{"id":27348,"date":"2021-01-27T13:00:41","date_gmt":"2021-01-27T13:00:41","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27348"},"modified":"2024-07-07T23:45:06","modified_gmt":"2024-07-07T23:45:06","slug":"4%e7%a7%8d%e5%bf%85%e4%b8%8d%e5%8f%af%e5%b0%91%e7%9a%84%e6%8e%a8%e7%90%86%e6%8a%80%e5%b7%a7","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/4%e7%a7%8d%e5%bf%85%e4%b8%8d%e5%8f%af%e5%b0%91%e7%9a%84%e6%8e%a8%e7%90%86%e6%8a%80%e5%b7%a7\/","title":{"rendered":"4\u79cd\u5fc5\u4e0d\u53ef\u5c11\u7684\u63a8\u7406\u6280\u5de7"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u5b66\u4e60 4 \u4e2a\u5fc5\u5907\u7684\u63a8\u7406\u6280\u5de7<\/h1>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><em><strong>\u6458\u8981\uff1a<\/strong><\/br>\u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u63cf\u8ff0\u4e86 4 \u79cd\u547d\u9898\u903b\u8f91\u7684\u63a8\u7406\u6280\u5de7\uff0c\u4ee5\u4e30\u5bcc\u8fc4\u4eca\u4e3a\u6b62\u5c55\u793a\u7684\u521d\u6b65\u547d\u9898\u8ba1\u7b97\u3002\u6211\u4eec\u4ecb\u7ecd\u4e86\u5047\u8bbe\u89c4\u5219\u53ca\u5176\u4e0e\u5355\u8c03\u6027\u89c4\u5219\u7684\u7ed3\u5408\uff0c\u4ee5\u53ca\u5047\u8bbe\u4e09\u6bb5\u8bba\u548c\u4e24\u79cd\u83b7\u5f97\u8be5\u63a8\u7406\u89c4\u5219\u7684\u65b9\u6cd5\u3002\u8fd8\u89e3\u91ca\u4e86\u53cc\u91cd\u5426\u5b9a\u7b49\u4ef7\u548c\u8574\u6db5\u7684\u9006\u5426\u547d\u9898\u3002<\/em><\/p>\n<p style=\"text-align:center;\"><strong><u>\u5b66\u4e60\u76ee\u6807<\/u>\uff1a<\/strong><br \/>\u5728\u672c\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f<\/p>\n<ol>\n<li><strong>\u56de\u5fc6<\/strong>\u63a8\u7406\u7684\u7ed3\u6784\u548c\u7b80\u5355\u7684\u4f8b\u5b50\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u5047\u8bbe\u89c4\u5219\u53ca\u5176\u4e0e\u63a8\u7406\u5b9a\u7406\u7684\u5173\u7cfb\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u5047\u8bbe\u4e09\u6bb5\u8bba\u53ca\u5176\u4e0e\u80af\u5b9a\u524d\u4ef6\u6cd5\u5219\u7684\u5173\u7cfb\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u63a8\u7406\u5b9a\u7406\u4e8e\u547d\u9898\u903b\u8f91\u4e2d\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u5355\u8c03\u6027\u89c4\u5219\u4e8e\u8868\u8fbe\u5f0f\u63a8\u7406\u4e2d\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u547d\u9898\u903b\u8f91\u4e2d\u7684\u53cc\u91cd\u5426\u5b9a\u7b49\u4ef7\u548c\u8574\u6db5\u7684\u9006\u5426\u547d\u9898\u3002<\/li>\n<li><strong>\u4e86\u89e3<\/strong>\u63a8\u7406\u6280\u5de7\u7684\u8bc1\u660e\uff0c\u5e76\u80fd\u5728\u5b9e\u8df5\u4e2d\u5e94\u7528\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u5185\u5bb9\u76ee\u5f55<\/strong><br \/>\n<a href=\"#1\">\u5047\u8bbe\u89c4\u5219 (PRE)<\/a><br \/>\n<a href=\"#2\">\u5047\u8bbe\u4e09\u6bb5\u8bba (SH)<\/a><br \/>\n<a href=\"#3\">\u53cc\u91cd\u5426\u5b9a\u7b49\u4ef7 (DN)<\/a><br \/>\n<a href=\"#4\">\u8574\u6db5\u7684\u9006\u5426\u547d\u9898\u7b49\u4ef7 (CPI)<\/a>\n<\/p>\n<p><center><br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/6f_aavuC4E0\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p style=\"text-align: justify; color: #000000;\">\u6211\u4eec\u5df2\u7ecf\u770b\u5230\u4e86\u63a8\u7406\u7684\u7ed3\u6784\u548c\u7b80\u5355\u7684\u4f8b\u5b50\u3002\u73b0\u5728\u6211\u4eec\u5c06\u901a\u8fc7 <strong>4 \u79cd\u547d\u9898\u903b\u8f91\u7684\u63a8\u7406\u6280\u5de7<\/strong> \u6765\u68c0\u9a8c\u8fd9\u4e9b\u77e5\u8bc6\u3002\u901a\u8fc7\u8fd9\u70b9\uff0c\u6211\u4eec\u4e0d\u4ec5\u4f1a\u770b\u5230\u8fd9\u4e9b\u4e1c\u897f\u5982\u4f55\u5de5\u4f5c\uff0c\u800c\u4e14\u8fd8\u4f1a\u5f00\u59cb\u5f15\u5165\u4e00\u4e9b\u4e30\u5bcc\u7684\u7a0b\u5e8f\uff0c\u8fd9\u5c06\u4f7f\u8fc4\u4eca\u4e3a\u6b62\u5c55\u793a\u7684\u521d\u6b65\u547d\u9898\u8ba1\u7b97\u6446\u8131\u5176\u521d\u6b65\u72b6\u6001\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>\u5982\u679c <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span>\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span> \u662f\u547d\u9898\u8ba1\u7b97\u7684\u8868\u8fbe\u5f0f\uff0c\u90a3\u4e48\u53ef\u4ee5\u4ece\u57fa\u7840\u63a8\u5bfc\u51fa\u4ee5\u4e0b\u63a8\u7406\u6280\u5de7\uff1a<\/strong><\/p>\n<p><a name=\"1\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u5047\u8bbe\u89c4\u5219 (Pre)<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=6f_aavuC4E0&amp;t=168s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u6700\u7b80\u5355\u7684\u63a8\u7406\u89c4\u5219<\/span><\/strong><\/a> \u662f\u5047\u8bbe\u89c4\u5219\u3002\u8fd9\u662f\u901a\u8fc7\u5bf9\u5b9a\u7406 <span class=\"katex-eq\" data-katex-display=\"false\">\\vdash(\\alpha\\rightarrow\\alpha)<\/span> \u5e94\u7528 <strong>\u63a8\u7406\u5b9a\u7406\u7684\u9006\u547d\u9898<\/strong> \u76f4\u63a5\u83b7\u5f97\u7684\u3002\u5982\u679c\u8fd9\u4e9b\u542c\u8d77\u6765\u50cf\u662f\u6666\u6da9\u96be\u61c2\u7684\u8bed\u8a00\uff0c\u90a3\u4e48\u4f60\u9700\u8981\u77e5\u9053\u7684\u4e00\u5207\u90fd\u5728 <a href=\"http:\/\/toposuranos.com\/material\/zh\/%e5%bd%a2%e5%bc%8f%e6%bc%94%e7%bb%8e%e7%b3%bb%e7%bb%9f%ef%bc%9a%e5%ae%9a%e4%b9%89%e4%b8%8e%e7%a4%ba%e4%be%8b\/\" rel=\"noopener\" target=\"_blank\"><strong>\u8fd9\u91cc<\/strong><\/a>\u3002<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\}\\vdash \\alpha <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u4e0e\u5355\u8c03\u6027\u89c4\u5219\u7ed3\u5408\uff0c\u5b83\u5c06\u5141\u8bb8\u4f60\u5728\u63a8\u7406\u4e2d\u6dfb\u52a0\u65b9\u4fbf\u7684\u8868\u8fbe\u5f0f\u3002<\/p>\n<p><a name=\"2\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u5047\u8bbe\u4e09\u6bb5\u8bba (SH)<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=6f_aavuC4E0&amp;t=206s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5047\u8bbe\u4e09\u6bb5\u8bba<\/span><\/strong><\/a>\uff0c\u6216\u8574\u6db5\u7684\u4f20\u9012\u6027\uff0c\u662f\u80af\u5b9a\u524d\u4ef6\u6cd5\u5219\u7684\u4e00\u79cd\u6f14\u53d8\u3002\u5176\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha\\rightarrow\\beta), (\\beta\\rightarrow\\gamma)\\}\\vdash (\\alpha\\rightarrow\\gamma)<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u6709\u51e0\u79cd\u65b9\u6cd5\u53ef\u4ee5\u83b7\u5f97\u8fd9\u4e2a\u63a8\u7406\u89c4\u5219\uff0c\u6211\u4eec\u5f88\u5feb\u5c31\u4f1a\u770b\u5230\u5176\u4e2d\u7684\u4e00\u4e9b\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c\u6211\u4eec\u4ece\u8868\u8fbe\u5f0f\u5f00\u59cb\u63a8\u7406\uff0c\u6784\u5efa\u4ee5\u4e0b\u63a8\u7406\u5c06\u5f88\u5bb9\u6613\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\rightarrow \\beta)<\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(\\beta\\rightarrow \\gamma)<\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/td>\n<td>; MP(1,2)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span><\/td>\n<td>; MP(4,3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center; color: #000000;\">\u56e0\u6b64<span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha,(\\alpha\\rightarrow\\beta),(\\beta\\rightarrow\\gamma)\\}\\vdash\\gamma<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\uff0c\u5e94\u7528\u63a8\u7406\u5b9a\u7406\u5728\u8fd9\u4e2a\u6700\u540e\u7684\u8868\u8fbe\u5f0f\u4e0a\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{(\\alpha\\rightarrow\\beta),(\\beta\\rightarrow\\gamma)\\}\\vdash(\\alpha\\rightarrow \\gamma)<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u53e6\u4e00\u79cd\u83b7\u5f97\u8fd9\u4e2a\u89c4\u5219\u7684\u8bc1\u660e\u65b9\u6cd5\u662f\u901a\u8fc7\u63a8\u7406\u63a8\u7406\uff0c\u5229\u7528\u5047\u8bbe\u548c\u5355\u8c03\u6027\u6784\u5efa\u3002\u8bf7\u89c2\u5bdf\u4ee5\u4e0b\u63a8\u7406\u63a8\u7406\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha, (\\alpha\\rightarrow \\beta), (\\beta\\rightarrow\\gamma)\\}\\vdash \\alpha <\/span><\/td>\n<td>; \u5047\u8bbe\u548c\u5355\u8c03\u6027<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha, (\\alpha\\rightarrow \\beta), (\\beta\\rightarrow\\gamma)\\}\\vdash (\\alpha\\rightarrow \\beta) <\/span><\/td>\n<td>; \u5047\u8bbe\u548c\u5355\u8c03\u6027<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha, (\\alpha\\rightarrow \\beta), (\\beta\\rightarrow\\gamma)\\}\\vdash (\\beta\\rightarrow\\gamma) <\/span><\/td>\n<td>; \u5047\u8bbe\u548c\u5355\u8c03\u6027<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha, (\\alpha\\rightarrow \\beta), (\\beta\\rightarrow\\gamma)\\}\\vdash \\beta <\/span><\/td>\n<td>; MP(1,2)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha, (\\alpha\\rightarrow \\beta), (\\beta\\rightarrow\\gamma)\\}\\vdash \\gamma <\/span><\/td>\n<td>; MP(4,3)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha\\rightarrow \\beta), (\\beta\\rightarrow\\gamma)\\}\\vdash (\\alpha \\rightarrow \\gamma) <\/span><\/td>\n<td>; TD(5)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u4f60\u5e94\u8be5\u6ce8\u610f\u5230\uff0c\u8fd9\u4e24\u79cd\u8bc1\u660e\u662f\u76f8\u540c\u7684\uff0c\u53ea\u662f\u7528\u4e0d\u540c\u7684\u98ce\u683c\u5f00\u53d1\u7684\u3002\u5728\u5b9e\u8df5\u4e2d\uff0c\u4f60\u53ef\u4ee5\u6839\u636e\u81ea\u5df1\u89c9\u5f97\u66f4\u8212\u9002\u7684\u60c5\u51b5\u5728\u4e24\u79cd\u98ce\u683c\u4e4b\u95f4\u4ea4\u66ff\u3002<\/p>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u53cc\u91cd\u5426\u5b9a\u7b49\u4ef7 (DN)<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=6f_aavuC4E0&amp;t=500s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u53cc\u91cd\u5426\u5b9a\u7b49\u4ef7<\/span><\/strong><\/a> \u590d\u73b0\u4e86\u76f4\u89c2\u7684\u6982\u5ff5\uff0c\u5373\u4e00\u4e2a\u547d\u9898\u7684\u53cc\u91cd\u5426\u5b9a\u7b49\u4e8e\u8be5\u547d\u9898\u672c\u8eab\u3002\u8fd9\u7528\u7b26\u53f7\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha\\dashv\\vdash\\neg\\neg\\alpha<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u73b0\u5728\u6211\u4eec\u6765\u770b\u4e00\u4e2a\u8bc1\u660e\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg\\neg \\alpha \\rightarrow (\\neg\\neg\\neg\\neg \\alpha \\rightarrow\\neg\\neg\\alpha))<\/span><\/td>\n<td>; A1<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash ((\\neg\\neg\\neg\\neg\\alpha \\rightarrow \\neg\\neg\\alpha)\\rightarrow(\\neg\\alpha \\rightarrow \\neg\\neg\\neg\\alpha))<\/span><\/td>\n<td>; A3<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash ((\\neg\\alpha \\rightarrow \\neg\\neg\\neg\\alpha)\\rightarrow(\\neg\\neg\\alpha \\rightarrow \\alpha))<\/span><\/td>\n<td>; A3<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash ((\\neg\\neg\\neg\\neg\\alpha \\rightarrow \\neg\\neg\\alpha)\\rightarrow(\\neg\\neg\\alpha \\rightarrow \\alpha))<\/span><\/td>\n<td>; SH(2,3)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg\\neg \\alpha \\} \\vdash (\\neg\\neg\\neg\\neg \\alpha \\rightarrow\\neg\\neg\\alpha)<\/span><\/td>\n<td>; RTD(1)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg\\neg \\alpha \\} \\vdash ((\\neg\\neg\\neg\\neg\\alpha \\rightarrow \\neg\\neg\\alpha)\\rightarrow(\\neg\\neg\\alpha \\rightarrow \\alpha))<\/span><\/td>\n<td>; \u5355\u8c03\u6027(4)<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg\\neg \\alpha \\} \\vdash (\\neg\\neg\\alpha \\rightarrow \\alpha)<\/span><\/td>\n<td>; MP(5,6)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg\\neg \\alpha \\} \\vdash \\alpha<\/span><\/td>\n<td>; RTD(7)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center; color: #000000;\">\u56e0\u6b64<span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg\\neg \\alpha \\} \\vdash \\alpha <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u4e3a\u4e86\u4ece\u53e6\u4e00\u4e2a\u65b9\u5411\u8fdb\u884c\u8bc1\u660e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u521a\u624d\u7684\u8bc1\u660e\uff0c\u901a\u8fc7\u7b80\u5355\u7684\u66ff\u6362\u6765\u91cd\u65b0\u9002\u5e94\uff0c\u5f97\u5230\u4ee5\u4e0b\u7ed3\u679c\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg\\neg \\neg \\alpha \\} \\vdash \\neg \\alpha <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u7136\u540e\u4ece\u8fd9\u4e00\u70b9\u5f00\u59cb\u6784\u5efa\u76f8\u53cd\u65b9\u5411\u7684\u8bc1\u660e\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg\\neg \\neg \\alpha \\} \\vdash \\neg \\alpha <\/span><\/td>\n<td>; \u521a\u624d\u7684\u8bc1\u660e<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash(\\neg\\neg \\neg \\alpha\\rightarrow \\neg \\alpha) <\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash((\\neg\\neg \\neg \\alpha\\rightarrow \\neg \\alpha) \\rightarrow(\\alpha \\rightarrow\\neg\\neg\\alpha)) <\/span><\/td>\n<td>; A3<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash(\\alpha \\rightarrow\\neg\\neg\\alpha) <\/span><\/td>\n<td>; MP(2,3)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\}\\vdash\\neg\\neg\\alpha <\/span><\/td>\n<td>; RTD(4)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center; color: #000000;\">\u56e0\u6b64 <span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha \\} \\vdash \\neg\\neg \\alpha <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\uff0c\u901a\u8fc7\u8fd9\u4e24\u4e2a\u8bc1\u660e\uff0c\u6211\u4eec\u5f97\u51fa <span class=\"katex-eq\" data-katex-display=\"false\"> \\alpha \\dashv\\vdash \\neg\\neg \\alpha <\/span>\u3002<\/p>\n<p><a name=\"4\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u8574\u6db5\u7684\u9006\u5426\u547d\u9898\u7b49\u4ef7 (CpI)<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=6f_aavuC4E0&amp;t=948s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u8fd9\u5bf9\u5e94\u4e8e<\/span><\/strong><\/a> \u4ee5\u4e0b\u7b49\u4ef7\u5173\u7cfb<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\rightarrow \\beta) \\dashv\\vdash (\\neg\\beta \\rightarrow \\neg\\alpha)<\/span>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n(\\neg\\alpha\\rightarrow\\beta)\\dashv\\vdash (\\neg\\beta\\rightarrow\\alpha)<\/span>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha\\rightarrow\\neg\\beta) \\dashv\\vdash (\\beta\\rightarrow\\neg\\alpha)<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u7b2c\u4e00\u4e2a\u5173\u7cfb\u7684\u8bc1\u660e\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u4ece\u4e00\u4e2a\u65b9\u9762\uff0c\u5b83\u53ef\u4ee5\u76f4\u63a5\u4ece\u7b2c\u4e09\u516c\u7406\u83b7\u5f97\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash ((\\neg\\beta\\rightarrow \\neg\\alpha) \\rightarrow (\\alpha \\rightarrow\\beta))<\/span><\/td>\n<td>; A3<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\beta\\rightarrow \\neg\\alpha)\\}\\vdash (\\alpha \\rightarrow \\beta)<\/span><\/td>\n<td>; RTD(1)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center; color: #000000;\">\u56e0\u6b64 <span class=\"katex-eq\" data-katex-display=\"false\"> \\{(\\neg\\beta\\rightarrow \\neg\\alpha)\\}\\vdash (\\alpha \\rightarrow \\beta)<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u5728\u53e6\u4e00\u4e2a\u65b9\u5411\u4e0a\uff0c\u8bc1\u660e\u53ef\u4ee5\u4ece\u4ee5\u4e0b\u63a8\u7406\u4e2d\u83b7\u5f97\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\neg\\neg\\alpha \\dashv \\vdash \\alpha<\/span><\/td>\n<td>; DN<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\neg\\neg \\alpha \\rightarrow \\alpha)<\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\neg\\neg\\beta \\dashv \\vdash \\beta<\/span><\/td>\n<td>; DN<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\beta \\rightarrow \\neg\\neg \\beta)<\/span><\/td>\n<td>; TD(3)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\rightarrow \\beta)\\}\\vdash (\\neg\\neg \\alpha \\rightarrow \\alpha)<\/span><\/td>\n<td>; \u5355\u8c03\u6027(2)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\rightarrow \\beta)\\}\\vdash (\\alpha \\rightarrow \\beta)<\/span><\/td>\n<td>; \u5047\u8bbe<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\rightarrow \\beta)\\}\\vdash (\\neg\\neg \\alpha \\rightarrow\\beta)<\/span><\/td>\n<td>; SH(5,6)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\{(\\alpha \\rightarrow \\beta)\\} \\vdash (\\beta \\rightarrow \\neg\\neg \\beta)<\/span><\/td>\n<td>; \u5355\u8c03\u6027(4)<\/td>\n<\/tr>\n<tr>\n<td>(9)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\rightarrow \\beta)\\}\\vdash (\\neg\\neg \\alpha \\rightarrow \\neg\\neg \\beta)<\/span><\/td>\n<td>; SH(7,8)<\/td>\n<\/tr>\n<tr>\n<td>(10)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\neg\\neg \\alpha \\rightarrow \\neg\\neg \\beta) \\rightarrow (\\neg \\beta \\rightarrow \\neg \\alpha )<\/span><\/td>\n<td>; A3<\/td>\n<\/tr>\n<tr>\n<td>(11)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\rightarrow \\beta)\\}\\vdash ((\\neg\\neg \\alpha \\rightarrow \\neg\\neg \\beta) \\rightarrow (\\neg \\beta \\rightarrow \\neg \\alpha ))<\/span><\/td>\n<td>; \u5355\u8c03\u6027(10)<\/td>\n<\/tr>\n<tr>\n<td>(11)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\rightarrow \\beta)\\}\\vdash (\\neg \\beta \\rightarrow \\neg \\alpha )<\/span><\/td>\n<td>; SH(10;11)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center; color: #000000;\">\u56e0\u6b64 <span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\rightarrow \\beta)\\}\\vdash (\\neg \\beta \\rightarrow \\neg \\alpha )<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u6b64\uff0c\u4ece\u524d\u9762\u7684\u4e24\u4e2a\u63a8\u7406\u4e2d\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\"> (\\alpha \\rightarrow \\beta) \\dashv\\vdash (\\neg \\beta \\rightarrow \\neg \\alpha ) <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u4e3a\u4e86\u8bc1\u660e\u7b2c\u4e8c\u4e2a\u7b49\u4ef7\u5173\u7cfb\uff0c\u6211\u4eec\u53ef\u4ee5\u505a\u4ee5\u4e0b\u4e24\u4e2a\u63a8\u7406\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\beta \\dashv\\vdash \\neg\\neg\\beta<\/span><\/td>\n<td>; DN<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\neg\\neg\\neg\\alpha \\dashv\\vdash \\neg\\alpha<\/span><\/td>\n<td>; DN<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\beta \\rightarrow \\neg\\neg\\beta)<\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\neg\\neg\\neg\\alpha \\rightarrow \\neg\\alpha)<\/span><\/td>\n<td>; TD(2)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\rightarrow \\beta)\\}\\vdash (\\neg\\alpha \\rightarrow \\beta)<\/span><\/td>\n<td>; \u5047\u8bbe<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\rightarrow \\beta)\\}\\vdash (\\beta \\rightarrow \\neg\\neg\\beta)<\/span><\/td>\n<td>; \u5355\u8c03\u6027(3)<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\rightarrow \\beta)\\}\\vdash (\\neg\\neg\\neg\\alpha \\rightarrow \\neg\\alpha)<\/span><\/td>\n<td>; \u5355\u8c03\u6027(4)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\rightarrow \\beta)\\}\\vdash (\\neg\\alpha \\rightarrow \\neg\\neg\\beta)<\/span><\/td>\n<td>; SH(5,6)<\/td>\n<\/tr>\n<tr>\n<td>(9)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\rightarrow \\beta)\\}\\vdash (\\neg\\neg\\neg\\alpha \\rightarrow \\neg\\neg\\beta)<\/span><\/td>\n<td>; SH(7,8)<\/td>\n<\/tr>\n<tr>\n<td>(10)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\neg\\neg\\neg\\alpha \\rightarrow \\neg\\neg\\beta) \\rightarrow (\\neg\\beta \\rightarrow \\neg\\neg\\alpha)<\/span><\/td>\n<td>; A3<\/td>\n<\/tr>\n<tr>\n<td>(11)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\rightarrow \\beta)\\}\\vdash ((\\neg\\neg\\neg\\alpha \\rightarrow \\neg\\neg\\beta) \\rightarrow (\\neg\\beta \\rightarrow \\neg\\neg\\alpha))<\/span><\/td>\n<td>; \u5355\u8c03\u6027(10)<\/td>\n<\/tr>\n<tr>\n<td>(12)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\rightarrow \\beta)\\}\\vdash (\\neg\\beta \\rightarrow \\neg\\neg\\alpha)<\/span><\/td>\n<td>; MP(9,11)<\/td>\n<\/tr>\n<tr>\n<td>(13)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\neg\\neg \\alpha \\dashv \\vdash \\alpha<\/span><\/td>\n<td>; DN<\/td>\n<\/tr>\n<tr>\n<td>(14)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg\\neg \\alpha\\rightarrow \\alpha)<\/span><\/td>\n<td>; TD(13)<\/td>\n<\/tr>\n<tr>\n<td>(15)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\rightarrow \\beta)\\} \\vdash (\\neg\\neg \\alpha\\rightarrow \\alpha)<\/span><\/td>\n<td>; \u5355\u8c03\u6027(14)<\/td>\n<\/tr>\n<tr>\n<td>(16)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\rightarrow \\beta)\\} \\vdash(\\neg\\beta \\rightarrow \\alpha)<\/span><\/td>\n<td>; SH(12,15)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center; color: #000000;\">\u56e0\u6b64 <span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\rightarrow \\beta)\\} \\vdash(\\neg\\beta \\rightarrow \\alpha) <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u73b0\u5728\u6211\u4eec\u9700\u8981\u505a\u51fa\u76f8\u53cd\u65b9\u5411\u7684\u8bc1\u660e\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u63a8\u7406\u6765\u5b9e\u73b0\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha \\dashv \\vdash \\neg\\neg\\alpha<\/span><\/td>\n<td>; DN<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\alpha \\rightarrow \\neg\\neg\\alpha)<\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\beta\\rightarrow\\alpha)\\}\\vdash (\\neg\\beta\\rightarrow\\alpha)<\/span><\/td>\n<td>; \u5047\u8bbe<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\beta\\rightarrow\\alpha)\\}\\vdash (\\alpha \\rightarrow \\neg\\neg\\alpha)<\/span><\/td>\n<td>; \u5355\u8c03\u6027(2)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\beta\\rightarrow\\alpha)\\}\\vdash (\\neg\\beta\\rightarrow\\neg\\neg\\alpha)<\/span><\/td>\n<td>; SH(3,4)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\neg\\beta\\rightarrow\\neg\\neg\\alpha)\\rightarrow (\\neg\\alpha \\rightarrow \\beta) <\/span><\/td>\n<td>; A3<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\beta\\rightarrow\\alpha)\\}\\vdash ((\\neg\\beta\\rightarrow\\neg\\neg\\alpha)\\rightarrow (\\neg\\alpha \\rightarrow \\beta)) <\/span><\/td>\n<td>; \u5355\u8c03\u6027(6)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\beta\\rightarrow\\alpha)\\}\\vdash (\\neg\\alpha \\rightarrow \\beta) <\/span><\/td>\n<td>; MP(5,7)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center; color: #000000;\">\u56e0\u6b64 <span class=\"katex-eq\" data-katex-display=\"false\"> \\{(\\neg\\beta\\rightarrow\\alpha)\\}\\vdash (\\neg\\alpha \\rightarrow \\beta) <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\uff0c\u901a\u8fc7\u8fd9\u4e24\u4e2a\u63a8\u7406\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa <span class=\"katex-eq\" data-katex-display=\"false\"> (\\neg\\beta\\rightarrow\\alpha) \\dashv \\vdash (\\neg\\alpha \\rightarrow \\beta) <\/span>\uff0c\u8fd9\u5c31\u662f\u6211\u4eec\u60f3\u8981\u8bc1\u660e\u7684\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\u4e00\u4e2a\u7b49\u4ef7\u5173\u7cfb\u5c06\u4f5c\u4e3a\u7ec3\u4e60\u3002\u4e3a\u4e86\u8bc1\u660e\u5b83\uff0c\u4f60\u53ef\u4ee5\u53c2\u8003\u6211\u5df2\u7ecf\u7ed9\u51fa\u7684\u4e24\u4e2a\u8bc1\u660e\u3002\u8fd9\u662f\u638c\u63e1\u63a8\u7406\u6280\u5de7\u7684\u6700\u4f73\u65b9\u5f0f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b66\u4e60 4 \u4e2a\u5fc5\u5907\u7684\u63a8\u7406\u6280\u5de7 \u6458\u8981\uff1a\u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u63cf\u8ff0\u4e86 4 \u79cd\u547d\u9898\u903b\u8f91\u7684\u63a8\u7406\u6280\u5de7\uff0c\u4ee5\u4e30\u5bcc\u8fc4\u4eca\u4e3a\u6b62\u5c55\u793a\u7684\u521d\u6b65\u547d\u9898\u8ba1\u7b97\u3002\u6211\u4eec\u4ecb\u7ecd\u4e86\u5047\u8bbe\u89c4\u5219\u53ca\u5176\u4e0e\u5355\u8c03\u6027\u89c4\u5219\u7684\u7ed3\u5408\uff0c\u4ee5\u53ca\u5047\u8bbe\u4e09\u6bb5\u8bba\u548c\u4e24\u79cd\u83b7\u5f97\u8be5\u63a8\u7406\u89c4\u5219\u7684\u65b9\u6cd5\u3002\u8fd8\u89e3\u91ca\u4e86\u53cc\u91cd\u5426\u5b9a\u7b49\u4ef7\u548c\u8574\u6db5\u7684\u9006\u5426\u547d\u9898\u3002 \u5b66\u4e60\u76ee\u6807\uff1a\u5728\u672c\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f \u56de\u5fc6\u63a8\u7406\u7684\u7ed3\u6784\u548c\u7b80\u5355\u7684\u4f8b\u5b50\u3002 \u7406\u89e3\u5047\u8bbe\u89c4\u5219\u53ca\u5176\u4e0e\u63a8\u7406\u5b9a\u7406\u7684\u5173\u7cfb\u3002 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