{"id":28135,"date":"2021-04-08T13:00:56","date_gmt":"2021-04-08T13:00:56","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28135"},"modified":"2024-08-22T08:27:27","modified_gmt":"2024-08-22T08:27:27","slug":"completude-et-fiabilite-en-logique-propositionnelle","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/","title":{"rendered":"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>R\u00c9SUM\u00c9<\/strong><br \/><em>Ce cours aborde la relation entre la compl\u00e9tude et la fiabilit\u00e9 en logique propositionnelle. Bien que les techniques de d\u00e9duction et la s\u00e9mantique en logique propositionnelle aient \u00e9t\u00e9 largement discut\u00e9es, peu d&#8217;attention a \u00e9t\u00e9 accord\u00e9e \u00e0 la relation entre ces deux aspects. La fiabilit\u00e9 se r\u00e9f\u00e8re \u00e0 la propri\u00e9t\u00e9 d&#8217;un syst\u00e8me logique o\u00f9, chaque fois qu&#8217;une expression G peut \u00eatre d\u00e9duite d&#8217;un ensemble d&#8217;expressions \u0393, G est cons\u00e9quemment une cons\u00e9quence (s\u00e9mantique) de \u0393. D&#8217;autre part, la compl\u00e9tude se r\u00e9f\u00e8re \u00e0 la propri\u00e9t\u00e9 d&#8217;un syst\u00e8me logique o\u00f9, si G est une cons\u00e9quence s\u00e9mantique d&#8217;un ensemble d&#8217;expressions \u0393, alors il existe une preuve formelle avec des pr\u00e9misses \u0393 \u00e0 partir de laquelle G peut \u00eatre d\u00e9duite. Il est d\u00e9montr\u00e9 que la logique propositionnelle est fiable et compl\u00e8te, et une explication d\u00e9taill\u00e9e de chaque propri\u00e9t\u00e9 est pr\u00e9sent\u00e9e. En particulier, il est montr\u00e9 comment la fiabilit\u00e9 d\u00e9coule de la constitution du syst\u00e8me d\u00e9ductif de la logique propositionnelle, et comment la compl\u00e9tude est d\u00e9duite de mani\u00e8re simple. Cette analyse est d&#8217;une grande importance pour comprendre le fonctionnement de la logique propositionnelle et l&#8217;appliquer efficacement dans divers domaines de la connaissance.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>OBJECTIFS D&#8217;APPRENTISSAGE :<\/strong><br \/>\n\u00c0 la fin de ce cours, l&#8217;\u00e9tudiant sera capable de :\n<\/p>\n<ol>\n<li><strong>Distinguer<\/strong> entre la fiabilit\u00e9 et la compl\u00e9tude dans un syst\u00e8me logique.<\/li>\n<li><strong>Appliquer<\/strong> la table de v\u00e9rit\u00e9 pour les axiomes de \u0141ukasiewicz afin de d\u00e9montrer la fiabilit\u00e9 de la logique propositionnelle.<\/li>\n<li><strong>Expliquer<\/strong> comment le modus ponens peut \u00eatre r\u00e9\u00e9crit en utilisant la version s\u00e9mantique du th\u00e9or\u00e8me de d\u00e9duction.<\/li>\n<li><strong>Comprendre<\/strong> que la fiabilit\u00e9 et la compl\u00e9tude sont li\u00e9es et qu&#8217;elles peuvent \u00eatre d\u00e9duites l&#8217;une de l&#8217;autre.<\/li>\n<li><strong>Analyser<\/strong> le concept de tautologie et sa relation avec les th\u00e9or\u00e8mes en logique propositionnelle.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>INDEX<\/strong><br \/>\n<a href=\"#1\">COMPL\u00c9TUDE ET FIABILIT\u00c9 EN LOGIQUE PROPOSITIONNELLE<\/a><br \/>\n<a href=\"#2\">LA LOGIQUE PROPOSITIONNELLE EST FIABLE<\/a><br \/>\n<a href=\"#3\">LA LOGIQUE PROPOSITIONNELLE EST COMPL\u00c8TE<\/a><br \/>\n<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/dGrwsPMHa90\" title=\"YouTube video player\" 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><\/p>\n<h2>Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=dGrwsPMHa90&amp;t=181s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u00c0 ce stade, il est temps de parler de la compl\u00e9tude et de la fiabilit\u00e9 en logique propositionnelle.<\/span><\/strong><\/a> Il s&#8217;av\u00e8re que jusqu&#8217;\u00e0 pr\u00e9sent, beaucoup a \u00e9t\u00e9 dit sur les techniques de d\u00e9duction et la s\u00e9mantique de la logique propositionnelle, mais tout cela a \u00e9t\u00e9 fait d&#8217;une mani\u00e8re qui les fait appara\u00eetre comme deux aspects totalement ind\u00e9pendants sans aucune relation entre eux. La r\u00e9alit\u00e9 est tout \u00e0 fait oppos\u00e9e.