{"id":28060,"date":"2021-03-08T13:00:42","date_gmt":"2021-03-08T13:00:42","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28060"},"modified":"2024-08-18T09:44:39","modified_gmt":"2024-08-18T09:44:39","slug":"%e8%af%ad%e4%b9%89%e5%90%8e%e6%9e%9c%e4%b8%8e%e7%ad%89%e4%bb%b7","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e8%af%ad%e4%b9%89%e5%90%8e%e6%9e%9c%e4%b8%8e%e7%ad%89%e4%bb%b7\/","title":{"rendered":"\u8bed\u4e49\u540e\u679c\u4e0e\u7b49\u4ef7"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u8bed\u4e49\u540e\u679c\u4e0e\u7b49\u4ef7<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u6458\u8981<\/strong><br \/><em>\u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u7814\u7a76\u547d\u9898\u903b\u8f91\u4e2d\u7684\u8bed\u4e49\u540e\u679c\u4e0e\u7b49\u4ef7\uff0c\u8fd9\u662f\u5bf9\u4e4b\u524d\u5b66\u4e60\u5185\u5bb9\u7684\u81ea\u7136\u5ef6\u7eed\u3002\u6211\u4eec\u5c06\u5b66\u4e60\u5982\u4f55\u4ece\u771f\u503c\u5206\u914d\u4e2d\u5f97\u51fa\u8bed\u4e49\u540e\u679c\u7684\u6982\u5ff5\uff0c\u4ee5\u53ca\u8fd9\u4e00\u6982\u5ff5\u5982\u4f55\u4e0e\u63a8\u8bba\u5b9a\u7406\u76f8\u5173\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5c06\u901a\u8fc7\u771f\u503c\u8868\u7684\u4f7f\u7528\uff0c\u5b66\u4e60\u5982\u4f55\u83b7\u53d6\u5982\u5408\u53d6\u6d88\u53bb\u3001\u6790\u53d6\u5f15\u5165\u7b49\u6709\u7528\u7684\u6027\u8d28\u3002\u6211\u4eec\u8fd8\u5c06\u63a2\u8ba8\u8bed\u4e49\u7b49\u4ef7\u7684\u6982\u5ff5\uff0c\u5e76\u4e86\u89e3\u5176\u4e0e\u5df2\u77e5\u6027\u8d28\u7684\u5173\u7cfb\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u5c55\u793a\u5982\u4f55\u4f7f\u7528\u6a21\u578b\u548c\u63a8\u7406\u6280\u672f\u6765\u7b80\u5316\u8bed\u4e49\u540e\u679c\u4e0e\u7b49\u4ef7\u95ee\u9898\u7684\u7814\u7a76\u3002<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807:<\/strong><br \/>\n\u5b8c\u6210\u672c\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\n<\/p>\n<ol>\n<li><strong>\u7406\u89e3<\/strong>\u8bed\u4e49\u540e\u679c\u7684\u6982\u5ff5\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u7b26\u53f7\u22a8\u7684\u4e0d\u540c\u89e3\u91ca\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u63a8\u8bba\u5b9a\u7406\u7684\u8bed\u4e49\u7248\u672c\u53ca\u5176\u5728\u7814\u7a76\u8bed\u4e49\u540e\u679c\u548c\u7b49\u4ef7\u4e2d\u7684\u5e94\u7528\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u8bed\u4e49\u7b49\u4ef7\u7684\u5b9a\u4e49\u53ca\u5176\u4e0e\u771f\u503c\u7684\u5173\u7cfb\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u63a8\u8bba\u5b9a\u7406\u7684\u8bed\u4e49\u7248\u672c\uff0c\u5c06\u540e\u679c\u95ee\u9898\u8f6c\u5316\u4e3a\u6709\u6548\u6027\u95ee\u9898\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u771f\u503c\u8868\u7684\u6709\u7528\u6027\u8d28\uff0c\u8bc1\u660e\u8bed\u4e49\u7b49\u4ef7\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u5438\u6536\u5f8b\u3001\u5206\u914d\u5f8b\u548c\u5fb7\u6469\u6839\u5b9a\u5f8b\uff0c\u7b80\u5316\u590d\u6742\u8868\u8fbe\u5f0f\u3002<\/li>\n<li><strong>\u5206\u6790<\/strong>\u6a21\u578b\u4e0e\u63a8\u7406\u5728\u547d\u9898\u903b\u8f91\u7814\u7a76\u4e2d\u7684\u5173\u7cfb\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u76ee\u5f55<\/strong><br \/>\n<a href=\"#1\">\u8d4b\u503c\u4e0e\u6a21\u578b<\/a><br \/>\n<a href=\"#2\">\u63a8\u8bba\u5b9a\u7406\uff08\u8bed\u4e49\u7248\u672c\uff09<\/a><br \/>\n<a href=\"#3\">\u63a8\u8bba\u5b9a\u7406\u5728\u8bed\u4e49\u540e\u679c\u4e0e\u7b49\u4ef7\u7814\u7a76\u4e2d\u7684\u5e94\u7528<\/a><br \/>\n<a href=\"#4\">\u8bed\u4e49\u7b49\u4ef7\u53ca\u5176\u6027\u8d28<\/a><br \/>\n<a href=\"#5\">\u603b\u7ed3<\/a><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/vjkzDxbG8LY\" 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;\">\u5bf9\u8bed\u4e49\u540e\u679c\u4e0e\u7b49\u4ef7\u7684\u7814\u7a76\u662f\u6211\u4eec\u590d\u4e60<a href=\"https:\/\/toposuranos.com\/semantica-de-la-logica-proposicional\/\" rel=\"noopener\" target=\"_blank\">\u547d\u9898\u903b\u8f91\u8bed\u4e49<\/a>\u7684\u81ea\u7136\u5ef6\u7eed\u3002\u73b0\u5728\u6211\u4eec\u5c06\u590d\u4e60\u5982\u4f55\u4ece\u771f\u503c\u5206\u914d\u4e2d\u83b7\u5f97\u8bed\u4e49\u540e\u679c\u7684\u6982\u5ff5\uff0c\u4ee5\u53ca\u5982\u4f55\u4ece\u4e2d\u81ea\u7136\u5730\u5f97\u51fa\u63a8\u8bba\u5b9a\u7406\u7684\u8bed\u4e49\u7248\u672c\u3002\u6211\u4eec\u5c06\u5c55\u793a\u4f7f\u7528\u771f\u503c\u8868\u83b7\u53d6\u4e00\u4e9b\u6709\u7528\u6027\u8d28\u7684\u5b9e\u9645\u4f8b\u5b50\u3002\u4f60\u4e5f\u53ef\u4ee5\u5728<a href=\"https:\/\/www.youtube.com\/watch?v=vjkzDxbG8LY\" rel=\"noopener\" target=\"_blank\">YouTube\u9891\u9053<\/a>\u4e0a\u770b\u5230\u8fd9\u4e00\u5207\u3002<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u8d4b\u503c\u4e0e\u6a21\u578b<\/h2>\n<p style=\"text-align: justify; color: #000000;\">\u9996\u5148\uff0c\u8ba9\u6211\u4eec\u4ece\u4e00\u4e2a\u5b9a\u4e49\u5f00\u59cb\uff0c\u8fd9\u662f\u6211\u4eec\u5c06\u5728\u672c\u6587\u4e2d\u8ba8\u8bba\u7684\u5173\u952e\uff0c\u8bed\u4e49\u540e\u679c\u7684\u5b9a\u4e49\u3002<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; color: #000000;\"><span style=\"color: #880000;\"><strong>\u5b9a\u4e49:<\/strong><\/span> \u5982\u679c\u5bf9\u4e8e\u6bcf\u4e2a\u8d4b\u503c<span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span>\u90fd\u6210\u7acb<span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}\\models F \\Rightarrow \\mathcal{A}\\models G<\/span>\uff0c\u90a3\u4e48\u8868\u8fbe\u5f0f<span class=\"katex-eq\" data-katex-display=\"false\">G<\/span>\u662f\u53e6\u4e00\u4e2a\u8868\u8fbe\u5f0f<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u7684<strong>\u8bed\u4e49\u540e\u679c<\/strong>\u3002\u6211\u4eec\u7528<span class=\"katex-eq\" data-katex-display=\"false\">F\\models G<\/span>\u6765\u8868\u793a\uff0c\u8fd9\u610f\u5473\u7740\u201c\u8868\u8fbe\u5f0f<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u6a21\u578b\u8868\u8fbe\u5f0f<span class=\"katex-eq\" data-katex-display=\"false\">G<\/span>\u201d\u6216\u201c<span class=\"katex-eq\" data-katex-display=\"false\">G<\/span>\u662f<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u7684\u8bed\u4e49\u540e\u679c\u201d\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u6839\u636e\u8fd9\u4e00\u5b9a\u4e49\uff0c\u6211\u4eec\u5fc5\u987b\u6ce8\u610f\uff0c\u7b26\u53f7<span class=\"katex-eq\" data-katex-display=\"false\">\\models<\/span>\u5b9e\u9645\u4e0a\u5728\u4e0d\u540c\u7684\u4e0a\u4e0b\u6587\u4e2d\u6709\u4e0d\u540c\u7684\u89e3\u91ca\uff1a<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A} \\models F<\/span>\u610f\u5473\u7740<span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(F) = 1<\/span>\uff1b\u4e5f\u5c31\u662f\u8bf4\uff0c\u201c<span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span>\u6a21\u578b<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u3002\u201d<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">G \\models F<\/span>\u610f\u5473\u7740\u5982\u679c\u4efb\u4f55\u8d4b\u503c\u90fd\u6a21\u578b<span