{"id":33849,"date":"2021-02-12T13:10:56","date_gmt":"2021-02-12T13:10:56","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33849"},"modified":"2025-07-31T08:07:40","modified_gmt":"2025-07-31T08:07:40","slug":"%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/","title":{"rendered":"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u6982\u8981<\/strong><br \/><em>\u3053\u306e\u8b1b\u7fa9\u3067\u306f\u3001\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u306e\u305f\u3081\u306e\u53e4\u5178\u8ad6\u7406\u306e\u3044\u304f\u3064\u304b\u306e\u6280\u6cd5\u306b\u52a0\u3048\u3001\u6392\u4e2d\u5f8b\u304a\u3088\u3073\u77db\u76fe\u306e\u898f\u5247\uff08\u7206\u767a\u539f\u7406\u3068\u3057\u3066\u3082\u77e5\u3089\u308c\u308b\uff09\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u6280\u6cd5\u304a\u3088\u3073\u80cc\u7406\u6cd5\u306b\u3064\u3044\u3066\u3082\u8aac\u660e\u3057\u3001\u3053\u308c\u3089\u306f\u3044\u305a\u308c\u3082\u6570\u5b66\u7684\u30fb\u8ad6\u7406\u7684\u8a3c\u660e\u306b\u975e\u5e38\u306b\u6709\u7528\u3067\u3059\u3002\u5404\u6280\u6cd5\u306f\u5f62\u5f0f\u7684\u306b\u63d0\u793a\u3055\u308c\u3001\u7406\u89e3\u3092\u6df1\u3081\u308b\u305f\u3081\u306e\u6bb5\u968e\u7684\u306a\u8a3c\u660e\u304c\u63d0\u4f9b\u3055\u308c\u307e\u3059\u3002\u547d\u984c\u8ad6\u7406\u3092\u3055\u3089\u306b\u6df1\u304f\u5b66\u3073\u3001\u5b9a\u7406\u306e\u8a3c\u660e\u80fd\u529b\u3092\u9ad8\u3081\u305f\u3044\u65b9\u306b\u3068\u3063\u3066\u3001\u3053\u306e\u8b1b\u7fa9\u306f\u975e\u5e38\u306b\u6709\u76ca\u3067\u3059\u3002<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p><strong>\u5b66\u7fd2\u76ee\u6a19\uff1a<\/strong><\/p>\n<ol>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u6280\u6cd5\u306e\u6b63\u5f53\u5316\u3002<\/li>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u6392\u4e2d\u5f8b\u307e\u305f\u306f\u30c8\u30fc\u30c8\u30ed\u30b8\u30fc\uff08TAU\uff09\u306e\u6027\u8cea\u3002<\/li>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u77db\u76fe\u306e\u898f\u5247\uff08CON\uff09\u307e\u305f\u306f\u7206\u767a\u539f\u7406\u3002<\/li>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u9078\u8a00\u9664\u53bb\u6280\u6cd5\uff08\u2228-\u9664\u53bb3\uff09\u3002<\/li>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u6280\u6cd5\uff08CAS\uff09\u3002<\/li>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u80cc\u7406\u6cd5\u6280\u6cd5\uff08absurdo\uff09\u3002<\/li>\n<li><strong>\u5fdc\u7528\u3059\u308b<\/strong>\uff1a\u53e4\u5178\u8ad6\u7406\u306e\u5404\u7a2e\u6280\u6cd5\u3092\u7528\u3044\u3066\u8907\u96d1\u306a\u554f\u984c\u3084\u8a3c\u660e\u3092\u89e3\u6c7a\u3059\u308b\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u76ee\u6b21<\/strong><br \/>\n<a href=\"#1\"><strong>\u9023\u8a00\u304a\u3088\u3073\u9078\u8a00\u306e\u5c0e\u5165\u3068\u9664\u53bb<\/strong><\/a><br \/>\n<a href=\"#2\">\u2228-\u5c0e\u5165<\/a><br \/>\n<a href=\"#3\">\u2228-\u9664\u53bb<\/a><br \/>\n<a href=\"#4\">\u2227-\u5c0e\u5165<\/a><br \/>\n<a href=\"#5\">\u2227-\u9664\u53bb<\/a><br \/>\n<a href=\"#6\"><strong>\u77db\u76fe\u3068\u30c8\u30fc\u30c8\u30ed\u30b8\u30fc\u306e\u6280\u6cd5<\/strong><\/a><br \/>\n<a href=\"#7\">\u6392\u4e2d\u5f8b\u307e\u305f\u306f\u30c8\u30fc\u30c8\u30ed\u30b8\u30fc\u306e\u898f\u5247\uff08TAU\uff09<\/a><br \/>\n<a href=\"#8\">\u77db\u76fe\u306e\u898f\u5247\u307e\u305f\u306f\u7206\u767a\u539f\u7406<\/a><br \/>\n<a href=\"#9\">\u2228-\u9664\u53bb3<\/a><br \/>\n<a href=\"#10\">\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\uff08CAS\uff09<\/a><br \/>\n<a