<\/p>\n<table>\n<tbody>\n<tr>\n<td>\n<p style=\"text-align: justify; color: #000000;\"><strong>FIABILIT\u00c9 :<\/strong> Un syst\u00e8me logique est dit fiable lorsque, chaque fois qu&#8217;une expression G peut \u00eatre d\u00e9duite d&#8217;un ensemble d&#8217;expressions <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Gamma<\/span><\/span>, il en r\u00e9sulte que G est une cons\u00e9quence (s\u00e9mantique) de <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Gamma<\/span><\/span>.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"text-align: justify; color: #000000;\"><strong>COMPL\u00c9TUDE :<\/strong> D&#8217;autre part, un syst\u00e8me est dit complet lorsque, si G est une cons\u00e9quence s\u00e9mantique d&#8217;un ensemble d&#8217;expressions <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Gamma<\/span><\/span>, alors il existe une preuve formelle avec des pr\u00e9misses <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Gamma<\/span><\/span> \u00e0 partir de laquelle G peut \u00eatre d\u00e9duite.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-VKgbesdSWbQ\/YG6s7C9kkdI\/AAAAAAAAE2g\/K5hUDwI6KkAs5FNmmkTZ1RRV_LqV_kxlQCLcBGAsYHQ\/s0\/completitud%2By%2Bsolvencia.PNG\" alt=\"Compl\u00e9tude et Fiabilit\u00e9 en Logique Propositionnelle\" class=\"aligncenter lazyload\" width=\"285\" height=\"220\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-VKgbesdSWbQ\/YG6s7C9kkdI\/AAAAAAAAE2g\/K5hUDwI6KkAs5FNmmkTZ1RRV_LqV_kxlQCLcBGAsYHQ\/s0\/completitud%2By%2Bsolvencia.PNG\" alt=\"Compl\u00e9tude et Fiabilit\u00e9 en Logique Propositionnelle\" class=\"aligncenter lazyload\" width=\"285\" height=\"220\" \/><\/noscript><\/p>\n<p style=\"text-align: justify; color: #000000;\">En r\u00e9examinant ces id\u00e9es, nous verrons que la compl\u00e9tude et la fiabilit\u00e9 sont satisfaites pour la logique propositionnelle.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>La logique propositionnelle est fiable<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=dGrwsPMHa90&amp;t=292s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Il est facile d&#8217;obtenir la fiabilit\u00e9 de la logique propositionnelle<\/span><\/strong><\/a> en observant la constitution de son syst\u00e8me d\u00e9ductif. Si nous cr\u00e9ons la table de v\u00e9rit\u00e9 pour les axiomes de \u0141ukasiewicz, nous verrons qu&#8217;ils ont une structure telle qu&#8217;ils donnent toujours comme valeur la v\u00e9rit\u00e9, c&#8217;est-\u00e0-dire :<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\models (\\alpha \\rightarrow (\\beta \\rightarrow \\alpha))<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\models ((\\alpha \\rightarrow (\\beta \\rightarrow \\gamma))\\rightarrow ((\\alpha \\rightarrow \\beta) \\rightarrow (\\alpha \\rightarrow \\gamma)))<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\models ((\\neg\\beta \\rightarrow \\neg\\alpha)\\rightarrow(\\alpha \\rightarrow \\beta))<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">De m\u00eame, le modus ponens peut \u00eatre r\u00e9\u00e9crit sous la forme <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\alpha,(\\alpha\\rightarrow \\beta)\\}\\models \\beta.<\/span><\/span>, ce qui peut \u00eatre obtenu en utilisant la version s\u00e9mantique du th\u00e9or\u00e8me de d\u00e9duction. En fait, par ce moyen, nous obtenons <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{(\\alpha\\rightarrow \\beta)\\}\\models (\\alpha\\rightarrow \\beta),<\/span><\/span>, puis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\models ((\\alpha\\rightarrow \\beta)\\rightarrow (\\alpha\\rightarrow \\beta)),<\/span><\/span>, ce qui est \u00e9videmment une tautologie.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>La logique propositionnelle est compl\u00e8te<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=dGrwsPMHa90&amp;t=487s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">La compl\u00e9tude de la logique propositionnelle nous dit que<\/span><\/strong><\/a>, si B est une cons\u00e9quence s\u00e9mantique de A, alors B est d\u00e9duit de A. En d&#8217;autres termes : toutes les expressions vraies ont une d\u00e9monstration. C&#8217;est ce que nous appelons la compl\u00e9tude. Cela peut \u00eatre d\u00e9duit d&#8217;une mani\u00e8re simple.