class=\"katex-eq\" data-katex-display=\"false\">G<\/span>\uff0c\u90a3\u4e48\u5b83\u4e5f\u6a21\u578b<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\uff0c\u6211\u4eec\u8bfb\u4f5c\u201c<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u662f<span class=\"katex-eq\" data-katex-display=\"false\">G<\/span>\u7684\u8bed\u4e49\u540e\u679c\u3002\u201d<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\models F<\/span>\u610f\u5473\u7740<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u5728\u4efb\u4f55\u8d4b\u503c\u4e0b\u90fd\u6210\u7acb\uff1b\u4e5f\u5c31\u662f\u8bf4\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u662f\u4e00\u4e2a\u91cd\u8a00\u5f0f\u3002<\/li>\n<\/ul>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u6b64\uff0c\u5c3d\u7ba1\u7b26\u53f7<span class=\"katex-eq\" data-katex-display=\"false\">\\models<\/span>\u53ef\u80fd\u6709\u591a\u79cd\u89e3\u91ca\uff0c\u4f46\u4e0a\u4e0b\u6587\u5e76\u4e0d\u6a21\u7cca\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u8bed\u4e49\u540e\u679c\u7684\u6982\u5ff5\u4e0e\u6211\u4eec\u4e4b\u524d\u8ba8\u8bba\u7684\u201c\u8574\u6db5\u201d\u6982\u5ff5\u975e\u5e38\u63a5\u8fd1\uff0c\u5982\u679c<span class=\"katex-eq\" data-katex-display=\"false\">F\\models G<\/span>\u6210\u7acb\uff0c\u90a3\u4e48<span class=\"katex-eq\" data-katex-display=\"false\">\\models (F\\rightarrow G)<\/span>\u4e5f\u6210\u7acb\u3002\u5b9e\u9645\u4e0a\uff0c\u8fd9\u4e0e\u6211\u4eec\u4e4b\u524d\u51e0\u8282\u8bfe\u8ba8\u8bba\u7684\u63a8\u8bba\u5b9a\u7406\u975e\u5e38\u76f8\u4f3c\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u63a8\u8bba\u5b9a\u7406\uff08\u8bed\u4e49\u7248\u672c\uff09<\/h2>\n<p><strong><span style=\"color: #000000;\">[<a href=\"https:\/\/www.youtube.com\/watch?v=vjkzDxbG8LY&amp;t=444s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u89c2\u770b<\/span><\/a>]<\/span><\/strong><\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;\"><span style=\"color: #aa0000;\"><strong>\u5b9a\u7406:<\/strong><\/span> \u5982\u679c<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">G<\/span>\u662f\u4efb\u610f\u8868\u8fbe\u5f0f\uff0c\u90a3\u4e48<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> F\\models G \\Leftrightarrow \\models (F\\rightarrow G) <\/span>\n<p>\u6210\u7acb\u3002<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify;\"><span style=\"color: #0000aa;\"><strong>\u8bc1\u660e:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">\u901a\u8fc7\u89c2\u5bdf\u771f\u503c\u8868\uff0c\u53ef\u4ee5\u8f7b\u677e\u5f97\u51fa\u8fd9\u4e2a\u5b9a\u7406\u7684\u8bc1\u660e\u3002<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #dddddd;\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddddd;\"><span class=\"katex-eq\" data-katex-display=\"false\">G<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddddd;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg F<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddddd;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\rightarrow G):=(\\neg F \\vee G)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u5982\u679c\u6211\u4eec\u4e13\u6ce8\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">F\\models G<\/span>\u7684\u542b\u4e49\uff0c\u6211\u4eec\u5c06\u770b\u5230\u8fd9\u7b49\u540c\u4e8e\u8bf4<span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}\\models F \\Rightarrow \\mathcal{A}\\models