{"id":33925,"date":"2021-04-18T13:00:51","date_gmt":"2021-04-18T13:00:51","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33925"},"modified":"2025-08-01T02:32:23","modified_gmt":"2025-08-01T02:32:23","slug":"formae-normales-earumque-proprietates","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/formae-normales-earumque-proprietates\/","title":{"rendered":"Formae Normales earumque Proprietates"},"content":{"rendered":"<p><center><\/p>\n<h1>Formae Normales earumque Proprietates<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>SUMMARIUM<\/strong><br \/><em>Logica propositionis est instrumentum fundamentale in mathematica et informatica. In hac lectione exhibebitur propositio et utilis, ad formas normales pertinens. Propter hoc definientur notiones litteralis, formae normalis coniunctivae (FNC), atque formae normalis disiunctivae (FND). Praeterea demonstrabitur theorema formarum normalium, quod statuit omnes formulas logicae propositionis aequivalere alicui formulae in FND atque alii formulae in FNC. Demonstratio fiet per inductionem super complexitate formularum, quo pacto ostendetur omnes formulas logicae propositionis scribi posse tam in FND quam in FNC. Haec lectio valde utilis erit ad fundamenta logicae propositionis intellegenda atque ad varia scientiae ambita applicanda.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>METAE DISCENDI:<\/strong><br \/>\nAd finem huius lectionis, discipulus poterit:\n<\/p>\n<ol>\n<li><strong>Meminisse<\/strong> definitionem litteralis atque formarum normalium coniunctivarum et disiunctivarum.<\/li>\n<li><strong>Agnotare<\/strong> structuras formulae in FNC et FND.<\/li>\n<li><strong>Adhibere<\/strong> FNC aut FND ad formulas logicae propositionis simplicandas.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>INDEX<\/strong><br \/>\n<a href=\"#1\">DEFINITIO LITTERALIS<\/a><br \/>\n<a href=\"#2\">DEFINITIO FORMARUM NORMALIUM<\/a><br \/>\n<a href=\"#3\">THEOREMA FORMARUM NORMALIUM<\/a><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/CrTcmmE4Q6c\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p style=\"text-align: justify;\">Propositio et utilis in logica propositionis ad formas normales spectat. Ut haec accurate explicemus, primum quaedam vocabula recognoscenda sunt.<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Definitio Litteralis<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=CrTcmmE4Q6c&amp;t=309s\" target=\"_blank\" rel=\"noopener\"><strong>Litteralis est quaelibet<\/strong><\/a> expressio atomica aut negatio expressionis atomicae. Ex hoc distinguimus litterales affirmativos vel negativos, prout exprimuntur sine vel cum negatione. Exempli gratia: <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> est litteralis affirmativa, et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg A<\/span><\/span> est litteralis negativa.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Definitio Formarum Normalium<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=CrTcmmE4Q6c&amp;t=337s\" target=\"_blank\" rel=\"noopener\"><strong>Expressio <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> in forma normali<\/strong><\/a> coniunctiva (FNC) est, cum scribi potest ut coniunctio disiunctionum litteralium, id est:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F=\\bigwedge_{i=1}^n \\left( \\bigvee_{j=1}^m L_{ij}\\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Similiter, expressio est in forma normali disiunctiva (FND), si scribitur ut disiunctio coniunctionum litteralium<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F=\\bigvee_{i=1}^n \\left(\\bigwedge_{j=1}^m L_{ij}\\right)<\/span><\/span><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Theorema Formarum Normalium<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=CrTcmmE4Q6c&amp;t=446s\" target=\"_blank\" rel=\"noopener\"><strong>Omnes formulae logicae propositionis<\/strong><\/a> aequivalent alicui formulae in FND atque alii in FNC.<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000080;\"><strong>DEMONSTRATIO:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\">Hoc demonstrari potest per inductionem super complexitate formularum <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>.<\/p>\n<ul style=\"text-align: justify;\">\n<li><strong>Casus initialis:<\/strong> Si <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> est expressio atomica, tunc potest simul scribi tam in FNC quam in FND, quia: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F\\equiv F_D \\equiv F_C<\/span><\/span>, ubi <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_C:=((F\\vee F)\\wedge (F\\vee F)) <\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_D:=((F\\wedge F)\\vee (F\\wedge F)) <\/span><\/span><\/li>\n<li><strong>Gradus inductivus:<\/strong> Sint <span class=\"katex-eq\" data-katex-display=\"false\">G<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">H<\/span> duae formulae, quibus theorematis propositio iam valet; id est, exstant <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">H_C<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">G_C<\/span><\/span> in FNC, itemque <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">H_D<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">G_D<\/span><\/span> in FND tales ut\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">G\\equiv G_D \\equiv G_D<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">H\\equiv H_D \\equiv H_D<\/span><\/span><\/p>\n<p>Sic scribere possumus:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle G_D := \\bigvee_{i=1}^n \\bigwedge_{j=1}^m L_{ij}^{GD}<\/span><\/span> ; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle G_C := \\bigwedge_{i=1}^n \\bigvee_{j=1}^m L_{ij}^{GC}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle H_D := \\bigvee_{i=1}^n \\bigwedge_{j=1}^m L_{ij}^{HD}<\/span><\/span> ; <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle H_C := \\bigwedge_{i=1}^n \\bigvee_{j=1}^m