u65e0\u8bba\u6211\u4eec\u5bf9\u6f14\u7ece\u7cfb\u7edf\u548c\u547d\u9898\u903b\u8f91\u8bf4\u4e86\u591a\u5c11\u7cbe\u5f69\u7684\u8bdd\uff0c\u4e14\u90fd\u88ab\u7406\u89e3\u4e86\uff0c\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u5c31\u4e00\u5b9a\u80fd\u53d1\u5c55\u51fa\u6267\u884c\u8bc1\u660e\u6240\u9700\u7684\u80fd\u529b\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u6559\u6388\u5982\u4f55\u8fdb\u884c\u8bc1\u660e\uff0c\u6211\u4eec\u5c06\u56de\u987e\u4e00\u4e2a\u7b80\u5355\u5b9a\u7406\u7684\u8bc1\u660e\u3002<\/p>\n\u5b9a\u7406<\/strong><\/p>\n\u5982\u679c \\alpha<\/span> \u662f\u547d\u9898\u903b\u8f91\u4e2d\u7684\u4e00\u4e2a\u8868\u8fbe\u5f0f\uff0c\u90a3\u4e48\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6<\/p>\n\\vdash (\\alpha\\rightarrow \\alpha)<\/span>\n\u8bc1\u660e<\/strong><\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td> (\\alpha\\rightarrow ( \\alpha \\rightarrow \\alpha)) <\/span><\/td>\n<td>; A1<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td> (\\alpha\\rightarrow ((\\alpha\\rightarrow \\alpha)\\rightarrow\\alpha)) <\/span><\/td>\n<td>; A1<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td> ( (\\alpha\\rightarrow((\\alpha\\rightarrow\\alpha)\\rightarrow\\alpha)) \\rightarrow ((\\alpha\\rightarrow (\\alpha\\rightarrow\\alpha))\\rightarrow( \\alpha\\rightarrow \\alpha))) <\/span><\/td>\n<td>; A2<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td> ((\\alpha\\rightarrow (\\alpha\\rightarrow\\alpha))\\rightarrow( \\alpha\\rightarrow \\alpha)) <\/span><\/td>\n<td>; MP(2,3)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td> ( \\alpha\\rightarrow \\alpha) <\/span><\/td>\n<td>; MP(1,5)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u56e0\u6b64 \\vdash (\\alpha\\rightarrow\\alpha)<\/span>\n\u8bc1\u660e\u7ed3\u675f\u3002<\/p>\n\u6b63\u5982\u53ef\u4ee5\u770b\u5230\u7684\uff0c\u5728\u6f14\u7ece\u7cfb\u7edf\u548c\u547d\u9898\u903b\u8f91\u4e2d\uff0c\u8bc1\u660e\u4e0d\u662f\u5fae\u4e0d\u8db3\u9053\u7684\uff0c\u4f46\u4e00\u65e6\u6784\u5efa\u5b8c\u6210\u5c31\u5bb9\u6613\u590d\u5236\u3002<\/p>\n\u73b0\u5728\uff0c\u5728\u6211\u4eec\u5f00\u59cb\u4f7f\u7528\u8fd9\u4e9b\u6280\u672f\u8fdb\u884c\u63a8\u65ad\u4e4b\u524d\uff0c\u9996\u5148\u6211\u4eec\u5c06\u53d1\u5c55\u4e00\u4e9b\u5bf9\u8fd9\u9879\u5de5\u4f5c\u6781\u5176\u6709\u7528\u7684\u5c5e\u6027\u548c\u5b9a\u4e49\uff0c\u56e0\u4e3a\u5982\u679c\u6211\u4eec\u53ea\u7528\u8fd9\u4e9b\u8fdb\u884c\u63a8\u7406\uff0c\u6211\u4eec\u5c06\u9047\u5230\u4e25\u91cd\u7684\u95ee\u9898\u3002<\/p>\n<a