{"id":33865,"date":"2021-02-19T13:00:36","date_gmt":"2021-02-19T13:00:36","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33865"},"modified":"2025-08-01T00:00:44","modified_gmt":"2025-08-01T00:00:44","slug":"semantica-logicae-propositionalis","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/la\/semantica-logicae-propositionalis\/","title":{"rendered":"Semantica Logicae Propositionalis"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>Semantica Logicae Propositionalis<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>SUMMARIUM<\/strong><br \/><em>In hac lectione tractatur semantica logicae propositionalis, speciatim de attributione valorum veritatis expressionibus et de modo quo hi valores propagantur ab una expressione ad aliam per nexus logicos. Introducitur notio tabularum veritatis et exhibentur tabulae veritatis nexuum derivatorum, quales sunt negatio, disiunctio, coniunctio, implicatio, implicatio reciproca atque disiunctio exclusiva. Praeterea, exhibetur definitio attributionis super coetu expressionum atomicarum et explicatur quomodo illa naturaliter extendatur super omnes expressiones quae ex hoc coetu construi possunt. Postremo, definiuntur expressiones validae, satisfacibiles et insatisfacibiles, et afferuntur exempla tautologiarum et contradictionum. Attamen, agnoscitur calculum tabularum veritatis pro expressionibus complexis posse esse inefficax, unde commemoratur inquisitio de methodis alternativis ad quaestiones de validitate vel satisfacibilitate solvendas.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>METAE DISCENDI:<\/strong><br \/>\nPost hanc lectionem discipulus poterit\n<\/p>\n<ol>\n<li><strong>Explicare<\/strong> semanticam logicae propositionalis<\/li>\n<li><strong>Adhibere<\/strong> tabulas veritatis ad repraesentandas attributiones valorum veritatis expressionibus in logica propositionali<\/li>\n<li><strong>Formulare<\/strong> expressionem per attributionem in logica propositionali<\/li>\n<li><strong>Applicare<\/strong> regulas semanticas logicae propositionalis ad determinandum utrum expressio sit tautologia, contradictio vel contingentia<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>INDEX<\/strong><br \/>\n<a href=\"#1\">DE ATTRIBUTIONIBUS VALORUM VERITATIS<\/a><br \/>\n<a href=\"#2\">SEMANTICA NEXUUM LOGICAE PROPOSITIONALIS<\/a><br \/>\n<a href=\"#3\">ATTRIBUTIONES IN LOGICA PROPOSITIONALI<\/a><br \/>\n<a href=\"#4\">EXEMPLARIA IN LOGICA PROPOSITIONALI<\/a><br \/>\n<a href=\"#5\">PROBLEMA EFFICIENTIAE SEMANTICAE LOGICAE PROPOSITIONALIS<\/a><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/tX_JVhn-wl0\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/div>\n<p><a name=\"1\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>De Attributionibus Valoribus Veritatis<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=tX_JVhn-wl0&amp;t=7s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Priori tempore perlustramus<\/span><\/strong><\/a> syntaxim et systemata deductiva logicae propositionalis. Quamquam hoc nobis profuit ad perpendendum quomodo una expressio ex alia derivari possit<\/a>, tamen nihil adhuc diximus de attributione valorum veritatis. Cum iam exposuimus omnia quae ad technicas deductionis logicae propositionalis spectant, incipiemus nunc tractatum de semantica logicae propositionalis, ubi consideratur quomodo attributiones valorum veritatis ab una expressione ad aliam propagantur.<\/p>\n<p><a name=\"2\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>Semantica Nexuum Logicae Propositionalis<\/h2>\n<p style=\"text-align: justify;\">Semantica nexuum introducitur per <strong>tabulas veritatis,<\/strong> quae modum simplicem et ordinatum praebent ad omnes attributiones possibiles super expressionem repraesentandas.<\/p>\n<h3>Tabula Veritatis Negationis Coniunctae<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=tX_JVhn-wl0&amp;t=282s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Primum incipiemus<\/span><\/strong><\/a> a nexu omnium fundamentaliore, nempe negatione coniuncta. Huius tabula veritatis talis est:<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha\\downarrow\\beta)<\/span><\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Valores \u00ab1\u00bb et \u00ab0\u00bb respondent \u00abVerum\u00bb et \u00abFalsum\u00bb, respective. Quaeque linea in tabula veritatis repraesentat attributionem possibilis super variabiles (vel expressiones atomicas) ex quibus expressio (vel expressiones) examinanda constat. Similiter, quaeque columna in qua expressio ex his variabilibus composita reperitur, ostendit eventus possibiles harum attributionum. Sic, interpretatio huius tabulae declarat <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha\\downarrow\\beta<\/span><\/span> verum esse tantum cum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span> simul falsae sint, et falsum in ceteris casibus. Quamobrem, connector <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\downarrow<\/span><\/span> appellatur <strong>negatio coniuncta.