G<\/span>\uff0c\u8fd9\u672c\u8d28\u4e0a\u7b49\u540c\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}\\not\\models F \\vee \\mathcal{A}\\models G<\/span>\u3002\u73b0\u5728\uff0c\u5982\u679c\u6211\u4eec\u6ce8\u610f\u5230<span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}\\not\\models F<\/span>\u5b9e\u9645\u4e0a\u7b49\u540c\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}\\models \\neg F<\/span>\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u8bf4<span class=\"katex-eq\" data-katex-display=\"false\">F\\models G<\/span>\u7b49\u540c\u4e8e<span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A} \\models \\neg F \\vee \\mathcal{A}\\models G<\/span>\u3002\u5982\u679c\u6211\u4eec\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">F \\rightarrow G<\/span>\u521b\u5efa\u4e00\u4e2a\u771f\u503c\u8868\uff0c\u5e76\u5c06\u6ee1\u8db3\u6761\u4ef6<span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A} \\models \\neg F \\vee \\mathcal{A}\\models G<\/span>\u7684\u533a\u57df\u6807\u8bb0\u4e3a<span style=\"color: #008800;\"><strong>\u7eff\u8272<\/strong><\/span>\uff0c\u6211\u4eec\u4f1a\u770b\u5230\u5982\u4e0b\u6240\u793a\u7684\u60c5\u51b5\uff1a<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #dddddd;\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddddd;\"><span class=\"katex-eq\" data-katex-display=\"false\">G<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddddd;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg F<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddddd;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\rightarrow G):=(\\neg F \\vee G)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center; background-color: #008800; color: #ffffff;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center; background-color: #008800; color: #ffffff;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center; background-color: #008800; color: #ffffff;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center; background-color: #008800; color: #ffffff;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center; background-color: #008800; color: #ffffff;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center; background-color: #008800; color: #ffffff;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u7531\u6b64\u53ef\u89c1\uff0c\u5f53<span class=\"katex-eq\" data-katex-display=\"false\">F\\models G<\/span>\u6210\u7acb\u65f6\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">\\models (F \\rightarrow G)<\/span>\u4e5f\u6210\u7acb\uff0c\u53cd\u4e4b\u4ea6\u7136\uff0c\u8fd9\u5c31\u662f\u63a8\u8bba\u5b9a\u7406\u53ca\u5176\u8bed\u4e49\u7248\u672c\u7684\u9006\u5b9a\u7406\u3002<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u5047\u8bbe\u6211\u4eec\u60f3\u77e5\u9053\u8868\u8fbe\u5f0f<span class=\"katex-eq\" data-katex-display=\"false\">G<\/span>\u662f\u5426\u662f\u53e6\u4e00\u4e2a\u8868\u8fbe\u5f0f<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u7684\u540e\u679c\u3002\u6211\u4eec\u79f0\u4e4b\u4e3a<strong>\u540e\u679c\u95ee\u9898\u3002<\/strong>\u5229\u7528\u4e0a\u8ff0\u5b9a\u7406\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8be5\u95ee\u9898\u8f6c\u5316\u4e3a<strong>\u6709\u6548\u6027\u95ee\u9898<\/strong>\uff0c\u56e0\u4e3a\u201c\u5982\u679c<span class=\"katex-eq\" data-katex-display=\"false\">G<\/span>\u662f<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u7684\u540e\u679c\uff0c\u5219<span class=\"katex-eq\" data-katex-display=\"false\">(F\\rightarrow