name=\"6\"><\/a><\/p>\n<h2>\u8bc1\u660e\u7b49\u4ef7\u6027\u7684\u6982\u5ff5<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=1191s\" target=\"_blank\" rel=\"noopener\">\u5982\u679c \\alpha<\/span> \u548c \\beta<\/span> \u662f\u4efb\u610f\u8868\u8fbe\u5f0f\uff0c\u5e76\u4e14<\/span> <\/strong><\/a>\u540c\u65f6\u6ee1\u8db3 \\{\\alpha\\}\\vdash \\beta<\/span> \u548c \\{\\beta\\} \\vdash \\alpha<\/span>\uff0c\u90a3\u4e48\u6211\u4eec\u8bf4 \\alpha<\/span> \u548c \\beta<\/span> \u88ab\u8bc1\u660e\u662f\u7b49\u4ef7\u7684\uff0c\u5e76\u5199\u4f5c \\alpha \\dashv \\vdash \\beta<\/span>\u3002\u8fd9\u53ef\u4ee5\u7b26\u53f7\u5316\u5730\u6982\u62ec\u4e3a\uff1a<\/p>\n\\left(\\{\\alpha\\}\\vdash\\beta \\wedge \\{\\beta\\}\\vdash\\alpha \\right) \\Leftrightarrow \\left(\\alpha\\dashv\\vdash\\beta\\right)<\/span>\n\u8fd9\u8bfb\u4f5c\uff1a\u4ece \\alpha<\/span> \u63a8\u51fa \\beta<\/span>\uff0c\u4e14\u4ece \\beta<\/span> \u63a8\u51fa \\alpha<\/span> \u5f53\u4e14\u4ec5\u5f53 \\alpha<\/span> \u548c \\beta<\/span> \u88ab\u8bc1\u660e\u662f\u7b49\u4ef7\u7684\u3002<\/p>\n\u8fd9\u662f\u547d\u9898\u903b\u8f91\u7684\u4e00\u79cd\u5143\u6027\u8d28\u3002<\/p>\n<a name=\"7\"><\/a><\/p>\n<h2>\u6f14\u7ece\uff08\u5143\uff09\u5b9a\u7406<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=1355s\" target=\"_blank\" rel=\"noopener\">\u5982\u679c \\alpha<\/span> \u548c \\beta<\/span> \u662f\u547d\u9898\u6f14\u7b97\u7684\u8868\u8fbe\u5f0f\uff0c<\/span><\/strong><\/a>\u4e14 \\Gamma<\/span> \u662f\u4e00\u7ec4\u524d\u63d0\uff1b\u90a3\u4e48\u5982\u679c\u4ece \\Gamma \\cup \\{\\alpha\\}<\/span> \u53ef\u4ee5\u63a8\u5bfc\u51fa \\beta<\/span>\uff0c\u5219\u610f\u5473\u7740\u4ece \\Gamma<\/span> \u53ef\u4ee5\u63a8\u5bfc\u51fa (\\alpha \\rightarrow \\beta)<\/span>\u3002\u7b26\u53f7\u5316\u8868\u793a\u4e3a\uff1a<\/p>\n\\left(\\Gamma \\cup \\{\\alpha\\}\\vdash \\beta \\right) \\Rightarrow \\left( \\Gamma\\vdash(\\alpha\\rightarrow\\beta)\\right)\n\n<\/span>\n\u8bc1\u660e\uff1a<\/strong><\/p>\n\u4e3a\u4e86\u6ee1\u8db3 \\Gamma \\cup \\{\\alpha\\}\\vdash \\beta<\/span>\uff0c\u5fc5\u987b\u6709\u4ee5\u4e0b\u5f62\u5f0f\u7684\u63a8\u5bfc\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td>\\gamma_1<\/span><\/td>\n<td>; \\Gamma<\/span> \u7684\u7b2c1\u4e2a\u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>\\vdots<\/span><\/td>\n<td>\\vdots<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(n)<\/td>\n<td>\\gamma_n<\/span><\/td>\n<td>; \\Gamma<\/span> \u7684\u7b2cn\u4e2a\u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(n+1)<\/td>\n<td>\\overline{\\gamma}_1<\/span><\/td>\n<td>; \u4e4b\u524d\u67d0\u4e24\u884c\u4e4b\u95f4\u7684\u80af\u5b9a\u524d\u4ef6\u6cd5<\/td>\n<\/tr>\n<tr>\n<td>\\vdots<\/span><\/td>\n<td>\\vdots<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(n+m)<\/td>\n<td>\\overline{\\gamma}_m<\/span><\/td>\n<td>; \u4e4b\u524d\u67d0\u4e24\u884c\u4e4b\u95f4\u7684\u80af\u5b9a\u524d\u4ef6\u6cd5<\/td>\n<\/tr>\n<tr>\n<td>(n+m+1)<\/td>\n<td>\\alpha<\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(n+m+2)<\/td>\n<td>\\beta<\/span><\/td>\n<td>; \u80af\u5b9a\u524d\u4ef6\u6cd5 (n+m+1, \u5176\u4ed6\u4e4b\u524d\u7684\u6b65\u9aa4\uff0c\u9664\u4e86 n+m+1)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u56e0\u6b64 \\Gamma\\cup\\{\\alpha\\} \\vdash \\beta <\/span>\n\u8981\u4f7f\u8fd9\u6210\u4e3a\u53ef\u80fd\uff0c\u81f3\u5c11 \\gamma_1, \\cdots \\gamma_n,\\overline{\\gamma_1},\\cdots,\\overline{\\gamma_m}<\/span> \u4e2d\u7684\u4e00\u4e2a\u8868\u8fbe\u5f0f\u5fc5\u987b\u662f (\\alpha\\rightarrow \\beta)<\/span> \u7684\u5f62\u5f0f\uff0c\u4f46\u6240\u6709\u8fd9\u4e9b\u884c\u4ec5\u6d89\u53ca \\Gamma<\/span> \u548c \u0141ukasiewicz \u516c\u7406\u7684\u63a8\u5bfc\uff0c\u56e0\u6b64\u5fc5\u987b\u6ee1\u8db3 \\Gamma\\vdash (\\alpha \\rightarrow \\beta)<\/span>\u3002\u56e0\u6b64\u8bc1\u660e\u4e86\u5b9a\u7406<\/p>\n\u8bc1\u660e\u7ed3\u675f\u3002<\/p>\n<a name=\"8\"><\/a><\/p>\n<h2>\u6f14\u7ece\u5b9a\u7406\u7684\u9006\u5b9a\u7406<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=1668s\" target=\"_blank\" rel=\"noopener\">\u5728\u4e0e\u6f14\u7ece\u5b9a\u7406\u76f8\u540c\u7684\u6761\u4ef6\u4e0b\uff0c\u6211\u4eec\u5c06\u6709<\/span><\/strong><\/a><\/p>\n\n\\left(\\Gamma\\vdash(\\alpha \\rightarrow \\beta)\\right) \\Rightarrow \\left( \\Gamma \\cup \\{\\alpha\\}\\vdash \\beta \\right)\n\n<\/span>\n\u8bc1\u660e\uff1a<\/strong><\/p>\n\u5982\u679c\u6ee1\u8db3 \\Gamma\\vdash (\\alpha\\rightarrow \\beta)<\/span>\uff0c\u5219\u6709\u4ee5\u4e0b\u5f62\u5f0f\u7684\u63a8\u5bfc\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td>\\gamma_1<\/span><\/td>\n<td>; \\Gamma<\/span> \u7684\u7b2c1\u4e2a\u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>\\vdots<\/span><\/td>\n<td>\\vdots<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(n)<\/td>\n<td>\\gamma_n<\/span><\/td>\n<td>; \\Gamma<\/span> \u7684\u7b2cn\u4e2a\u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(n+1)<\/td>\n<td>(\\alpha \\rightarrow \\beta)<\/span><\/td>\n<td>; \u80af\u5b9a\u524d\u4ef6\u6cd5\uff08\u5728\u4e4b\u524d\u67d0\u4e24\u884c\u4e4b\u95f4\uff09<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u73b0\u5728\uff0c\u5982\u679c\u6211\u4eec\u5c06 \\alpha<\/span> \u4f5c\u4e3a\u989d\u5916\u7684\u524d\u63d0\u6dfb\u52a0\u5230\u8fd9\u4e2a\u63a8\u7406\u4e2d\uff0c\u90a3\u4e48\u6211\u4eec\u5c06\u6709\u4ee5\u4e0b\u884c\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(n+2)<\/td>\n<td>\\alpha<\/span><\/td>\n<td>; \u989d\u5916\u7684\u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(n+3)<\/td>\n<td>\\beta<\/span><\/td>\n<td>; MP(n+1,n+2)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u56e0\u6b64 \\Gamma \\cup \\{\\alpha\\} \\vdash \\beta<\/span>\n\u8fd9\u6b63\u662f\u6211\u4eec\u60f3\u8981\u8bc1\u660e\u7684\u3002<\/p>\n\u8bc1\u660e\u7ed3\u675f\u3002<\/p>\n<a name=\"9\"><\/a><\/p>\n<h2>\u5173\u4e8e\u8868\u8fbe\u5f0f\u7684\u63a8\u7406\u548c\u5173\u4e8e\u63a8\u7406\u7684\u63a8\u7406<\/h2>\n\u5c31\u50cf\u4e4b\u524d\u4e3a\u4e86\u5f97\u5230\u7ed3\u679c \\vdash (\\alpha\\rightarrow \\alpha)<\/span> \u6240\u505a\u7684\u6f14\u793a\u90a3\u6837\uff0c\u8fd9\u4e9b\u90fd\u662f\u57fa\u4e8e\u8868\u8fbe\u5f0f\u7684\u63a8\u5bfc\u6848\u4f8b\uff0c\u56e0\u4e3a\u6bcf\u4e00\u6b65\u90fd\u5305\u542b\u4e86\u4e00\u4e2a\u5177\u4f53\u7684\u8868\u8fbe\u5f0f\u3002\u7c7b\u4f3c\u5730\uff0c\u4e5f\u53ef\u4ee5\u57fa\u4e8e\u5176\u4ed6\u63a8\u5bfc\u8fdb\u884c\u63a8\u5bfc\uff0c\u5176\u4e2d\u6bcf\u4e00\u6b65\u672c\u8eab\u5c31\u662f\u4e00\u6b21\u63a8\u5bfc\u3002\u5728\u5b9e\u8df5\u4e2d\uff0c\u8fd9\u4e24\u79cd\u65b9\u5f0f\u7684\u64cd\u4f5c\u662f\u76f8\u4f3c\u7684\uff0c\u4f46\u540e\u8005\u8ba9\u6211\u4eec\u80fd\u591f\u5229\u7528\u6f14\u7ece\u5b9a\u7406\u53ca\u5176\u9006\u5b9a\u7406\uff0c\u4ece\u800c\u5927\u5927\u589e\u52a0\u4e86\u63a8\u7406\u6280\u5de7\u7684\u7075\u6d3b\u6027\u3002\u4e3a\u4e86\u5c55\u793a\u8fd9\u4e00\u70b9\uff0c\u8ba9\u6211\u4eec\u518d\u6b21\u8bc1\u660e \\vdash (\\alpha \\rightarrow \\alpha)<\/span>\uff0c\u4f46\u8fd9\u6b21\u4f7f\u7528\u63a8\u5bfc\u800c\u975e\u8868\u8fbe\u5f0f\u3002\u5176\u66ff\u4ee3\u65b9\u6848\u5982\u4e0b\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td>\\vdash (\\alpha \\rightarrow (\\alpha \\rightarrow \\alpha))<\/span><\/td>\n<td>; A1<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td>\\{\\alpha\\}\\vdash ( \\alpha \\rightarrow \\alpha)<\/span><\/td>\n<td>; TD\u7684\u9006(1)<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td>\\{\\alpha\\}\\cup \\{\\alpha\\}\\vdash \\alpha<\/span><\/td>\n<td>; TD\u7684\u9006(2)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td>\\{\\alpha\\}\\vdash \\alpha<\/span><\/td>\n<td>; \u6ce8\u610f \\{\\alpha\\}\\cup\\{\\alpha\\}=\\{\\alpha\\}<\/span><\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td>\\vdash (\\alpha\\rightarrow \\alpha)<\/span><\/td>\n<td>; TD(4)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u6ce8\u610f\uff0c\u8fd9\u4e2a\u63a8\u7406\u5e76\u4e0d\u6bd4\u6211\u4eec\u4e4b\u524d\u505a\u7684\u66f4\u77ed\uff0c\u4f46\u5b9e\u73b0\u8d77\u6765\u8981\u5bb9\u6613\u5f97\u591a\uff0c\u6211\u4eec\u53ea\u9700\u5229\u7528\u6f14\u7ece\u5b9a\u7406\u3001\u5176\u9006\u5b9a\u7406\u548c\u516c\u7406\u65b9\u6848A1\u6765\u6784\u5efa\u8bc1\u660e\u3002<\/p>\n\u4e4d\u4e00\u770b\uff0c\u6211\u4eec\u4f3c\u4e4e\u53ea\u4f7f\u7528\u4e86\u0141ukasiewicz\u7684\u4e00\u4e2a\u516c\u7406\uff0c\u5e76\u4e14\u5ffd\u7565\u4e86\u5176\u4ed6\u516c\u7406\u548c\u80af\u5b9a\u524d\u4ef6\u6cd5\u3002\u8fd9\u662f\u5426\u610f\u5473\u7740\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\u63a8\u7406\uff0c\u6211\u4eec\u5c31\u5ffd\u89c6\u4e86\u5176\u4ed6\u516c\u7406\u548c\u80af\u5b9a\u524d\u4ef6\u6cd5\uff1f\u7b54\u6848\u662f\u65e2\u662f\u53c8\u4e0d\u662f\u3002\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u53ef\u4ee5\u5047\u88c5\u5ffd\u7565\u4e86\u67d0\u4e9b\u516c\u7406\u548c\u80af\u5b9a\u524d\u4ef6\u6cd5\uff0c\u4ec5\u56e0\u4e3a\u6211\u4eec\u6ca1\u6709\u663e\u5f0f\u5730\u4f7f\u7528\u5b83\u4eec\uff0c\u4f46\u5fc5\u987b\u8bb0\u4f4f\uff0c\u6f14\u7ece\u5b9a\u7406\u53ca\u5176\u9006\u5b9a\u7406\u6b63\u662f\u57fa\u4e8e\u0141ukasiewicz\u7684\u516c\u7406\u548c\u80af\u5b9a\u524d\u4ef6\u6cd5\u800c\u4ea7\u751f\u7684\uff0c\u8fd9\u610f\u5473\u7740\uff0c\u6b63\u5982\u6211\u4eec\u5728\u521a\u624d\u7684\u63a8\u7406\u4e2d\u6240\u505a\u7684\u90a3\u6837\uff0c\u4f7f\u7528\u5b83\u4eec\u5b9e\u9645\u4e0a\u662f\u5728\u9690\u5f0f\u5730\u4f7f\u7528\u5b83\u4eec\u3002<\/p>\n<a