href=\"#11\">\u80cc\u7406\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>\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=439s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u53e4\u5178\u8ad6\u7406\u306e\u6280\u6cd5\u306e\u4e00\u3064<\/span><\/strong><\/a> \u306f\u3001\u63a5\u7d9a\u8a5e\uff08\u9023\u8a00\u304a\u3088\u3073\u9078\u8a00\uff09\u306e\u5c0e\u5165\u3068\u9664\u53bb\u306b\u95a2\u3059\u308b\u3082\u306e\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u6280\u6cd5\u306f\u3042\u308b\u7a0b\u5ea6\u76f4\u611f\u7684\u306b\u5b9f\u884c\u3055\u308c\u307e\u3059\u304c\u3001\u305d\u306e\u6b63\u5f53\u5316\u306f\u5fc5\u305a\u3057\u3082\u81ea\u660e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3057\u304b\u3057\u3001\u4ee5\u524d\u306e\u8b1b\u7fa9\u3067\u8a3c\u660e\u3057\u305f\u547d\u984c\u8ad6\u7406\u306e\u898f\u5247\u306b\u57fa\u3065\u3044\u3066\u5c0e\u51fa\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002\u5f62\u5f0f\u7684\u306b\u306f\u3001\u63a5\u7d9a\u8a5e\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u306b\u95a2\u3059\u308b\u6280\u6cd5\u306f\u6b21\u306e\u901a\u308a\u3067\u3059\uff1a<\/p>\n<table style=\"text-align: justify;\">\n<tbody>\n<tr>\n<td>\u2228-\u5c0e\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-\u9664\u53bb<\/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-\u5c0e\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-\u9664\u53bb<\/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;\">\u3053\u308c\u3089\u306e\u547d\u984c\u8ad6\u7406\u306b\u57fa\u3065\u304f\u8a3c\u660e\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a<\/p>\n<p><a name=\"2\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2228-\u5c0e\u5165<\/h3>\n<table style=\"text-align: justify;\">\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>; \u516c\u7406A1, \u30e2\u30ce\u30c8\u30cb\u30b7\u30c6\u30a3<\/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>; \u30e2\u30fc\u30c0\u30b9\u30dd\u30cd\u30f3\u30b9 (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\u7fa9 (3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2228-\u9664\u53bb<\/h3>\n<table style=\"text-align: justify;\">\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\u7fa9 (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>; \u30e2\u30fc\u30c0\u30b9\u30dd\u30cd\u30f3\u30b9 (2,3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2227-\u5c0e\u5165<\/h3>\n<table style=\"text-align: justify;\">\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> \u9664\u53bb<\/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>; \u5358\u8abf\u6027\u00d72 (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>; \u4e8c\u91cd\u5426\u5b9a\u5c0e\u5165 (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>; \u4e8c\u91cd\u5426\u5b9a\u5c0e\u5165 (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\u7fa9 (11)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"5\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u2227-\u9664\u53bb<\/h3>\n<table style=\"text-align: justify;\">\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> \u5c0e\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\u7fa9 (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>; \u5358\u8abf\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\u3068\u30c8\u30fc\u30c8\u30ed\u30b8\u30fc\u306e\u6280\u6cd5<\/h2>\n<p><a name=\"7\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u6392\u4e2d\u5f8b\u307e\u305f\u306f\u30c8\u30fc\u30c8\u30ed\u30b8\u30fc\u306e\u898f\u5247\uff08tau\uff09<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1208s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u3082\u3046\u4e00\u3064\u306e\u9855\u8457\u306a\u7279\u5fb4<\/span><\/strong><\/a> \u306f\u3001\u6392\u4e2d\u5f8b\uff08tertium non