G)<\/span>\u662f\u5b9a\u7406\u201d\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u63a8\u8bba\u5b9a\u7406\u5728\u8bed\u4e49\u540e\u679c\u4e0e\u7b49\u4ef7\u7814\u7a76\u4e2d\u7684\u5e94\u7528<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=vjkzDxbG8LY&amp;t=796s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u901a\u8fc7\u771f\u503c\u8868<\/span><\/strong><\/a>\u53ef\u4ee5\u63a8\u5bfc\u51fa\u4e00\u4e9b\u4e0e\u6211\u4eec\u4ee5\u524d\u89c1\u8fc7\u7684\u7c7b\u4f3c\u7684\u6027\u8d28\u3002<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td colspan=\"2\" style=\"text-align: justify;\"><strong><span style=\"color: #000088;\">\u793a\u4f8b:<\/span><\/strong> \u4f7f\u7528\u771f\u503c\u8868\u8bc1\u660e\u4ee5\u4e0b\u6027\u8d28\uff1a<\/td>\n<\/tr>\n<tr>\n<td>\u5408\u53d6\u6d88\u53bb:<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(F\\wedge G)\\models F<\/span><\/td>\n<\/tr>\n<tr>\n<td>\u6790\u53d6\u5f15\u5165:<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">F\\models (F\\vee G)<\/span><\/td>\n<\/tr>\n<tr>\n<td>\u77db\u76fe:<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(F\\wedge\\neg F)\\models G<\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\"><span style=\"color: #008800;\"><strong>\u89e3\u51b3\u65b9\u6cd5:<\/strong><\/span><span style=\"color: #000000;\"> \u4f7f\u7528\u6211\u4eec\u521a\u521a\u56de\u987e\u7684\u63a8\u8bba\u5b9a\u7406\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u540e\u679c\u95ee\u9898\u8f6c\u5316\u4e3a\u6709\u6548\u6027\u95ee\u9898\u3002<\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u4e3a\u4e86\u89e3\u51b3<strong>\u5408\u53d6\u6d88\u53bb<\/strong>\uff0c\u6211\u4eec\u53ef\u4ee5\u6784\u5efa\u4ee5\u4e0b\u771f\u503c\u8868\uff1a<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/td>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">G<\/span><\/td>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\wedge G)<\/span><\/td>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">((F\\wedge G) \\rightarrow F)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u901a\u8fc7\u8fd9\u4e00\u771f\u503c\u8868\uff0c\u6211\u4eec\u8bc1\u660e\u4e86<span class=\"katex-eq\" data-katex-display=\"false\">((F\\wedge G)\\rightarrow F)<\/span>\u662f\u4e00\u4e2a\u91cd\u8a00\u5f0f\uff0c\u56e0\u6b64\uff0c\u4f9d\u636e\u63a8\u8bba\u5b9a\u7406\u7684\u9006\u5b9a\u7406\uff0c\u6211\u4eec\u5f97\u5230<span class=\"katex-eq\" data-katex-display=\"false\">(F\\wedge G) \\models F<\/span>\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\"><strong>\u6790\u53d6\u5f15\u5165<\/strong>\u901a\u8fc7\u6784\u5efa\u9002\u5f53\u7684\u771f\u503c\u8868\u4ee5\u7c7b\u4f3c\u7684\u65b9\u5f0f\u89e3\u51b3\u3002<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/td>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">G<\/span><\/td>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\vee G)<\/span><\/td>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\rightarrow(F\\vee G))<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u5728\u8fd9\u91cc\u6211\u4eec\u770b\u5230<span class=\"katex-eq\" data-katex-display=\"false\">(F\\rightarrow (F\\vee G))<\/span>\u662f\u4e00\u4e2a\u91cd\u8a00\u5f0f\uff0c\u56e0\u6b64\uff0c\u6839\u636e\u63a8\u8bba\u5b9a\u7406\u7684\u9006\u5b9a\u7406\uff0c\u6211\u4eec\u5f97\u5230<span class=\"katex-eq\" data-katex-display=\"false\">F\\models (F\\vee