name=\"10\"><\/a><\/p>\n<h2>\u5355\u8c03\u6027\u89c4\u5219<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=1972s\" target=\"_blank\" rel=\"noopener\">\u5982\u679c \\tau<\/span> \u662f\u4e00\u4e2a\u5b9a\u7406\uff0c<\/span><\/strong><\/a>\u90a3\u4e48\u5bf9\u4e8e\u4efb\u4f55\u8868\u8fbe\u5f0f \\beta<\/span>\uff0c\u5c06\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/p>\n\\{\\beta\\}\\vdash\\tau<\/span>\n\u8fd9\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u975e\u5e38\u5bb9\u6613\u8bc1\u660e\u7684\u89c4\u5219\uff0c\u56e0\u4e3a\u4f5c\u4e3a\u5b9a\u7406\u7684 \\tau<\/span> \u610f\u5473\u7740 \\vdash \\tau<\/span>\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b58\u5728\u4e00\u4e2a\u63a8\u7406\uff0c\u65e0\u9700\u6dfb\u52a0\u4efb\u4f55\u524d\u63d0\u5c31\u80fd\u5f97\u5230\u8868\u8fbe\u5f0f \\tau<\/span>\uff0c\u56e0\u6b64\u6dfb\u52a0\u4e00\u4e2a\u989d\u5916\u7684\u8868\u8fbe\u5f0f\u5230\uff08\u7a7a\u7684\uff09\u524d\u63d0\u4e2d\u4e0d\u4f1a\u4ea7\u751f\u5dee\u5f02\u3002<\/p>\n\u4e0e\u6b64\u7c7b\u4f3c\uff0c\u53ef\u4ee5\u63d0\u51fa\u4ee5\u4e0b\u7ed3\u679c\uff1a\u5982\u679c\u4ece\u4e00\u7ec4\u524d\u63d0 \\Gamma<\/span> \u63a8\u51fa \\gamma<\/span>\uff0c\u90a3\u4e48\u5c06\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/p>\n\\Gamma\\cup\\{\\alpha\\}\\vdash\\gamma<\/span>\n\u5176\u4e2d \\alpha<\/span> \u662f\u4efb\u610f\u8868\u8fbe\u5f0f\u3002<\/p>\n<a name=\"11\"><\/a><\/p>\n<h2>\u5bf9\u6f14\u7ece\u7cfb\u7edf\u548c\u547d\u9898\u903b\u8f91\u7684\u7efc\u5408\u601d\u8003<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=1933s\" target=\"_blank\" rel=\"noopener\">\u5f53\u6211\u4eec\u4e3a\u547d\u9898\u903b\u8f91\u8bed\u8a00\u63d0\u4f9b\u4e00\u4e2a\u63a8\u7406\u89c4\u5219\u548c\u57fa\u672c\u8868\u8fbe\u5f0f\u65f6\uff1a<\/span><\/strong><\/a>\u80af\u5b9a\u524d\u4ef6\u6cd5\u548c\u0141ukasiewicz\u516c\u7406\uff0c\u6211\u4eec\u6240\u505a\u7684\u7c7b\u4f3c\u4e8e\u6784\u5efa\u4e00\u4e2a\u201c\u6f14\u7ece\u673a\u5668\u201d\u548c\u63d0\u4f9b\u201c\u542f\u52a8\u5176\u8fd0\u52a8\u7684\u80fd\u91cf\u201d\u3002\u4ece\u8fd9\u91cc\u