{"id":27466,"date":"2021-02-12T13:00:57","date_gmt":"2021-02-12T13:00:57","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27466"},"modified":"2024-07-09T04:47:29","modified_gmt":"2024-07-09T04:47:29","slug":"%e7%bb%8f%e5%85%b8%e9%80%bb%e8%be%91%e6%8a%80%e6%9c%af%e6%bc%94%e7%a4%ba","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e7%bb%8f%e5%85%b8%e9%80%bb%e8%be%91%e6%8a%80%e6%9c%af%e6%bc%94%e7%a4%ba\/","title":{"rendered":"\u7ecf\u5178\u903b\u8f91\u6280\u672f\u6f14\u793a"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u7ecf\u5178\u903b\u8f91\u6280\u672f\u6f14\u793a<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u6458\u8981<\/strong><br \/><em>\u672c\u8bfe\u4ecb\u7ecd\u4e86\u7ecf\u5178\u903b\u8f91\u7684\u51e0\u79cd\u6280\u672f\uff0c\u7528\u4e8e\u5f15\u5165\u548c\u6d88\u9664\u5408\u53d6\u548c\u6790\u53d6\uff0c\u4ee5\u53ca\u6392\u4e2d\u5f8b\u548c\u77db\u76fe\u5f8b\uff0c\u4e5f\u79f0\u4e3a\u7206\u70b8\u539f\u7406\u3002\u6b64\u5916\uff0c\u8fd8\u89e3\u91ca\u4e86\u6848\u4f8b\u8bc1\u660e\u548c\u5f52\u8c2c\u6cd5\uff0c\u8fd9\u4e24\u8005\u5728\u6570\u5b66\u548c\u903b\u8f91\u6f14\u793a\u4e2d\u90fd\u975e\u5e38\u6709\u7528\u3002\u6bcf\u79cd\u6280\u672f\u90fd\u8fdb\u884c\u4e86\u6b63\u5f0f\u7684\u4ecb\u7ecd\uff0c\u5e76\u63d0\u4f9b\u4e86\u9010\u6b65\u6f14\u793a\u4ee5\u4fbf\u7406\u89e3\u3002\u5982\u679c\u60a8\u60f3\u6df1\u5165\u4e86\u89e3\u547d\u9898\u903b\u8f91\u5e76\u63d0\u9ad8\u60a8\u7684\u5b9a\u7406\u6f14\u793a\u6280\u80fd\uff0c\u672c\u8bfe\u5c06\u5bf9\u60a8\u975e\u5e38\u6709\u7528\u3002<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><\/p>\n<ol>\n<li><strong>\u7406\u89e3<\/strong>\u5f15\u5165\u548c\u6d88\u9664\u5408\u53d6\u548c\u6790\u53d6\u6280\u672f\u7684\u4f9d\u636e\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u7ecf\u5178\u903b\u8f91\u4e2d\u7684\u6392\u4e2d\u5f8b\u6216\u91cd\u8a00\u5f0f\uff08TAU\uff09\u7684\u6027\u8d28\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u7ecf\u5178\u903b\u8f91\u4e2d\u7684\u77db\u76fe\u5f8b\uff08CON\uff09\u6216\u7206\u70b8\u539f\u7406\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u7ecf\u5178\u903b\u8f91\u4e2d\u7684\u6790\u53d6\u6d88\u9664\u6280\u672f\uff08\u2228-\u6d88\u96643\uff09\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u7ecf\u5178\u903b\u8f91\u4e2d\u7684\u6848\u4f8b\u8bc1\u660e\u6280\u672f\uff08CAS\uff09\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u7ecf\u5178\u903b\u8f91\u4e2d\u7684\u5f52\u8c2c\u6cd5\uff08absurdo\uff09\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u7ecf\u5178\u903b\u8f91\u7684\u5404\u79cd\u6280\u672f\u77e5\u8bc6\u6765\u89e3\u51b3\u590d\u6742\u95ee\u9898\u548c\u6f14\u793a\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u76ee\u5f55<\/strong><br \/>\n<a href=\"#1\"><strong>\u5408\u53d6\u4e0e\u6790\u53d6\u7684\u5f15\u5165\u4e0e\u6d88\u9664<\/strong><\/a><br \/>\n<a href=\"#2\">\u2228-\u5f15\u5165<\/a><br \/>\n<a href=\"#3\">\u2228-\u6d88\u9664<\/a><br \/>\n<a href=\"#4\">\u2227-\u5f15\u5165<\/a><br \/>\n<a href=\"#5\">\u2227-\u6d88\u9664<\/a><br \/>\n<a href=\"#6\"><strong>\u77db\u76fe\u4e0e\u91cd\u8a00\u5f0f\u6280\u672f<\/strong><\/a><br \/>\n<a href=\"#7\">\u6392\u4e2d\u5f8b\u6216\u91cd\u8a00\u5f0f\uff08TAU\uff09<\/a><br \/>\n<a href=\"#8\">\u77db\u76fe\u5f8b\u6216\u7206\u70b8\u539f\u7406<\/a><br \/>\n<a href=\"#9\">\u2228-\u6d88\u96643<\/a><br \/>\n<a href=\"#10\">\u6848\u4f8b\u8bc1\u660e\uff08CAS\uff09<\/a><br \/>\n<a