L_{ij}^{HC}<\/span><\/span><\/p>\n<p>Sine generalitatis iactura videre possumus, si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F:= \\neg G<\/span><\/span>, tunc adhibendo <strong>theorema substitutionis<\/strong> una cum <strong>legibus generalizatis De Morgan<\/strong> habebitur:<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F:= \\neg G \\equiv \\left\\{ \\begin{matrix}\n\n\\neg G_D := \\neg \\bigvee_{i=1}^n \\bigwedge_{j=1}^m L_{ij}^{GD} \\equiv\\bigwedge_{i=1}^n \\neg \\bigwedge_{j=1}^m L_{ij}^{GD} \\equiv \\bigwedge_{i=1}^n \\bigvee_{j=1}^m \\neg L_{ij}^{GD} \\\\ \\\\ \\neg G_C := \\neg \\bigwedge_{i=1}^n \\bigvee_{j=1}^m L_{ij}^{GC} \\equiv \\bigvee_{i=1}^n \\neg \\bigvee_{j=1}^m L_{ij}^{GC} \\equiv \\bigvee_{i=1}^n \\bigwedge_{j=1}^m \\neg L_{ij}^{GC} \\end{matrix}\\right. <\/span>\n<p>Ex altera parte, si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F:=G\\wedge H<\/span><\/span>, habebitur per theorema substitutionis:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F:=G\\wedge H \\equiv G_C \\wedge H_C := \\bigwedge_{i=1}^n \\bigvee_{j=1}^m L_{ij}^{GC} \\wedge \\bigwedge_{i=1}^{n^\\prime} \\bigvee_{j=1}^{m^\\prime} L_{ij}^{HC} <\/span><\/span><\/p>\n<p>quae est forma normalis coniunctiva. Similiter, si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F:=H\\vee G,<\/span><\/span> tunc:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle F:=G\\wedge H \\equiv G_D \\vee H_D := \\bigvee_{i=1}^n \\bigwedge_{j=1}^m L_{ij}^{GD} \\vee \\bigvee_{i=1}^{\\overline{n}} \\bigwedge_{j=1}^{\\overline{m}} L_{ij}^{HD} <\/span><\/span><\/p>\n<p>id est, forma normalis disiunctiva.<\/p>\n<p>Ergo inductio completa est, et omnes expressiones logicae propositionis scribi possunt tam in FND quam in FNC.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Investigatio formarum normalium, scilicet coniunctivae (FNC) et disiunctivae (FND), in logica propositionis fundamentalis est ad simplificationem atque resolutionem problematum in mathematicis et informatica. Theorema quod statuit omnem expressionem logicam posse scribi et in FND et in FNC magni est momenti, quoniam permittit propositiones structurare modo tractabili et normato, quo earum analysis et tractatio facilius fiant. Huius resultati momentum consistit in eo quod firmam basim praebet ad consilium algorithmi, ad optimizationem expressionum logicarum, atque ad solvendum problemata efficaciter in variis scientiae campis, ut sunt intelligentia artificialis et verificatio programmatis. Praeterea, ars inductionis adhibita ad hoc theorema demonstrandum firmat intellectum proprietatum fundamentalium expressionum logicarum earumque usum in aliis contextibus mathematicis.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Formae Normales earumque Proprietates SUMMARIUMLogica propositionis est instrumentum fundamentale in mathematica et informatica. In hac lectione exhibebitur propositio et utilis, ad formas normales pertinens. Propter hoc definientur notiones litteralis, formae normalis coniunctivae (FNC), atque formae normalis disiunctivae (FND). Praeterea demonstrabitur theorema formarum normalium, quod statuit omnes formulas logicae propositionis aequivalere alicui formulae in FND atque [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28305,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":32,"footnotes":""},"categories":[1352,1358,1298],"tags":[],"class_list":["post-33925","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-logica-mathematica","category-logica-propositionalis","category-mathematica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Formae Normales earumque Proprietates - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Forma normalis est structura logica normata quae expressiones propositionales in mathematicis et informatica simpliciores reddit\" \/>\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\/la\/formae-normales-earumque-proprietates\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Formae Normales earumque Proprietates\" \/>\n<meta property=\"og:description\" content=\"Forma normalis est structura logica normata quae expressiones propositionales in mathematicis et informatica simpliciores reddit\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/la\/formae-normales-earumque-proprietates\/\" \/>\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=\"2021-04-18T13:00:51+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-08-01T02:32:23+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/formanormal-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Formae Normales earumque Proprietates\" \/>\n<meta name=\"twitter:description\" content=\"Forma normalis est structura logica normata quae expressiones propositionales in mathematicis et informatica simpliciores reddit\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/formanormal.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\/la\/formae-normales-earumque-proprietates\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/formae-normales-earumque-proprietates\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Formae Normales earumque Proprietates\",\"datePublished\":\"2021-04-18T13:00:51+00:00\",\"dateModified\":\"2025-08-01T02:32:23+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/formae-normales-earumque-proprietates\/\"},\"wordCount\":801,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/formae-normales-earumque-proprietates\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/formanormal.jpg\",\"articleSection\":[\"Logica Mathematica\",\"Logica Propositionalis\",\"Mathematica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/la\/formae-normales-earumque-proprietates\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/formae-normales-earumque-proprietates\/\",\"url\":\"http:\/\/toposuranos.com\/material\/la\/formae-normales-earumque-proprietates\/\",\"name\":\"Formae Normales earumque Proprietates - 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