<\/strong><\/p>\n<h3>Tabulae Veritatis Nexuum Derivatorum<\/h3>\n<p style=\"text-align: justify;\">Ex semantica negationis coniunctae, semantica aliorum nexuum obtineri potest per definitiones eorum. Hae sunt:<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td><span><strong>Negatio:<\/strong><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg \\alpha<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha\\downarrow\\alpha)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>Disiunctio Inclusiva:<\/strong><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\vee \\beta)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\alpha\\downarrow\\beta)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>Coniunctio:<\/strong><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\wedge \\beta)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\neg\\alpha\\vee \\neg\\beta)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>Implicatio:<\/strong><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\rightarrow \\beta)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\neg\\alpha\\vee \\beta)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>Implicatio Duplex:<\/strong><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\leftrightarrow \\beta)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">((\\alpha\\rightarrow \\beta)\\wedge(\\beta \\rightarrow \\alpha))<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><strong>Disiunctio Exclusiva:<\/strong><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha \\underline{\\vee} \\beta)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">:=<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg(\\alpha\\leftrightarrow \\beta)<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Ex his definitionibus licet tabulas veritatis aliorum nexuum computare:<\/p>\n<h4>Negatio<\/h4>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg \\alpha<\/span><\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=tX_JVhn-wl0&amp;t=335s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Hinc oritur<\/span><\/strong><\/a> proprietas connectoris negationis, qui valorem veritatis expressionis cui applicatur invertere potest.<\/p>\n<h4>Disiunctio Inclusiva<\/h4>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha\\vee\\beta)<\/span><\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=tX_JVhn-wl0&amp;t=383s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Quam ob rem<\/span><\/strong><\/a> disiunctio inclusiva (vel simpliciter \u00abdisiunctio\u00bb) inter duas expressiones vera est si saltem una ex expressionibus vera est, et falsa est si ambae expressiones simul falsae sunt.<\/p>\n<h4>Coniunctio<\/h4>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha\\wedge\\beta)<\/span><\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=tX_JVhn-wl0&amp;t=444s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Ex quo sequitur,<\/span><\/strong><\/a> coniunctio inter duas expressiones vera est tantum si ambae expressiones simul verae sunt, et falsa est alioquin. Propter hoc, nomen aptum pro hoc connectore etiam esse potest <strong>affirmatio coniuncta<\/strong>.<\/p>\n<h4>Implicatio<\/h4>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha\\rightarrow\\beta)<\/span><\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=tX_JVhn-wl0&amp;t=555s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Itaque<\/span><\/strong><\/a> tabula veritatis implicationis breviter exprimit notionem quod expressio vera tantum expressionem veram implicare potest, dum expressio falsa potest quidlibet implicare.<\/p>\n<h4>Implicatio Duplex<\/h4>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha\\leftrightarrow\\beta)<\/span><\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=tX_JVhn-wl0&amp;t=641s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Implicatio duplex<\/span><\/strong><\/a> expressionem veram format quoties ambae expressiones eiusdem valoris veritatis sunt, et est falsa aliter.<\/p>\n<h4>Disiunctio Exclusiva<\/h4>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta<\/span><\/span><\/strong><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\alpha\\underline{\\vee}\\beta)<\/span><\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center; background-color: #ccffcc;\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=tX_JVhn-wl0&amp;t=702s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Disiunctio exclusiva<\/span><\/strong><\/a> inter duas expressiones vera est cum una, et tantum una earum vera est, et falsa aliter.<\/p>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>Attributiones in Logica Propositionali<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=tX_JVhn-wl0&amp;t=857s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Ex ante dictis<\/span><\/strong><\/a> habemus notionem simplicem attributionis; attamen, ad progressus postea considerandos opus erit definitione accuratiore. Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S=\\{A_1, A_2, \\cdots, A_n\\}<\/span><\/span> coetus expressionum atomicarum est et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{F}(S)<\/span><\/span> coetus omnium expressionum quae ex elementis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S<\/span><\/span> constitui possunt, tunc habetur sequens definitio:<\/p>\n<p><\/br><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #880000;\"><strong>DEFINITIO:<\/strong><\/span> <strong>Attributio<\/strong> super <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S<\/span><\/span> est functio <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}: S \\longrightarrow \\{0,1\\}<\/span><\/span><\/p>\n<p><\/br><\/p>\n<p style=\"text-align: justify;\">Id est, attributio super <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S<\/span><\/span> unicuique expressioni atomicae in <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S<\/span><\/span> valorem veritatis tribuit. Attributio <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span><\/span> ex <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S<\/span><\/span> naturaliter extenditur ad omnes elementos <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{F}(S)<\/span><\/span>. Si expressio <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F\\in \\mathcal{F}(S)<\/span><\/span> est, tunc attributio <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span><\/span> super <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S<\/span><\/span> respondet unicae lineae in tabula veritatis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span>, et dicitur <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(F)<\/span><\/span> esse valor veritatis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> in illa linea.