href=\"#11\">\u5f52\u8c2c\u6cd5\uff08ABSURDO\uff09<\/a><\/p>\n<p><center><br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/qAJ_oaSfd9k\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p><a name=\"1\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u5408\u53d6\u4e0e\u6790\u53d6\u7684\u5f15\u5165\u4e0e\u6d88\u9664<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=439s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u7ecf\u5178\u903b\u8f91\u7684\u4e00\u4e2a\u6280\u672f<\/span><\/strong><\/a>\u662f\u5f15\u5165\u548c\u6d88\u9664\u8fde\u63a5\u8bcd\u548c\u6790\u53d6\u8bcd\u3002\u867d\u7136\u8fd9\u4e9b\u6280\u672f\u7684\u6267\u884c\u65b9\u5f0f\u6216\u591a\u6216\u5c11\u662f\u76f4\u89c2\u7684\uff0c\u4f46\u5176\u4f9d\u636e\u5e76\u4e0d\u5b8c\u5168\u663e\u800c\u6613\u89c1\uff0c\u4f46\u53ef\u4ee5\u4ece\u6211\u4eec\u5728\u524d\u51e0\u8bfe\u4e2d\u5df2\u7ecf\u8bc1\u660e\u7684\u547d\u9898\u903b\u8f91\u89c4\u5219\u4e2d\u5f97\u51fa\u3002\u6b63\u5f0f\u6765\u8bf4\uff0c\u5f15\u5165\u548c\u6d88\u9664\u8fde\u63a5\u8bcd\u548c\u6790\u53d6\u8bcd\u7684\u6280\u672f\u5982\u4e0b\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>\u2228-\u5f15\u5165<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha \\} \\vdash (\\alpha \\vee \\beta)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>\u2228-\u6d88\u9664<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha\\vee\\beta), \\neg\\alpha \\} \\vdash\\beta <\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>\u2227-\u5f15\u5165<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha.\\beta \\} \\vdash(\\alpha \\wedge \\beta) <\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>\u2227-\u6d88\u9664<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge \\beta) \\} \\vdash \\alpha <\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u5b83\u4eec\u7684\u547d\u9898\u903b\u8f91\u8bc1\u660e\u5982\u4e0b\uff1a<\/p>\n<p><a name=\"2\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2228-\u5f15\u5165<\/h3>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\} \\vdash \\alpha<\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\} \\vdash( \\alpha \\rightarrow (\\neg \\beta \\rightarrow \\alpha))<\/span><\/span><\/td>\n<td>; A1, \u5355\u8c03\u6027<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\} \\vdash (\\neg \\beta \\rightarrow \\alpha)<\/span><\/span><\/td>\n<td>; MP(1,2)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{\\alpha\\} \\vdash (\\beta \\vee \\alpha)}<\/span><\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\rightarrow<\/span><\/span>-\u5b9a\u4e49(3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2228-\u6d88\u9664<\/h3>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee \\beta), \\neg\\alpha\\}\\vdash (\\alpha \\vee\\beta)<\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee \\beta), \\neg\\alpha\\}\\vdash \\neg\\alpha <\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\vee \\beta), \\neg\\alpha\\}\\vdash (\\neg \\alpha \\rightarrow \\beta)<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\rightarrow<\/span><\/span>-\u5b9a\u4e49 (1)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{(\\alpha \\vee \\beta), \\neg\\alpha\\}\\vdash \\beta}<\/span><\/span><\/span><\/td>\n<td>; MP(2,3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2227-\u5f15\u5165<\/h3>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\vee \\neg \\beta), \\neg\\neg\\beta\\} \\vdash \\neg\\alpha<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span><\/span>-\u6d88\u9664<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg\\neg\\beta\\} \\vdash ((\\neg\\alpha \\vee \\neg \\beta) \\rightarrow \\neg\\alpha)<\/span><\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg\\neg\\beta\\} \\vdash (\\neg \\neg\\alpha \\rightarrow \\neg (\\neg\\alpha \\vee \\neg \\beta))<\/span><\/span><\/td>\n<td>; CPI(2))<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg\\neg\\beta \\rightarrow (\\neg \\neg\\alpha \\rightarrow \\neg (\\neg\\alpha \\vee \\neg \\beta)))<\/span><\/span><\/td>\n<td>; TD(3)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash (\\neg\\neg\\beta \\rightarrow (\\neg \\neg\\alpha \\rightarrow \\neg (\\neg\\alpha \\vee \\neg \\beta)))<\/span><\/span><\/td>\n<td>; \u5355\u8c03\u6027 x2 (4)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash \\beta<\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash \\neg\\neg\\beta<\/span><\/span><\/td>\n<td>; DN(6)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash (\\neg \\neg\\alpha \\rightarrow \\neg (\\neg\\alpha \\vee \\neg \\beta))<\/span><\/span><\/td>\n<td>; MP(7,5)<\/td>\n<\/tr>\n<tr>\n<td>(9)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash \\alpha<\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(10)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash \\neg\\neg\\alpha<\/span><\/span><\/td>\n<td>; DN(9)<\/td>\n<\/tr>\n<tr>\n<td>(11)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha, \\beta \\} \\vdash \\neg (\\neg\\alpha \\vee \\neg \\beta)<\/span><\/span><\/td>\n<td>; MP(10,8)<\/td>\n<\/tr>\n<tr>\n<td>(12)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{\\alpha, \\beta \\} \\vdash (\\alpha \\wedge \\beta)}<\/span><\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span><\/span>-\u5b9a\u4e49(11)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"5\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2227-\u6d88\u9664<\/h3>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha \\wedge \\beta)\\} \\vdash (\\alpha \\wedge \\beta)<\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg \\alpha\\} \\vdash (\\neg \\alpha \\vee \\neg\\beta)<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span><\/span>-\u5f15\u5165<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg \\alpha \\rightarrow (\\neg \\alpha \\vee \\neg\\beta))<\/span><\/span><\/td>\n<td>; TD(2)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg(\\neg \\alpha \\vee \\neg\\beta) \\rightarrow \\alpha)<\/span><\/span><\/td>\n<td>; CPI(3))<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash ( ( \\alpha \\wedge \\beta) \\rightarrow \\alpha)<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span><\/span>-\u5b9a\u4e49(4)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{(\\alpha \\wedge \\beta)\\} \\vdash ( ( \\alpha \\wedge \\beta) \\rightarrow \\alpha)<\/span><\/span><\/td>\n<td>; \u5355\u8c03\u6027(5)<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{(\\alpha \\wedge \\beta)\\} \\vdash \\alpha}<\/span><\/span><\/span><\/td>\n<td>; MP(1,6)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"6\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u77db\u76fe\u4e0e\u91cd\u8a00\u5f0f\u6280\u672f<\/h2>\n<p><a