datur\uff09\u306e\u6027\u8cea\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u3042\u308b\u4e3b\u5f35\u3068\u305d\u306e\u5426\u5b9a\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u3044\u305a\u308c\u304b\u4e00\u65b9\u306f\u5fc5\u305a\u771f\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3001\u3068\u3044\u3046\u539f\u7406\u3067\u3059\u3002\u5225\u306e\u8a00\u3044\u65b9\u3092\u3059\u308c\u3070\u3001\u4e00\u65b9\u304c\u4ed6\u65b9\u3092\u5426\u5b9a\u3059\u308b2\u3064\u306e\u547d\u984c\u306e\u9078\u8a00\u306f\u5fc5\u7136\u7684\u306b\u30c8\u30fc\u30c8\u30ed\u30b8\u30fc\u306b\u306a\u308a\u307e\u3059\u3002\u5f62\u5f0f\u7684\u306b\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\"><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;\">\u3053\u306e\u8a3c\u660e\u306f\u6bd4\u8f03\u7684\u7c21\u5358\u306b\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<table style=\"text-align: justify;\">\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>; (2) \u3088\u308a\u3002\u306a\u305c\u306a\u3089 <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;\">\u6392\u4e2d\u5f8b\u3092\u5225\u306e\u5f62\u3067\u8ff0\u3079\u308b\u3068\u3001\u305d\u308c\u306f<strong>\u77db\u76fe\u5f8b<\/strong>\u3068\u306a\u308a\u307e\u3059\u3002\u77db\u76fe\u5f8b\u306f\u3001\u3042\u308b\u547d\u984c\u304c\u540c\u6642\u306b\u771f\u3067\u3042\u308a\u507d\u3067\u3042\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3068\u3059\u308b\u539f\u7406\u3067\u3042\u308a\u3001\u6b21\u306e\u3088\u3046\u306b\u5f62\u5f0f\u7684\u306b\u8868\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\"><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;\">\u3053\u306e\u6027\u8cea\u306f\u8a3c\u660e\u3092\u5fc5\u8981\u3068\u3057\u307e\u305b\u3093\u3002\u306a\u305c\u306a\u3089\u3001\u305d\u308c\u81ea\u4f53\u304c\u81ea\u660e\u3068\u3044\u3046\u610f\u5473\u3067\u306f\u306a\u304f\u3001\u6392\u4e2d\u5f8b\u306b\u304a\u3051\u308b\u9023\u8a00\u306e\u5b9a\u7fa9\u304b\u3089\u76f4\u63a5\u5c0e\u304b\u308c\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<p><a name=\"8\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h3>\u77db\u76fe\u306e\u898f\u5247\u307e\u305f\u306f\u7206\u767a\u539f\u7406<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1410s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u3082\u3046\u4e00\u3064\u306e\u65e2\u77e5\u306e\u6027\u8cea<\/span><\/strong><\/a> \u306f\u3001\u7206\u767a\u539f\u7406\u3067\u3059\u3002\u3053\u308c\u306f\u901a\u5e38\u300c\u77db\u76fe\u3057\u305f\u524d\u63d0\u304b\u3089\u306f\u4efb\u610f\u306e\u7d50\u8ad6\u304c\u5c0e\u3051\u308b\u300d\u3068\u3044\u3063\u305f\u5f62\u3067\u8868\u73fe\u3055\u308c\u307e\u3059\u3002\u6b21\u306e\u3044\u305a\u308c\u304b\u306e\u5f62\u5f0f\u3067\u63d0\u793a\u3055\u308c\u308b\u3053\u3068\u304c\u4e00\u822c\u7684\u3067\u3059\uff1a<\/p>\n<p style=\"text-align: center;\"><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;\"><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;\">\u3053\u306e\u898f\u5247\u306e\u8a3c\u660e\u306f\u7c21\u5358\u3067\u3059\uff1a<\/p>\n<table style=\"text-align: justify;\">\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> \u5c0e\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\u7fa9 (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-\u9664\u53bb3<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1555s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u30e2\u30fc\u30c0\u30b9\u30fb\u30dd\u30cd\u30f3\u30b9\uff08modus ponens\uff09\u306f<\/span><\/strong><\/a> \u4e8c\u901a\u308a\u306e\u7570\u306a\u308b\u5f62\u3067\u8a18\u8ff0\u3067\u304d\u307e\u3059\u3002\u3088\u304f\u77e5\u3089\u308c\u3066\u3044\u308b\u5f62\u5f0f\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha,(\\alpha \\rightarrow \\beta)\\}\\vdash \\beta<\/span><\/span> \u3067\u3059\u304c\u3001\u3082\u3046\u4e00\u3064\u306e\u5f62\u5f0f\u306f\u3084\u3084\u99b4\u67d3\u307f\u304c\u8584\u3044\u304b\u3082\u3057\u308c\u307e\u305b\u3093\uff1a<\/p>\n<p style=\"text-align: center;\"><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;\">\u3053\u306e2\u3064\u76ee\u306e\u5f62\u5f0f\u306b\u6ce8\u76ee\u3059\u308b\u3068\u3001\u305d\u3053\u304b\u3089\u767a\u5c55\u7684\u306b\u5c0e\u304b\u308c\u308b\u898f\u5247\u3068\u3057\u3066 <strong>\u2228-\u9664\u53bb3<\/strong> \u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u3042\u308b\u547d\u984c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u306e\u305d\u308c\u305e\u308c\u304b\u3089\u5c0e\u51fa\u3055\u308c\u3001\u3055\u3089\u306b\u305d\u308c\u3089\u306e\u9078\u8a00 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\vee \\beta)<\/span><\/span> \u304c\u5b9a\u7406\u3067\u3042\u308b\u5834\u5408\u306b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span><\/span> \u3082\u307e\u305f\u5b9a\u7406\u3067\u3042\u308b\u3001\u3068\u3044\u3046\u8003\u3048\u65b9\u3067\u3059\u3002\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u5f62\u5f0f\u7684\u306b\u8868\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\"><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;\">\u3053\u306e\u53e4\u5178\u8ad6\u7406\u306e\u6280\u6cd5\u306b\u95a2\u3059\u308b\u8a3c\u660e\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a<\/p>\n<table style=\"text-align: justify;\">\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> \u5c0e\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\u7fa9<\/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>; (13) \u3092\u4e21\u8fba\u5426\u5b9a<\/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>; (14) \u306b\u304a\u3044\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A:=\\neg\\alpha<\/span><\/span>, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B:=\\neg\\beta<\/span><\/span> \u3092\u4ee3\u5165<\/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>\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\uff08cas\uff09<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=qAJ_oaSfd9k&amp;t=1957s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u53e4\u5178\u8ad6\u7406\u306e\u3082\u3046\u4e00\u3064\u306e\u6280\u6cd5<\/span><\/a> \u306b\u300c\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u300d\u304c\u3042\u308a\u307e\u3059\u3002\u3042\u308b\u5f0f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u304c\u3001\u3042\u308b\u5f0f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u3068\u305d\u306e\u5426\u5b9a\u306e\u4e21\u65b9\u304b\u3089\u5c0e\u304b\u308c\u308b\u5834\u5408\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> \u306f\u5fc5\u7136\u7684\u306b\u5b9a\u7406\u3067\u3042\u308b\u3068\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u5f62\u5f0f\u7684\u306b\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\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\u305d\u306e\u8a3c\u660e\u306f\u6b21\u306e\u901a\u308a\u3067\u3059\uff1a<\/p>\n<p><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\uff08\u6392\u4e2d\u5f8b\uff09 \\\\\n\n(4) &amp; \\vdash \\beta &amp;; \u2228-\u9664\u53bb3 (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>\u80cc\u7406\u6cd5\uff08absurdo\uff09<\/h3>\n<p style=\"text-align: justify;\">\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3044\u3066\u6700\u3082\u5e83\u304f\u4f7f\u308f\u308c\u308b\u6280\u6cd5\u306e\u4e00\u3064\u304c\u300c\u80cc\u7406\u6cd5\u300d\u3067\u3059\u3002\u7279\u306b\u6570\u5b66\u306e\u8a3c\u660e\u306b\u304a\u3044\u3066\u983b\u7e41\u306b\u767b\u5834\u3057\u307e\u3059\u3002\u3053\u306e\u6280\u6cd5\u306f\u3001\u3042\u308b\u547d\u984c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u304b\u3089\u77db\u76fe\uff08\u547d\u984c\u3068\u305d\u306e\u5426\u5b9a\u306e\u4e21\u7acb\uff09\u304c\u5c0e\u304b\u308c\u308b\u5834\u5408\u3001\u305d\u306e\u547d\u984c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u306e\u5426\u5b9a\u304c\u30c8\u30fc\u30c8\u30ed\u30b8\u30fc\uff08\u5e38\u306b\u771f\uff09\u3067\u3042\u308b\u3001\u3068\u3044\u3046\u3082\u306e\u3067\u3059\u3002\u5f62\u5f0f\u7684\u306b\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\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\u305d\u306e\u8a3c\u660e\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a<\/p>\n<table>\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>\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e \u6982\u8981\u3053\u306e\u8b1b\u7fa9\u3067\u306f\u3001\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u306e\u305f\u3081\u306e\u53e4\u5178\u8ad6\u7406\u306e\u3044\u304f\u3064\u304b\u306e\u6280\u6cd5\u306b\u52a0\u3048\u3001\u6392\u4e2d\u5f8b\u304a\u3088\u3073\u77db\u76fe\u306e\u898f\u5247\uff08\u7206\u767a\u539f\u7406\u3068\u3057\u3066\u3082\u77e5\u3089\u308c\u308b\uff09\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u6280\u6cd5\u304a\u3088\u3073\u80cc\u7406\u6cd5\u306b\u3064\u3044\u3066\u3082\u8aac\u660e\u3057\u3001\u3053\u308c\u3089\u306f\u3044\u305a\u308c\u3082\u6570\u5b66\u7684\u30fb\u8ad6\u7406\u7684\u8a3c\u660e\u306b\u975e\u5e38\u306b\u6709\u7528\u3067\u3059\u3002\u5404\u6280\u6cd5\u306f\u5f62\u5f0f\u7684\u306b\u63d0\u793a\u3055\u308c\u3001\u7406\u89e3\u3092\u6df1\u3081\u308b\u305f\u3081\u306e\u6bb5\u968e\u7684\u306a\u8a3c\u660e\u304c\u63d0\u4f9b\u3055\u308c\u307e\u3059\u3002\u547d\u984c\u8ad6\u7406\u3092\u3055\u3089\u306b\u6df1\u304f\u5b66\u3073\u3001\u5b9a\u7406\u306e\u8a3c\u660e\u80fd\u529b\u3092\u9ad8\u3081\u305f\u3044\u65b9\u306b\u3068\u3063\u3066\u3001\u3053\u306e\u8b1b\u7fa9\u306f\u975e\u5e38\u306b\u6709\u76ca\u3067\u3059\u3002 \u5b66\u7fd2\u76ee\u6a19\uff1a \u7406\u89e3\u3059\u308b\uff1a\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u6280\u6cd5\u306e\u6b63\u5f53\u5316\u3002 \u7406\u89e3\u3059\u308b\uff1a\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u6392\u4e2d\u5f8b\u307e\u305f\u306f\u30c8\u30fc\u30c8\u30ed\u30b8\u30fc\uff08TAU\uff09\u306e\u6027\u8cea\u3002 \u7406\u89e3\u3059\u308b\uff1a\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u77db\u76fe\u306e\u898f\u5247\uff08CON\uff09\u307e\u305f\u306f\u7206\u767a\u539f\u7406\u3002 \u7406\u89e3\u3059\u308b\uff1a\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u9078\u8a00\u9664\u53bb\u6280\u6cd5\uff08\u2228-\u9664\u53bb3\uff09\u3002 \u7406\u89e3\u3059\u308b\uff1a\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u6280\u6cd5\uff08CAS\uff09\u3002 \u7406\u89e3\u3059\u308b\uff1a\u53e4\u5178\u8ad6\u7406\u306b\u304a\u3051\u308b\u80cc\u7406\u6cd5\u6280\u6cd5\uff08absurdo\uff09\u3002 \u5fdc\u7528\u3059\u308b\uff1a\u53e4\u5178\u8ad6\u7406\u306e\u5404\u7a2e\u6280\u6cd5\u3092\u7528\u3044\u3066\u8907\u96d1\u306a\u554f\u984c\u3084\u8a3c\u660e\u3092\u89e3\u6c7a\u3059\u308b\u3002 \u76ee\u6b21 \u9023\u8a00\u304a\u3088\u3073\u9078\u8a00\u306e\u5c0e\u5165\u3068\u9664\u53bb \u2228-\u5c0e\u5165 \u2228-\u9664\u53bb \u2227-\u5c0e\u5165 \u2227-\u9664\u53bb \u77db\u76fe\u3068\u30c8\u30fc\u30c8\u30ed\u30b8\u30fc\u306e\u6280\u6cd5 \u6392\u4e2d\u5f8b\u307e\u305f\u306f\u30c8\u30fc\u30c8\u30ed\u30b8\u30fc\u306e\u898f\u5247\uff08TAU\uff09 \u77db\u76fe\u306e\u898f\u5247\u307e\u305f\u306f\u7206\u767a\u539f\u7406 \u2228-\u9664\u53bb3 \u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\uff08CAS\uff09 \u80cc\u7406\u6cd5\uff08ABSURDO\uff09 \u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb \u53e4\u5178\u8ad6\u7406\u306e\u6280\u6cd5\u306e\u4e00\u3064 \u306f\u3001\u63a5\u7d9a\u8a5e\uff08\u9023\u8a00\u304a\u3088\u3073\u9078\u8a00\uff09\u306e\u5c0e\u5165\u3068\u9664\u53bb\u306b\u95a2\u3059\u308b\u3082\u306e\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u6280\u6cd5\u306f\u3042\u308b\u7a0b\u5ea6\u76f4\u611f\u7684\u306b\u5b9f\u884c\u3055\u308c\u307e\u3059\u304c\u3001\u305d\u306e\u6b63\u5f53\u5316\u306f\u5fc5\u305a\u3057\u3082\u81ea\u660e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3057\u304b\u3057\u3001\u4ee5\u524d\u306e\u8b1b\u7fa9\u3067\u8a3c\u660e\u3057\u305f\u547d\u984c\u8ad6\u7406\u306e\u898f\u5247\u306b\u57fa\u3065\u3044\u3066\u5c0e\u51fa\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002\u5f62\u5f0f\u7684\u306b\u306f\u3001\u63a5\u7d9a\u8a5e\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u306b\u95a2\u3059\u308b\u6280\u6cd5\u306f\u6b21\u306e\u901a\u308a\u3067\u3059\uff1a \u2228-\u5c0e\u5165 \u2228-\u9664\u53bb \u2227-\u5c0e\u5165 \u2227-\u9664\u53bb \u3053\u308c\u3089\u306e\u547d\u984c\u8ad6\u7406\u306b\u57fa\u3065\u304f\u8a3c\u660e\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a \u2228-\u5c0e\u5165 (1) ; \u524d\u63d0 (2) ; \u516c\u7406A1, \u30e2\u30ce\u30c8\u30cb\u30b7\u30c6\u30a3 (3) ; \u30e2\u30fc\u30c0\u30b9\u30dd\u30cd\u30f3\u30b9 (1,2) (4) ; \u5b9a\u7fa9 (3) \u2228-\u9664\u53bb (1) ; \u524d\u63d0 (2) ; \u524d\u63d0 (3) ; [&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":5,"footnotes":""},"categories":[1362,1300,1356],"tags":[],"class_list":["post-33849","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-1362","category--ja","category-1356"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u53e4\u5178\u8ad6\u7406\uff1a\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u3001\u6392\u4e2d\u5f8b\u3001\u7206\u767a\u539f\u7406\u3001\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u3001\u305d\u3057\u3066\u80cc\u7406\u6cd5\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/ja\/\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e\" \/>\n<meta property=\"og:description\" content=\"\u53e4\u5178\u8ad6\u7406\uff1a\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u3001\u6392\u4e2d\u5f8b\u3001\u7206\u767a\u539f\u7406\u3001\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u3001\u305d\u3057\u3066\u80cc\u7406\u6cd5\u3002\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/ja\/\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-02-12T13:10:56+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-07-31T08:07:40+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/logicaclasica.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e\" \/>\n<meta name=\"twitter:description\" content=\"\u53e4\u5178\u8ad6\u7406\uff1a\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u3001\u6392\u4e2d\u5f8b\u3001\u7206\u767a\u539f\u7406\u3001\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u3001\u305d\u3057\u3066\u80cc\u7406\u6cd5\u3002\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/logicaclasica.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/#article\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e\",\"datePublished\":\"2021-02-12T13:10:56+00:00\",\"dateModified\":\"2025-07-31T08:07:40+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/\"},\"wordCount\":880,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/logicaclasica.jpg\",\"articleSection\":[\"\u547d\u984c\u8ad6\u7406\",\"\u6570\u5b66\",\"\u6570\u7406\u8ad6\u7406\u5b66\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/\",\"name\":\"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/#primaryimage\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/logicaclasica.jpg\",\"datePublished\":\"2021-02-12T13:10:56+00:00\",\"dateModified\":\"2025-07-31T08:07:40+00:00\",\"description\":\"\u53e4\u5178\u8ad6\u7406\uff1a\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u3001\u6392\u4e2d\u5f8b\u3001\u7206\u767a\u539f\u7406\u3001\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u3001\u305d\u3057\u3066\u80cc\u7406\u6cd5\u3002\",\"breadcrumb\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/#primaryimage\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/logicaclasica.jpg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/07\\\/logicaclasica.jpg\",\"width\":1024,\"height\":356},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ja\\\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"name\":\"toposuranos.com\\\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\",\"name\":\"toposuranos.com\\\/material\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\\\/material\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/groups\\\/toposuranos\",\"https:\\\/\\\/x.com\\\/topuranos\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\\\/\\\/www.linkedin.com\\\/company\\\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\\\/\\\/toposuranos.com\\\/material\"],\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/author\\\/giorgio-reveco\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e - toposuranos.com\/material","description":"\u53e4\u5178\u8ad6\u7406\uff1a\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u3001\u6392\u4e2d\u5f8b\u3001\u7206\u767a\u539f\u7406\u3001\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u3001\u305d\u3057\u3066\u80cc\u7406\u6cd5\u3002","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/toposuranos.com\/material\/ja\/\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e\/","og_locale":"es_ES","og_type":"article","og_title":"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e","og_description":"\u53e4\u5178\u8ad6\u7406\uff1a\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u3001\u6392\u4e2d\u5f8b\u3001\u7206\u767a\u539f\u7406\u3001\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u3001\u305d\u3057\u3066\u80cc\u7406\u6cd5\u3002","og_url":"http:\/\/toposuranos.com\/material\/ja\/\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-02-12T13:10:56+00:00","article_modified_time":"2025-07-31T08:07:40+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/logicaclasica.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e","twitter_description":"\u53e4\u5178\u8ad6\u7406\uff1a\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u3001\u6392\u4e2d\u5f8b\u3001\u7206\u767a\u539f\u7406\u3001\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u3001\u305d\u3057\u3066\u80cc\u7406\u6cd5\u3002","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/logicaclasica.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e","datePublished":"2021-02-12T13:10:56+00:00","dateModified":"2025-07-31T08:07:40+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/"},"wordCount":880,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/logicaclasica.jpg","articleSection":["\u547d\u984c\u8ad6\u7406","\u6570\u5b66","\u6570\u7406\u8ad6\u7406\u5b66"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/","url":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/","name":"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/logicaclasica.jpg","datePublished":"2021-02-12T13:10:56+00:00","dateModified":"2025-07-31T08:07:40+00:00","description":"\u53e4\u5178\u8ad6\u7406\uff1a\u9023\u8a00\u3068\u9078\u8a00\u306e\u5c0e\u5165\u304a\u3088\u3073\u9664\u53bb\u3001\u6392\u4e2d\u5f8b\u3001\u7206\u767a\u539f\u7406\u3001\u4e8b\u4f8b\u306b\u3088\u308b\u8a3c\u660e\u3001\u305d\u3057\u3066\u80cc\u7406\u6cd5\u3002","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/logicaclasica.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/07\/logicaclasica.jpg","width":1024,"height":356},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/ja\/%e5%8f%a4%e5%85%b8%e8%ab%96%e7%90%86%e6%8a%80%e6%b3%95%e3%81%ae%e8%a8%bc%e6%98%8e\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u53e4\u5178\u8ad6\u7406\u6280\u6cd5\u306e\u8a3c\u660e"}]},{"@type":"WebSite","@id":"http:\/\/toposuranos.com\/material\/#website","url":"http:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"http:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"http:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/33849","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=33849"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/33849\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/27451"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=33849"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=33849"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=33849"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}