<\/p>\n<p style=\"text-align: justify;\">Attributio <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span><\/span> ex <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S<\/span><\/span> extendi etiam potest ad quasdam expressiones quae non sunt in <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{F}(S)<\/span><\/span>. Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_0<\/span><\/span> expressio est quae non est in <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{F}(S)<\/span><\/span>, et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S_0<\/span><\/span> est coetus subformulis atomicarum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_0<\/span><\/span>, tunc si omnes extensiones <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span><\/span> ad <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S\\cup S_0<\/span><\/span> eundem valorem praebent pro <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_0<\/span><\/span>, tunc definitur <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(F_0)<\/span><\/span> esse illum valorem.<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000088;\">EXEMPLUM:<\/span> Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> sunt expressiones atomicae et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span><\/span> attributio est super <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{A,B\\}<\/span><\/span> definita per <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(A)=1<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(B)=0<\/span><\/span>, tunc habetur:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(A\\wedge B)=0<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(A\\vee B)=1<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Et quamquam nulla attributio definita est pro variabili <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C<\/span><\/span>, dici potest:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(A\\wedge (C\\vee \\neg C))=1<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(B\\vee (C\\wedge \\neg C))=0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Hoc fit in his duabus expressionibus finalibus, quia, cuiuscumque sit valor attributus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C<\/span><\/span>, semper erit verum quod<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(C\\vee\\neg C)=1<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(C\\wedge\\neg C)=0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Quod facile inspici potest per computationem tabularum veritatis.<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg C<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(C\\wedge \\neg C)<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(C \\vee \\neg C)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u25a0 Finis Exempli<\/p>\n<p><a name=\"4\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>Exemplaria in Logica Propositionali<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=tX_JVhn-wl0&amp;t=1323s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">Consideremus attributionem<\/span><\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span><\/span> super coetum expressionum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">S<\/span><\/span>. Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F\\in S<\/span><\/span> est talis ut <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}(F)=1<\/span><\/span>, tunc dicitur attributionem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span><\/span> <em>exemplar esse<\/em> pro <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span>, sive <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> sustineri per attributionem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}<\/span><\/span>, et id repraesentamus scripto<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathcal{A}\\models F<\/span><\/span>.<\/p>\n<p style=\"text-align: justify;\">Ex hoc statuuntur definitiones sequentes:<\/p>\n<p><\/br><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #880000;\"><strong>DEFINITIO:<\/strong><\/span> Expressio <strong>valida<\/strong> dicitur cum sub qualibet attributione sustinetur. Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> valida est, tunc scribitur <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\models F <\/span><\/span>. Expressionum validarum alium nomen est <strong>tautologia.<\/strong><\/p>\n<p><\/br><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000088;\">EXEMPLUM:<\/span> Expressio <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(C\\vee \\neg C)<\/span><\/span>, quam iam vidimus, est <strong>tautologia.<\/strong><\/p>\n<p>\u25a0 Finis Exempli<\/p>\n<p><\/br><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #880000;\"><strong>DEFINITIO:<\/strong><\/span> Expressio <strong>satisfacibilis<\/strong> dicitur si est ab aliqua attributione sustentata. Expressiones satisfacibiles quae non sunt tautologiae vocantur <strong>contingentes.<\/strong><\/p>\n<p><\/br><\/p>\n<p><\/br><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #880000;\"><strong>DEFINITIO:<\/strong><\/span> Expressio <strong>insatisfacibilis<\/strong> dicitur si nulla attributione sustentatur. Tales expressiones vocantur <strong>contradictiones.<\/strong> Si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> contradictio est, tunc scribitur <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\not\\models F <\/span><\/span>.<\/p>\n<p><\/br><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000088;\">EXEMPLUM:<\/span> Expressio <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(C\\wedge \\neg C)<\/span><\/span>, quam iam vidimus, est <strong>contradictio.