name=\"7\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u6392\u4e2d\u5f8b\u6216\u91cd\u8a00\u5f0f\uff08tau\uff09<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1208s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u7ecf\u5178\u903b\u8f91\u7684\u53e6\u4e00\u663e\u8457\u7279\u5f81<\/span><\/strong><\/a>\u662f\u6392\u4e2d\u5f8b\uff08tertium non datur\uff09\u7684\u6027\u8d28\u3002\u5b83\u6307\u51fa\uff0c\u5982\u679c\u6709\u4e24\u4e2a\u9648\u8ff0\uff0c\u5176\u4e2d\u4e00\u4e2a\u5426\u5b9a\u4e86\u53e6\u4e00\u4e2a\uff0c\u90a3\u4e48\u5176\u4e2d\u4e00\u4e2a\u5fc5\u987b\u662f\u771f\u7684\uff1b\u6362\u53e5\u8bdd\u8bf4\uff0c\u5728\u4e24\u4e2a\u9648\u8ff0\u4e2d\uff0c\u4e00\u4e2a\u5426\u5b9a\u53e6\u4e00\u4e2a\u7684\u5408\u53d6\u5fc5\u7136\u5f62\u6210\u4e00\u4e2a\u91cd\u8a00\u5f0f\u3002\u6b63\u5f0f\u6765\u8bf4\uff0c\u8fd9\u8868\u8fbe\u4e3a\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\neg\\alpha \\vee\\alpha)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5b83\u7684\u8bc1\u660e\u5f88\u5bb9\u6613\u5f97\u51fa\u3002<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\}\\vdash \\alpha<\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\alpha \\rightarrow \\alpha)<\/span><\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\vdash (\\neg \\alpha \\vee \\alpha)}<\/span><\/span><\/span><\/td>\n<td>; \u4ece (2) \u56e0\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\rightarrow \\beta) := (\\neg \\alpha \\vee \\beta)<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u53e6\u4e00\u79cd\u8868\u8ff0\u6392\u4e2d\u5f8b\u7684\u65b9\u6cd5\u662f\u901a\u8fc7<strong>\u4e0d\u77db\u76fe\u5f8b<\/strong>\uff0c\u5b83\u6307\u51fa\u4e00\u4e2a\u9648\u8ff0\u4e0d\u80fd\u540c\u65f6\u4e3a\u771f\u548c\u5047\uff0c\u5e76\u4e14\u6b63\u5f0f\u8868\u8ff0\u4e3a\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash \\neg(\\neg\\alpha \\wedge \\alpha)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u4e2a\u6027\u8d28\u4e0d\u9700\u8981\u8bc1\u660e\uff0c\u4e0d\u662f\u56e0\u4e3a\u5b83\u672c\u8eab\u663e\u800c\u6613\u89c1\uff0c\u800c\u662f\u56e0\u4e3a\u5b83\u53ef\u4ee5\u76f4\u63a5\u901a\u8fc7\u5e94\u7528\u5408\u53d6\u5b9a\u4e49\u4e8e\u6392\u4e2d\u5f8b\u5f97\u51fa\u3002<\/p>\n<p><a name=\"8\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u77db\u76fe\u5f8b\u6216\u7206\u70b8\u539f\u7406<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1410s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u7ecf\u5178\u903b\u8f91\u7684\u53e6\u4e00\u5df2\u77e5\u7279\u6027<\/span><\/strong><\/a>\u662f\u7206\u70b8\u539f\u7406\uff0c\u901a\u5e38\u901a\u8fc7\u00bb\u4ece\u77db\u76fe\u7684\u524d\u63d0\u4e2d\u53ef\u4ee5\u5f97\u51fa\u4efb\u4f55\u7ed3\u8bba\u00bb\u6765\u8868\u8ff0\u3002\u5176\u8868\u8ff0\u901a\u5e38\u4ee5\u4ee5\u4e0b\u4e24\u79cd\u65b9\u5f0f\u4e4b\u4e00\u5448\u73b0\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\neg\\alpha \\wedge \\alpha)\\}\\vdash \\beta<\/span><\/span><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha, \\neg\\alpha\\}\\vdash \\beta<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u4e2a\u89c4\u5219\u7684\u8bc1\u660e\u5f88\u7b80\u5355\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha ,\\neg\\alpha\\} \\vdash \\neg\\alpha <\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha ,\\neg\\alpha\\} \\vdash (\\neg\\alpha \\vee \\beta) <\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vee<\/span><\/span>-\u5f15\u5165<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha ,\\neg\\alpha\\} \\vdash (\\alpha \\rightarrow \\beta) <\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\rightarrow<\/span><\/span>-\u5b9a\u4e49(2)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha ,\\neg\\alpha\\} \\vdash \\alpha <\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{\\alpha ,\\neg\\alpha\\} \\vdash \\beta}<\/span><\/span><\/span><\/td>\n<td>; MP(4,3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"9\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2228-\u6d88\u96643<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1555s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u63a8\u7406\u89c4\u5219\uff08modus ponens\uff09\u53ef\u4ee5\u7528\u4e24\u79cd\u4e0d\u540c\u65b9\u5f0f\u5199\u51fa<\/span><\/strong><\/a>\u3002\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u7684\u4e00\u79cd\u5f62\u5f0f\u662f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha,(\\alpha \\rightarrow \\beta)\\}\\vdash \\beta<\/span><\/span>\u3002\u53e6\u4e00\u79cd\u5f62\u5f0f\u5219\u7a0d\u5fae\u4e0d\u90a3\u4e48\u719f\u6089\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\}\\vdash\\beta \\; \\wedge \\; \\vdash \\alpha \\; \\Longrightarrow \\; \\vdash \\beta<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u96c6\u4e2d\u4e8e\u8fd9\u79cd\u7b2c\u4e8c\u79cd\u5f62\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u8fd9\u4e00\u89c4\u5219\u7684\u6269\u5c55\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a<strong>\u2228-\u6d88\u96643<\/strong>\uff0c\u56e0\u4e3a\u5b83\u7c7b\u4f3c\u4e8e\u4ece\u6790\u53d6\u4e2d\u5f97\u5230\u7684\u7b80\u5316\u3002\u8fd9\u544a\u8bc9\u6211\u4eec\uff0c\u5982\u679c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span><\/span>\u53ef\u4ee5\u4ece<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\u548c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span>\u4e2d\u540c\u65f6\u63a8\u65ad\u51fa\u6765\uff0c\u5e76\u4e14<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\u548c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span>\u4e4b\u95f4\u7684\u6790\u53d6\u662f\u4e00\u4e2a\u5b9a\u7406\uff0c\u90a3\u4e48<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span><\/span>\u5c31\u662f\u4e00\u4e2a\u5b9a\u7406\u3002\u8fd9\u53ef\u4ee5\u6b63\u5f0f\u603b\u7ed3\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\alpha\\}\\vdash\\gamma\\; \\wedge \\; \\{\\beta\\}\\vdash\\gamma \\; \\wedge \\; \\vdash (\\alpha \\vee \\beta)<\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Longrightarrow<\/span><\/span> <span style=\"color: #000088;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash \\gamma<\/span><\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u79cd\u7ecf\u5178\u903b\u8f91\u6280\u672f\u7684\u8bc1\u660e\u5982\u4e0b\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\alpha \\vdash \\gamma}<\/span><\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\beta \\vdash \\gamma}<\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\vdash (\\alpha \\vee \\beta)}<\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\alpha \\rightarrow \\gamma)<\/span><\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\beta \\rightarrow \\gamma)<\/span><\/span><\/td>\n<td>; TD(2)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg \\gamma \\rightarrow \\neg \\alpha)<\/span><\/span><\/td>\n<td>; CPI(4)<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg \\gamma \\rightarrow \\neg \\beta)<\/span><\/span><\/td>\n<td>; CPI(5)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\neg \\gamma \\}\\vdash \\neg \\alpha<\/span><\/span><\/td>\n<td>; RTD(6)<\/td>\n<\/tr>\n<tr>\n<td>(9)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\neg \\gamma\\}\\vdash \\neg \\beta<\/span><\/span><\/td>\n<td>; RTD(7)<\/td>\n<\/tr>\n<tr>\n<td>(10)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{\\neg \\gamma\\}\\vdash (\\neg \\alpha \\wedge \\neg \\beta)<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span><\/span>-\u5f15\u5165(8,9)<\/td>\n<\/tr>\n<tr>\n<td>(11)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg \\gamma \\rightarrow (\\neg \\alpha \\wedge \\neg \\beta))<\/span><\/span><\/td>\n<td>; TD(10)<\/td>\n<\/tr>\n<tr>\n<td>(12)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash (\\neg(\\neg \\alpha \\wedge \\neg \\beta)\\rightarrow \\gamma )<\/span><\/span><\/td>\n<td>; CPI(11)<\/td>\n<\/tr>\n<tr>\n<td>(13)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> (A \\wedge B) := \\neg(\\neg A \\vee \\neg B)<\/span><\/span><\/td>\n<td>; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\wedge<\/span><\/span> &#8211; \u5b9a\u4e49<\/td>\n<\/tr>\n<tr>\n<td>(14)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\neg(A \\wedge B) := \\neg\\neg(\\neg A \\vee \\neg B)<\/span><\/span><\/td>\n<td>; \u5426\u5b9a (13) \u4e2d\u7684\u4e24\u8fb9<\/td>\n<\/tr>\n<tr>\n<td>(15)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\neg(\\neg\\alpha \\wedge \\neg\\beta) := \\neg\\neg(\\neg\\neg\\alpha \\vee \\neg\\neg\\beta)<\/span><\/span><\/td>\n<td>; \u66ff\u6362 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A:=\\neg\\alpha<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B:=\\neg\\beta<\/span><\/span> \u5728 (14)<\/td>\n<\/tr>\n<tr>\n<td>(16)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\neg(\\neg\\alpha \\wedge \\neg\\beta) \\dashv \\vdash (\\alpha \\vee \\beta)<\/span><\/span><\/td>\n<td>; DN(15)<\/td>\n<\/tr>\n<tr>\n<td>(17)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash ((\\alpha \\vee \\beta) \\rightarrow \\neg(\\neg\\alpha \\wedge \\neg\\beta) )<\/span><\/span><\/td>\n<td>; TD(16)<\/td>\n<\/tr>\n<tr>\n<td>(17)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vdash ((\\alpha \\vee \\beta) \\rightarrow \\gamma )<\/span><\/span><\/td>\n<td>; SH(17,12)<\/td>\n<\/tr>\n<tr>\n<td>(18)<\/td>\n<td><span style=\"color: #000088;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{ \\vdash \\gamma}<\/span><\/span><\/span><\/td>\n<td>; MP(3,17)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"10\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u6848\u4f8b\u8bc1\u660e\uff08cas\uff09<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1957s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u7ecf\u5178\u903b\u8f91\u7684\u53e6\u4e00\u6280\u672f<\/span><\/a>\u662f\u6848\u4f8b\u8bc1\u660e\u3002\u5982\u679c\u4e00\u4e2a\u8868\u8fbe\u5f0f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span>\u53ef\u4ee5\u4ece\u53e6\u4e00\u4e2a\u8868\u8fbe\u5f0f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\u53ca\u5176\u5426\u5b9a\u4e2d\u63a8\u65ad\u51fa\uff0c\u90a3\u4e48\u8868\u8fbe\u5f0f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span>\u5fc5\u7136\u662f\u4e00\u4e2a\u5b9a\u7406\u3002\u8fd9\u6b63\u5f0f\u8868\u8ff0\u4e3a\uff1a<span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha \\vdash \\beta \\; \\wedge \\; \\neg\\alpha \\vdash \\beta <\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Longrightarrow<\/span><\/span> <span