G)<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\uff0c\u4f7f\u7528\u76f8\u540c\u7684\u65b9\u6cd5\u8bc1\u660e\u4e86<strong>\u77db\u76fe<\/strong>\u6027\u8d28\u3002<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/td>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg F<\/span><\/td>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\wedge \\neg F)<\/span><\/td>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">G<\/span><\/td>\n<td style=\"text-align: center; background-color: #bbbbbb;\"><span class=\"katex-eq\" data-katex-display=\"false\">((F\\wedge \\neg F)\\rightarrow G)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<td style=\"text-align: center; background-color: #dddd00;\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u901a\u8fc7\u8fd9\u4e2a\u771f\u503c\u8868\uff0c\u6211\u4eec\u8bc1\u660e\u4e86<span class=\"katex-eq\" data-katex-display=\"false\">((F\\wedge \\neg F)\\rightarrow G)<\/span>\u662f\u4e00\u4e2a\u91cd\u8a00\u5f0f\uff0c\u56e0\u6b64\uff0c\u6839\u636e\u63a8\u8bba\u5b9a\u7406\u7684\u9006\u5b9a\u7406\uff0c\u6211\u4eec\u5f97\u5230<span class=\"katex-eq\" data-katex-display=\"false\">(F\\wedge \\neg F)\\models G<\/span>\u3002<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u8bed\u4e49\u7b49\u4ef7\u53ca\u5176\u6027\u8d28<\/h2>\n<p><span style=\"color: #000000;\"><strong>[<a href=\"https:\/\/www.youtube.com\/watch?v=vjkzDxbG8LY&amp;t=1058s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u89c2\u770b<\/span><\/a>]<\/strong><\/span><\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: justify; color: #000000;\"><span style=\"color: #880000;\"><strong>\u5b9a\u4e49:<\/strong><\/span> \u5982\u679c\u540c\u65f6\u6210\u7acb<span class=\"katex-eq\" data-katex-display=\"false\">F\\models G<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">G\\models F<\/span>\uff0c\u90a3\u4e48\u6211\u4eec\u8bf4<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">G<\/span>\u5728\u8bed\u4e49\u4e0a\u662f<strong>\u7b49\u4ef7\u7684<\/strong>\u3002\u8fd9\u53ef\u4ee5\u8868\u793a\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">F\\equiv G<\/span>\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\"><strong>\u6839\u636e\u8fd9\u4e00\u5b9a\u4e49\uff0c\u4e24\u79cd\u8868\u8fbe\u5f0f\u5728\u8bed\u4e49\u4e0a\u662f\u7b49\u4ef7\u7684\uff0c\u5f53\u4e14\u4ec5\u5f53\u5b83\u4eec\u5177\u6709\u76f8\u540c\u7684\u771f\u503c\u3002<\/strong><\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;\"><strong><span style=\"color: #000088;\">\u793a\u4f8b:<\/span><\/strong> \u53ef\u4ee5\u901a\u8fc7\u771f\u503c\u8868\u8bc1\u660e\u5bf9\u79f0\u7684<strong>\u8bed\u4e49\u7b49\u4ef7<\/strong>\u662f\u6210\u7acb\u7684\u3002<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\downarrow G) \\equiv (G\\downarrow F)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\vee G) \\equiv (G\\vee F)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\wedge G) \\equiv (G\\wedge F)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\leftrightarrow G) \\equiv (G\\leftrightarrow F)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\underline{\\vee} G) \\equiv (G\\underline{\\vee} F)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;\"><strong><span style=\"color: #000088;\">\u793a\u4f8b:<\/span><\/strong> \u5982\u679c<span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>\u662f\u4efb\u610f\u8868\u8fbe\u5f0f\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">\\top<\/span>\u662f\u91cd\u8a00\u5f0f\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">\\bot<\/span>\u662f\u77db\u76fe\u5f0f\uff0c\u90a3\u4e48\u53ef\u4ee5\u901a\u8fc7\u771f\u503c\u8868\u8bc1\u660e\u4ee5\u4e0b\u8bed\u4e49\u7b49\u4ef7\u6210\u7acb<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\wedge \\top) \\equiv F<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\vee \\top) \\equiv \\top<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\wedge \\bot) \\equiv \\bot<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\vee \\bot) \\equiv F<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify;\">\u8fd9\u4e9b\u7b49\u4ef7\u88ab\u79f0\u4e3a<strong>\u5438\u6536\u5b9a\u5f8b<\/strong>\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;\"><strong><span style=\"color: #000088;\">\u793a\u4f8b:<\/span><\/strong> \u5728\u547d\u9898\u903b\u8f91\u8bed\u4e49\u4e2d\uff0c\u5408\u53d6\u548c\u6790\u53d6\u7684\u5206\u914d\u5f8b\u4e5f\u6210\u7acb\u3002<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\wedge (G\\vee H)) \\equiv ((F\\wedge G) \\vee (F\\wedge H))<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">(F\\vee (G\\wedge H)) \\equiv ((F\\vee G) \\wedge (F\\vee H))<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;\"><strong><span style=\"color: #000088;\">\u793a\u4f8b:<\/span><\/strong> \u5728\u547d\u9898\u903b\u8f91\u8bed\u4e49\u4e2d\uff0c\u5fb7\u6469\u6839\u5b9a\u5f8b\u4e5f\u6210\u7acb\u3002<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(F\\wedge G) \\equiv (\\neg F \\vee \\neg G)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(F\\vee G) \\equiv (\\neg F \\wedge \\neg G)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;\"><strong><span style=\"color: #880000;\">\u7ec3\u4e60:<\/span><\/strong> \u4e00\u4e2a\u597d\u7684\u7ec3\u4e60\u662f\u901a\u8fc7\u771f\u503c\u8868\u8bc1\u660e\u5438\u6536\u5b9a\u5f8b\u3001\u5206\u914d\u5f8b\u548c\u5fb7\u6469\u6839\u5b9a\u5f8b\u7684\u8bed\u4e49\u7b49\u4ef7\u786e\u5b9e\u6210\u7acb\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;\"><strong><span style=\"color: #000088;\">\u793a\u4f8b:<\/span><\/strong> \u4f7f\u7528\u8bed\u4e49\u7b49\u4ef7\u8bc1\u660e\u4ee5\u4e0b\u7b49\u4ef7\u6210\u7acb\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">((C\\wedge D) \\vee A) \\wedge (C\\wedge D) \\vee B) \\wedge (E \\vee \\neg E))\\equiv ((A\\wedge B)\\vee(C\\wedge D))<\/span>\u3002<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"color: #000000;\"><span style=\"color: #008800;\"><strong>\u89e3\u51b3\u65b9\u6cd5:<\/strong><\/span> \u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u771f\u503c\u8868\u8bc1\u660e\u6b64\u7b49\u4ef7\u6027\uff0c\u4f46\u662f\u5982\u679c\u8fd9\u6837\u505a\uff0c\u6211\u4eec\u5c06\u9762\u4e345\u4e2a\u547d\u9898\u53d8\u91cf\u7684\u8868\u8fbe\u5f0f\uff0c\u8fd9\u610f\u5473\u7740\u9700\u8981\u5236\u4f5c\u4e00\u4e2a\u5177\u6709<span class=\"katex-eq\" data-katex-display=\"false\">2^5 = 32<\/span>\u884c\u7684\u771f\u503c\u8868\uff0c\u8fd9\u6700\u597d\u80fd\u907f\u514d\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u6211\u4eec\u5df2\u7ecf\u5c55\u793a\u7684\u7b49\u4ef7\u6027\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u9996\u5148\u6ce8\u610f<span class=\"katex-eq\" data-katex-display=\"false\">(E\\vee \\neg E)<\/span>\u662f\u4e00\u4e2a\u91cd\u8a00\u5f0f\u3002\u6211\u4eec\u5c06\u8fd9\u4e00\u91cd\u8a00\u5f0f\u8bb0\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">\\top<\/span>\u3002\u7136\u540e\uff0c\u4f7f\u7528\u5438\u6536\u5b9a\u5f8b\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">((C\\wedge