<\/strong><\/p>\n<p>\u25a0 Finis Exempli<\/p>\n<h3>Exempla Tautologiarum et Contradictionum<\/h3>\n<p style=\"text-align: justify;\">Ponamus nos velle scire utrum expressio sit valida necne. Hoc ipsum est <strong>quaestio decisionis<\/strong> in ambitu Semanticae Logicae Propositionalis. Quaestio decisionis est quaelibet quaestio cui, data quaedam inputatio, respondetur per \u00abita\u00bb aut \u00abnon\u00bb. Si expressio <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> proposita est et quaeritur an sit valida, versamur in <strong>quaestione validitatis.<\/strong> Similiter, si quaeritur an sit satisfacibilis, versamur in <strong>quaestione satisfacibilitatis.<\/strong> In logica propositionali, tabulae veritatis methodum systematicam praebent ad has quaestiones solvendas: si omnes valores veritatis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> sunt \u00ab1\u00bb, tunc <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> est valida; si quidam tantum sunt \u00ab1\u00bb, est satisfacibilis; et si omnes sunt \u00ab0\u00bb, est insatisfacibilis.<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000088;\">EXEMPLUM:<\/span> Consideremus expressionem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">((A\\wedge (A \\rightarrow B)) \\rightarrow B)<\/span><\/span>. Ad cognoscendum utrum haec expressio sit valida, satisfacibilis an contradictoria, conficienda est eius tabula veritatis.<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #eeeeee;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(A\\rightarrow B)<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(A\\wedge(A\\rightarrow B))<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">((A\\wedge(A\\rightarrow B))\\rightarrow B)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #aaffaa;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #aaffaa;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #aaffaa;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #aaffaa;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Ex hoc videmus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">((A\\wedge(A\\rightarrow B))\\rightarrow B)<\/span><\/span> habere valorem veritatis \u00ab1\u00bb pro omnibus attributionibus possibilibus, unde sequitur expressionem esse tautologiam.<\/p>\n<p>\u25a0 Finis Exempli<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000088;\">EXEMPLUM:<\/span> Consideremus nunc expressionem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(((A\\rightarrow B)\\rightarrow A)\\wedge \\neg A)<\/span><\/span>. Calculus tabulae veritatis dat quod sequitur infra:<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #eeeeee;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(A\\rightarrow B)<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">((A\\rightarrow B)\\rightarrow A)<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\neg A<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(((A\\rightarrow B)\\rightarrow A)\\wedge \\neg A)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #aaffaa;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #aaffaa;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #aaffaa;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span><\/td>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<td style=\"text-align: center; background-color: #aaffaa;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Itaque eventus est contradictio.<\/p>\n<p>\u25a0 Finis Exempli<br \/>\n<a name=\"5\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>Quaestio Efficientiae Semanticae Logicae Propositionalis Substat<\/h2>\n<p style=\"text-align: justify;\">Theoretice, possumus determinare utrum expressio sit valida, contingens vel insatisfacibilis simpliciter computando eius tabulam veritatis, quod non est per se difficile; sed, proh dolor, facilitas exsecutionis pretio efficaciae redimitur. Si habemus expressionem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> compositam ex <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> expressionibus atomicis, tunc conficienda est tabula veritatis cum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2^n<\/span><\/span> lineis; ita, exempli gratia, si <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> constat ex 23 expressionibus atomicis, eius tabula veritatis habebit 8.388.608 lineas computandas. Hoc modo procedendo, licet mechanicum et facile ad perficiendum sit, calculus celeriter incipit esse non exsecutabilis dum complexitas expressionum augetur. Quam ob rem, unum ex nostris propositis futuris erit modum reperire quaestiones de validitate vel satisfacibilitate solvendi sine necessitate computandi tabulas veritatis. Investigatio talium methodorum est una ex quaestionibus fundamentalibus in qualibet logica.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Semantica Logicae Propositionalis SUMMARIUMIn hac lectione tractatur semantica logicae propositionalis, speciatim de attributione valorum veritatis expressionibus et de modo quo hi valores propagantur ab una expressione ad aliam per nexus logicos. Introducitur notio tabularum veritatis et exhibentur tabulae veritatis nexuum derivatorum, quales sunt negatio, disiunctio, coniunctio, implicatio, implicatio reciproca atque disiunctio exclusiva. Praeterea, exhibetur definitio [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28002,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":14,"footnotes":""},"categories":[1352,1358,1298],"tags":[],"class_list":["post-33865","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>Semantica Logicae Propositionalis - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Disce semanticam logicae propositionalis per hunc commentarium. 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