style=\"color: #000088;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash \\beta<\/span><\/span><\/span>\u3002\u5176\u8bc1\u660e\u5982\u4e0b\uff1a<\/p>\n<p style=\"color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rll}\n\n(1) &amp; \\alpha \\vdash \\beta &amp;; \u524d\u63d0\\\\\n\n(2) &amp; \\neg \\alpha \\vdash \\beta &amp;; \u524d\u63d0 \\\\\n\n(3) &amp; \\vdash \\alpha \\vee \\neg\\alpha &amp;; TAU \\\\\n\n(4) &amp; \\vdash \\beta &amp;; \\vee-\u6d88\u96643(1,2,3)\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<p><a name=\"11\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u5f52\u8c2c\u6cd5\uff08absurdo\uff09<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u7ecf\u5178\u903b\u8f91\u4e2d\u6700\u5e38\u7528\u7684\u6280\u672f\u4e4b\u4e00\uff0c\u7279\u522b\u662f\u5728\u6570\u5b66\u4e2d\u7684\u6f14\u793a\uff0c\u662f\u5f52\u8c2c\u6cd5\u3002\u8fd9\u8868\u793a\uff0c\u5982\u679c\u4ece\u4e00\u4e2a\u8868\u8fbe\u5f0f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\u4e2d\u63a8\u5bfc\u51fa\u4e00\u4e2a\u77db\u76fe\uff08\u4e00\u4e2a\u9648\u8ff0\u53ca\u5176\u5426\u5b9a\uff09\uff0c\u90a3\u4e48<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>\u7684\u5426\u5b9a\u5c31\u662f\u4e00\u4e2a\u91cd\u8a00\u5f0f\u3002\u6b63\u5f0f\u6765\u8bf4\uff0c\u5b83\u8868\u8ff0\u4e3a\uff1a<span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha\\}\\vdash \\beta \\; \\wedge \\; \\{\\alpha\\}\\vdash \\neg\\beta<\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Longrightarrow<\/span><\/span> <span style=\"color: #000088;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash \\neg\\alpha<\/span><\/span><\/span>\u3002\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u63a8\u7406\u8bc1\u660e\uff1a<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{\\alpha\\}\\vdash \\beta}<\/span><\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span style=\"color: #880000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\{\\alpha\\}\\vdash \\neg\\beta}<\/span><\/span><\/td>\n<td>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\alpha \\rightarrow \\beta)<\/span><\/span><\/td>\n<td>; TD(1)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\alpha \\rightarrow \\neg\\beta)<\/span><\/span><\/td>\n<td>; TD(2)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\neg \\beta \\rightarrow \\neg \\alpha)<\/span><\/span><\/td>\n<td>; CPI(3)<\/td>\n<\/tr>\n<tr>\n<td>(6)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash (\\beta \\rightarrow \\neg \\alpha)<\/span><\/span><\/td>\n<td>; CPI(4)<\/td>\n<\/tr>\n<tr>\n<td>(7)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\neg \\beta \\}\\vdash \\neg \\alpha<\/span><\/span><\/td>\n<td>; RTD(5)<\/td>\n<\/tr>\n<tr>\n<td>(8)<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\beta \\}\\vdash \\neg \\alpha<\/span><\/span><\/td>\n<td>; RTD(6)<\/td>\n<\/tr>\n<tr>\n<td>(9)<\/td>\n<td><span style=\"color: #000088;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\vdash \\neg \\alpha}<\/span><\/span><\/span><\/td>\n<td>; CAS(7,8)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>\u7ecf\u5178\u903b\u8f91\u6280\u672f\u6f14\u793a \u6458\u8981\u672c\u8bfe\u4ecb\u7ecd\u4e86\u7ecf\u5178\u903b\u8f91\u7684\u51e0\u79cd\u6280\u672f\uff0c\u7528\u4e8e\u5f15\u5165\u548c\u6d88\u9664\u5408\u53d6\u548c\u6790\u53d6\uff0c\u4ee5\u53ca\u6392\u4e2d\u5f8b\u548c\u77db\u76fe\u5f8b\uff0c\u4e5f\u79f0\u4e3a\u7206\u70b8\u539f\u7406\u3002\u6b64\u5916\uff0c\u8fd8\u89e3\u91ca\u4e86\u6848\u4f8b\u8bc1\u660e\u548c\u5f52\u8c2c\u6cd5\uff0c\u8fd9\u4e24\u8005\u5728\u6570\u5b66\u548c\u903b\u8f91\u6f14\u793a\u4e2d\u90fd\u975e\u5e38\u6709\u7528\u3002\u6bcf\u79cd\u6280\u672f\u90fd\u8fdb\u884c\u4e86\u6b63\u5f0f\u7684\u4ecb\u7ecd\uff0c\u5e76\u63d0\u4f9b\u4e86\u9010\u6b65\u6f14\u793a\u4ee5\u4fbf\u7406\u89e3\u3002\u5982\u679c\u60a8\u60f3\u6df1\u5165\u4e86\u89e3\u547d\u9898\u903b\u8f91\u5e76\u63d0\u9ad8\u60a8\u7684\u5b9a\u7406\u6f14\u793a\u6280\u80fd\uff0c\u672c\u8bfe\u5c06\u5bf9\u60a8\u975e\u5e38\u6709\u7528\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u7406\u89e3\u5f15\u5165\u548c\u6d88\u9664\u5408\u53d6\u548c\u6790\u53d6\u6280\u672f\u7684\u4f9d\u636e\u3002 \u7406\u89e3\u7ecf\u5178\u903b\u8f91\u4e2d\u7684\u6392\u4e2d\u5f8b\u6216\u91cd\u8a00\u5f0f\uff08TAU\uff09\u7684\u6027\u8d28\u3002 \u7406\u89e3\u7ecf\u5178\u903b\u8f91\u4e2d\u7684\u77db\u76fe\u5f8b\uff08CON\uff09\u6216\u7206\u70b8\u539f\u7406\u3002 \u7406\u89e3\u7ecf\u5178\u903b\u8f91\u4e2d\u7684\u6790\u53d6\u6d88\u9664\u6280\u672f\uff08\u2228-\u6d88\u96643\uff09\u3002 \u7406\u89e3\u7ecf\u5178\u903b\u8f91\u4e2d\u7684\u6848\u4f8b\u8bc1\u660e\u6280\u672f\uff08CAS\uff09\u3002 \u7406\u89e3\u7ecf\u5178\u903b\u8f91\u4e2d\u7684\u5f52\u8c2c\u6cd5\uff08absurdo\uff09\u3002 \u5e94\u7528\u7ecf\u5178\u903b\u8f91\u7684\u5404\u79cd\u6280\u672f\u77e5\u8bc6\u6765\u89e3\u51b3\u590d\u6742\u95ee\u9898\u548c\u6f14\u793a\u3002 \u76ee\u5f55 \u5408\u53d6\u4e0e\u6790\u53d6\u7684\u5f15\u5165\u4e0e\u6d88\u9664 \u2228-\u5f15\u5165 \u2228-\u6d88\u9664 \u2227-\u5f15\u5165 \u2227-\u6d88\u9664 \u77db\u76fe\u4e0e\u91cd\u8a00\u5f0f\u6280\u672f \u6392\u4e2d\u5f8b\u6216\u91cd\u8a00\u5f0f\uff08TAU\uff09 \u77db\u76fe\u5f8b\u6216\u7206\u70b8\u539f\u7406 \u2228-\u6d88\u96643 \u6848\u4f8b\u8bc1\u660e\uff08CAS\uff09 \u5f52\u8c2c\u6cd5\uff08ABSURDO\uff09 \u5408\u53d6\u4e0e\u6790\u53d6\u7684\u5f15\u5165\u4e0e\u6d88\u9664 \u7ecf\u5178\u903b\u8f91\u7684\u4e00\u4e2a\u6280\u672f\u662f\u5f15\u5165\u548c\u6d88\u9664\u8fde\u63a5\u8bcd\u548c\u6790\u53d6\u8bcd\u3002\u867d\u7136\u8fd9\u4e9b\u6280\u672f\u7684\u6267\u884c\u65b9\u5f0f\u6216\u591a\u6216\u5c11\u662f\u76f4\u89c2\u7684\uff0c\u4f46\u5176\u4f9d\u636e\u5e76\u4e0d\u5b8c\u5168\u663e\u800c\u6613\u89c1\uff0c\u4f46\u53ef\u4ee5\u4ece\u6211\u4eec\u5728\u524d\u51e0\u8bfe\u4e2d\u5df2\u7ecf\u8bc1\u660e\u7684\u547d\u9898\u903b\u8f91\u89c4\u5219\u4e2d\u5f97\u51fa\u3002\u6b63\u5f0f\u6765\u8bf4\uff0c\u5f15\u5165\u548c\u6d88\u9664\u8fde\u63a5\u8bcd\u548c\u6790\u53d6\u8bcd\u7684\u6280\u672f\u5982\u4e0b\uff1a \u2228-\u5f15\u5165 \u2228-\u6d88\u9664 \u2227-\u5f15\u5165 \u2227-\u6d88\u9664 \u5b83\u4eec\u7684\u547d\u9898\u903b\u8f91\u8bc1\u660e\u5982\u4e0b\uff1a \u2228-\u5f15\u5165 (1) ; \u524d\u63d0 (2) ; A1, \u5355\u8c03\u6027 (3) ; MP(1,2) (4) ; -\u5b9a\u4e49(3) \u2228-\u6d88\u9664 (1) ; \u524d\u63d0 (2) ; \u524d\u63d0 (3) ; -\u5b9a\u4e49 (1) (4) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27451,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":8,"footnotes":""},"categories":[623,575,609],"tags":[],"class_list":["post-27466","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-623","category-575","category-609"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u7ecf\u5178\u903b\u8f91\u6280\u672f\u6f14\u793a - toposuranos.com\/material<\/title>\n<meta name=\"description\" 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