D) \\vee A) \\wedge (C\\wedge D) \\vee B) \\wedge (E \\vee \\neg E)) \\equiv ((C\\wedge D) \\vee A) \\wedge (C\\wedge D) \\vee B)) <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u4f7f\u7528\u5206\u914d\u5f8b\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\"> ((C\\wedge D) \\vee A) \\wedge (C\\wedge D) \\vee B)) \\equiv ((C\\wedge D) \\vee (A\\wedge B))<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\uff0c\u901a\u8fc7\u5bf9\u79f0\u6027\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\"> ((C\\wedge D) \\vee (A\\wedge B)) \\equiv ((A\\wedge B) \\vee (C\\wedge D))<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u6b64\uff0c\u901a\u8fc7\u8fd9\u4e9b\u7b49\u4ef7\u6027\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">((C\\wedge D) \\vee A) \\wedge (C\\wedge D) \\vee B) \\wedge (E \\vee \\neg E)) \\equiv ((A\\wedge B) \\vee (C\\wedge D))<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u5c31\u662f\u6211\u4eec\u60f3\u8981\u8bc1\u660e\u7684\u5185\u5bb9\u3002<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u603b\u7ed3<\/h2>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c\u6211\u4eec\u89c2\u5bdf\u6700\u540e\u8fd9\u4e2a\u4f8b\u5b50\u7684\u5c55\u5f00\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\uff0c\u968f\u7740\u53d8\u91cf\u6570\u91cf\u7684\u589e\u52a0\uff0c\u7814\u7a76\u8bed\u4e49\u540e\u679c\u548c\u7b49\u4ef7\u95ee\u9898\u7684\u590d\u6742\u6027\u4f1a\u5448\u6307\u6570\u589e\u957f\uff0c\u5982\u679c\u6211\u4eec\u4f9d\u8d56\u771f\u503c\u8868\u3002\u7136\u800c\uff0c\u6211\u4eec\u770b\u5230\u4ece\u6a21\u578b\u7684\u6982\u5ff5\u53d1\u5c55\u51fa\u4e86\u4e00\u4e9b\u7c7b\u4f3c\u4e8e\u6211\u4eec\u4e4b\u524d\u8be6\u7ec6\u7814\u7a76\u7684\u63a8\u7406\u6280\u672f\u3002\u6a21\u578b\u548c\u63a8\u7406\u4e4b\u95f4\u7684\u8fd9\u79cd\u5173\u7cfb\u5c06\u5728\u4e0d\u4e45\u7684\u5c06\u6765\u8fdb\u4e00\u6b65\u63a2\u8ba8\uff0c\u7ed3\u5408\u4e24\u8005\u7684\u4f7f\u7528\u5c06\u6700\u7ec8\u4f7f\u6211\u4eec\u5728\u903b\u8f91\u7814\u7a76\u4e2d\u514d\u53d7\u65e0\u6570\u5934\u75db\u4e4b\u82e6\u3002<a href=\"https:\/\/amzn.to\/3t6XASK\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8bed\u4e49\u540e\u679c\u4e0e\u7b49\u4ef7 \u6458\u8981\u5728\u672c\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u7814\u7a76\u547d\u9898\u903b\u8f91\u4e2d\u7684\u8bed\u4e49\u540e\u679c\u4e0e\u7b49\u4ef7\uff0c\u8fd9\u662f\u5bf9\u4e4b\u524d\u5b66\u4e60\u5185\u5bb9\u7684\u81ea\u7136\u5ef6\u7eed\u3002\u6211\u4eec\u5c06\u5b66\u4e60\u5982\u4f55\u4ece\u771f\u503c\u5206\u914d\u4e2d\u5f97\u51fa\u8bed\u4e49\u540e\u679c\u7684\u6982\u5ff5\uff0c\u4ee5\u53ca\u8fd9\u4e00\u6982\u5ff5\u5982\u4f55\u4e0e\u63a8\u8bba\u5b9a\u7406\u76f8\u5173\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5c06\u901a\u8fc7\u771f\u503c\u8868\u7684\u4f7f\u7528\uff0c\u5b66\u4e60\u5982\u4f55\u83b7\u53d6\u5982\u5408\u53d6\u6d88\u53bb\u3001\u6790\u53d6\u5f15\u5165\u7b49\u6709\u7528\u7684\u6027\u8d28\u3002\u6211\u4eec\u8fd8\u5c06\u63a2\u8ba8\u8bed\u4e49\u7b49\u4ef7\u7684\u6982\u5ff5\uff0c\u5e76\u4e86\u89e3\u5176\u4e0e\u5df2\u77e5\u6027\u8d28\u7684\u5173\u7cfb\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u5c55\u793a\u5982\u4f55\u4f7f\u7528\u6a21\u578b\u548c\u63a8\u7406\u6280\u672f\u6765\u7b80\u5316\u8bed\u4e49\u540e\u679c\u4e0e\u7b49\u4ef7\u95ee\u9898\u7684\u7814\u7a76\u3002 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