5f00\u59cb\uff0c\u6240\u6709\u57fa\u672c\u7684\u6f14\u7ece\u89c4\u5219\u81ea\u7136\u5730\u5f00\u59cb\u6d8c\u73b0\uff0c\u5e76\u4e14\u6211\u4eec\u5c06\u5728\u8fd9\u4e4b\u540e\u7684\u90e8\u5206\u4e2d\u5f00\u59cb\u56de\u987e\u3002<\/p>\n\u8fd8\u6709\u4e00\u4e2a\u7ec6\u8282\u3002\u547d\u9898\u903b\u8f91\u7684\u8868\u8fbe\u5f0f\u5b9e\u9645\u4e0a\u662f\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\u4e24\u4e2a\u7b26\u53f7\u8bed\u8a00\u7684\u5143\u8868\u8fbe\u5f0f\u3002\u8bf7\u8bb0\u4f4f\uff0c\u8fd9\u4e9b\u5143\u8868\u8fbe\u5f0f\u7684\u7cbe\u5999\u4e4b\u5904\u5728\u4e8e\uff0c\u5b83\u4eec\u5141\u8bb8\u6211\u4eec\u7528\u4efb\u4f55\u8bed\u8a00\u7684\u8868\u8fbe\u5f0f\u66ff\u6362\u5b83\u4eec\u7684\u5143\u53d8\u91cf\uff0c\u4ece\u800c\u83b7\u5f97\u6ee1\u8db3\u8be5\u7ed3\u6784\u7684\u65b0\u8868\u8fbe\u5f0f\u3002\u5f53\u6211\u4eec\u4e3a\u547d\u9898\u903b\u8f91\u8bed\u8a00\u63d0\u4f9b\u516c\u7406\u6a21\u5f0f\u548c\u63a8\u7406\u89c4\u5219\u65f6\uff0c\u6211\u4eec\u6784\u5efa\u4e86\u547d\u9898\u903b\u8f91\u7684\u6f14\u7ece\u7cfb\u7edf\uff0c\u5b83\u5141\u8bb8\u751f\u6210\u8fde\u63a5\u8868\u8fbe\u5f0f\u7684\u63a8\u5bfc\u3002\u7ed3\u679c\u662f\u6211\u4eec\u62e5\u6709\u4e86\u4e00\u4e2a\u80fd\u591f\u5305\u542b\u65e0\u9650\u63a8\u5bfc\u7684\u6f14\u7ece\u6846\u67b6\uff1a\u6240\u6709\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u66ff\u6362\u5143\u53d8\u91cf\u4e3a\u6211\u4eec\u60f3\u8981\u7684\u8868\u8fbe\u5f0f\u800c\u83b7\u5f97\u7684\u63a8\u5bfc\u3002\u5f53\u6211\u4eec\u610f\u8bc6\u5230\u4e0d\u4ec5\u4ec5\u662f\u6211\u4eec\u4e00\u5f00\u59cb\u4f7f\u7528\u7684\u90a3\u4e9b\u4e24\u4e2a\u7b26\u53f7\u8bed\u8a00\u7684\u8868\u8fbe\u5f0f\uff0c\u800c\u662f\u5f53\u6211\u4eec\u4ee3\u66ff\u4f7f\u7528\u6211\u4eec\u901a\u5e38\u8bed\u8a00\u7684\u8868\u8fbe\u5f0f\u65f6\uff0c\u903b\u8f91\u7684\u529b\u91cf\u771f\u6b63\u5730\u88ab\u91ca\u653e\u51fa\u6765\uff0c\u56e0\u6b64\u6211\u4eec\u5bf9\u6b64\u611f\u5230\u60ca\u5947\u3002<\/p>\n<\/body> \n<\/html><\/p>\n","protected":false},"excerpt":{"rendered":"\u547d\u9898\u903b\u8f91\u4e2d\u7684\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf – \u5b8c\u6574\u6307\u5357 \u547d\u9898\u903b\u8f91\u4e2d\u7684\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf \u6458\u8981\uff1a\u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\u3002\u89e3\u91ca\u8fd9\u4e9b\u7cfb\u7edf\u5982\u4f55\u7528\u4e8e\u89e3\u5bc6\u903b\u8f91\u8868\u8fbe\u5f0f\u4e4b\u95f4\u53ef\u80fd\u5b58\u5728\u7684\u5173\u7cfb\uff0c\u4ee5\u53ca\u6784\u5efa\u8fd9\u4e9b\u8bc1\u660e\u7684\u57fa\u672c\u5143\u7d20\uff1a\u8bed\u8a00\u3001\u516c\u7406\u548c\u63a8\u7406\u89c4\u5219\u3002\u8fd9\u91cc\u63d0\u5230\u4e86\u0141ukasiewicz\u7684\u516c\u7406\uff0c\u5e76\u89e3\u91ca\u4e86\u547d\u9898\u6f14\u7b97\u7684\u6f14\u7ece\u5f15\u64ce modus ponens\u3002\u6b64\u5916\uff0c\u8fd8\u8ba8\u8bba\u4e86\u63a8\u7406\u3001\u5b9a\u7406\u548c\u524d\u63d0\uff0c\u5e76\u89e3\u91ca\u4e86\u5728\u6f14\u7ece\u7cfb\u7edf\u4e2d\u5982\u4f55\u6267\u884c\u63a8\u7406\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u7406\u89e3\u547d\u9898\u903b\u8f91\u4e2d\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\u7684\u6982\u5ff5\u3002 \u8bc6\u522b\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\u7684\u57fa\u672c\u7ec4\u6210\u90e8\u5206\u3002 \u4e86\u89e3\u547d\u9898\u6f14\u7b97\u4e2d\u0141ukasiewicz\u7684\u516c\u7406\u3002 \u7406\u89e3modus ponens\u4f5c\u4e3a\u547d\u9898\u6f14\u7b97\u7684\u6f14\u7ece\u5f15\u64ce\u3002 \u7406\u89e3\u6f14\u7ece\u7cfb\u7edf\u4e2d\u5982\u4f55\u6267\u884c\u63a8\u7406\u4ee5\u53ca\u524d\u63d0\u3001\u63a8\u7406\u548c\u5b9a\u7406\u4e4b\u95f4\u7684\u533a\u522b\u3002 \u7406\u89e3\u5982\u4f55\u901a\u8fc7\u516c\u7406\u6a21\u5f0f\u548c\u63a8\u7406\u89c4\u5219\u751f\u6210\u63a8\u7406\u3002 \u8ba4\u8bc6\u903b\u8f91\u8fde\u63a5\u8868\u8fbe\u5f0f\u5e76\u7528\u5e38\u7528\u8bed\u8a00\u66ff\u6362\u5b83\u4eec\u7684\u80fd\u529b\u3002 \u5185\u5bb9\u76ee\u5f55: \u4ec0\u4e48\u662f\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\uff1f \u547d\u9898\u903b\u8f91\u4e2d\u7684\u0141ukasiewicz\u516c\u7406 Modus Ponens\uff1a\u547d\u9898\u6f14\u7b97\u7684\u6f14\u7ece\u5f15\u64ce \u63a8\u7406\u3001\u5b9a\u7406\u548c\u524d\u63d0 \u5982\u4f55\u5728\u547d\u9898\u903b\u8f91\u4e2d\u8fdb\u884c\u8bc1\u660e\uff1f \u8bc1\u660e\u7b49\u4ef7\u6027\u7684\u6982\u5ff5 \u6f14\u7ece(Meta)\u5b9a\u7406 \u6f14\u7ece\u5b9a\u7406\u7684\u9006\u5b9a\u7406 \u5173\u4e8e\u8868\u8fbe\u5f0f\u7684\u63a8\u7406\u548c\u5173\u4e8e\u63a8\u7406\u7684\u63a8\u7406 \u5355\u8c03\u6027\u89c4\u5219 \u5bf9\u5f62\u5f0f\u6f14\u7ece\u7cfb\u7edf\u548c\u547d\u9898\u903b\u8f91\u7684\u7efc\u5408\u601d\u8003 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