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Cela peut \u00eatre d\u00e9duit d&#8217;une mani\u00e8re simple. Supposons que B ne puisse pas \u00eatre d\u00e9duit de A, ou plut\u00f4t <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(A\\vdash B)<\/span><\/span>, selon le th\u00e9or\u00e8me de d\u00e9duction, cela \u00e9quivaut \u00e0 dire : <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg (\\vdash A\\rightarrow B)<\/span><\/span> ; maintenant, si nous recourons \u00e0 la fiabilit\u00e9, cela conduit \u00e0 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\models A \\rightarrow B)<\/span><\/span>, ce qui, selon la version s\u00e9mantique du th\u00e9or\u00e8me de d\u00e9duction, \u00e9quivaut \u00e0 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(A\\models B)<\/span><\/span>. En r\u00e9sum\u00e9, nous obtenons :<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(A\\vdash B) \\Rightarrow \\neg(A\\models B) <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">Ce qui \u00e9quivaut \u00e0 dire<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(A\\models B) \\Rightarrow (A\\vdash B) <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">Cela signifie que, si A mod\u00e9lise B, alors B est d\u00e9duit de A. Et si nous utilisons les th\u00e9or\u00e8mes de d\u00e9duction correspondants, nous pouvons obtenir<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\models A\\rightarrow B) \\Rightarrow (\\vdash A \\rightarrow B) <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">C&#8217;est-\u00e0-dire : si une expression est une tautologie, alors c&#8217;est un th\u00e9or\u00e8me ; et comme nous l&#8217;avons vu, les th\u00e9or\u00e8mes sont le r\u00e9sultat d&#8217;une d\u00e9monstration.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle R\u00c9SUM\u00c9Ce cours aborde la relation entre la compl\u00e9tude et la fiabilit\u00e9 en logique propositionnelle. Bien que les techniques de d\u00e9duction et la s\u00e9mantique en logique propositionnelle aient \u00e9t\u00e9 largement discut\u00e9es, peu d&#8217;attention a \u00e9t\u00e9 accord\u00e9e \u00e0 la relation entre ces deux aspects. La fiabilit\u00e9 se r\u00e9f\u00e8re \u00e0 la propri\u00e9t\u00e9 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28119,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":2,"footnotes":""},"categories":[617,631,569],"tags":[],"class_list":["post-28135","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-logique-mathematique","category-logique-propositionnelle","category-mathematiques"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Comprenez enfin la relation entre la compl\u00e9tude et la fiabilit\u00e9 en logique propositionnelle, et comment ces propri\u00e9t\u00e9s fondamentales assurent la validit\u00e9 et la coh\u00e9rence des syst\u00e8mes logiques\" \/>\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\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle\" \/>\n<meta property=\"og:description\" content=\"Comprenez enfin la relation entre la compl\u00e9tude et la fiabilit\u00e9 en logique propositionnelle, et comment ces propri\u00e9t\u00e9s fondamentales assurent la validit\u00e9 et la coh\u00e9rence des syst\u00e8mes logiques\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/\" \/>\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=\"2021-04-08T13:00:56+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-08-22T08:27:27+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic-1024x576.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle\" \/>\n<meta name=\"twitter:description\" content=\"Comprenez enfin la relation entre la compl\u00e9tude et la fiabilit\u00e9 en logique propositionnelle, et comment ces propri\u00e9t\u00e9s fondamentales assurent la validit\u00e9 et la coh\u00e9rence des syst\u00e8mes logiques\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic.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\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle\",\"datePublished\":\"2021-04-08T13:00:56+00:00\",\"dateModified\":\"2024-08-22T08:27:27+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/\"},\"wordCount\":984,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic.jpg\",\"articleSection\":[\"Logique Math\u00e9matique\",\"Logique Propositionnelle\",\"Math\u00e9matiques\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/\",\"url\":\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/\",\"name\":\"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle - toposuranos.com\/material\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#primaryimage\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic.jpg\",\"datePublished\":\"2021-04-08T13:00:56+00:00\",\"dateModified\":\"2024-08-22T08:27:27+00:00\",\"description\":\"Comprenez enfin la relation entre la compl\u00e9tude et la fiabilit\u00e9 en logique propositionnelle, et comment ces propri\u00e9t\u00e9s fondamentales assurent la validit\u00e9 et la coh\u00e9rence des syst\u00e8mes logiques\",\"breadcrumb\":{\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#primaryimage\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic.jpg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic.jpg\",\"width\":1280,\"height\":720},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle\"}]},{\"@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\/#\/schema\/person\/image\/\",\"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":"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle - toposuranos.com\/material","description":"Comprenez enfin la relation entre la compl\u00e9tude et la fiabilit\u00e9 en logique propositionnelle, et comment ces propri\u00e9t\u00e9s fondamentales assurent la validit\u00e9 et la coh\u00e9rence des syst\u00e8mes logiques","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\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/","og_locale":"es_ES","og_type":"article","og_title":"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle","og_description":"Comprenez enfin la relation entre la compl\u00e9tude et la fiabilit\u00e9 en logique propositionnelle, et comment ces propri\u00e9t\u00e9s fondamentales assurent la validit\u00e9 et la coh\u00e9rence des syst\u00e8mes logiques","og_url":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-04-08T13:00:56+00:00","article_modified_time":"2024-08-22T08:27:27+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic-1024x576.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle","twitter_description":"Comprenez enfin la relation entre la compl\u00e9tude et la fiabilit\u00e9 en logique propositionnelle, et comment ces propri\u00e9t\u00e9s fondamentales assurent la validit\u00e9 et la coh\u00e9rence des syst\u00e8mes logiques","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic.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\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle","datePublished":"2021-04-08T13:00:56+00:00","dateModified":"2024-08-22T08:27:27+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/"},"wordCount":984,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic.jpg","articleSection":["Logique Math\u00e9matique","Logique Propositionnelle","Math\u00e9matiques"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/","url":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/","name":"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic.jpg","datePublished":"2021-04-08T13:00:56+00:00","dateModified":"2024-08-22T08:27:27+00:00","description":"Comprenez enfin la relation entre la compl\u00e9tude et la fiabilit\u00e9 en logique propositionnelle, et comment ces propri\u00e9t\u00e9s fondamentales assurent la validit\u00e9 et la coh\u00e9rence des syst\u00e8mes logiques","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/semantic.jpg","width":1280,"height":720},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/fr\/completude-et-fiabilite-en-logique-propositionnelle\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"Compl\u00e9tude et fiabilit\u00e9 en logique propositionnelle"}]},{"@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\/#\/schema\/person\/image\/","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\/28135","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=28135"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/28135\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/28119"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=28135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=28135"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=28135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}