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Esempio di informazione semantica - I
<p style="text-align: justify;">In un report del 1952 Carnap e Bar-Hillel presentarono la loro teoria dell'informazione semantica, proponendo numerosi esempi tratti da un linguaggio basato su predicati monadici con un numero finito di costanti individuali. In questa nota si vuole prendere spunto dal linguaggio utilizzato per esplicare i concetti fondamentali della teoria di Carnap; in particolare considereremo lo spazio logico e la determinazione della misura di probabilità.</p> <p style="text-align: justify;">Gli autori considerano un censimento svolto su una piccola comunità composta solo da 3 abitanti - {a,b,c,d} - e ha come obiettivo il determinare per ogni abitante il genere (maschio, femmina) e l'età (vecchio giovane). Il genere e l'età sono determinati da due predicati M (maschio - !M essendo Femmina - dove il simbolo ! indica il not logico) e Y (giovane - !Y equivale a vecchio). Abbiamo dunque a che fare con un linguaggio <img title="L_3^2" src="https://latex.codecogs.com/gif.latex?L_3^2" /> composto da 3 costanti individuali e 2 predicati. Un esempio di proposizione è 'Ma' che sta ad indicare come l'abitante 'a' sia un maschio; tale proposizione è anche una proposizione <strong>atomica</strong>. Un esempio di proposizione <strong>molecolare</strong> è la congiunzione (connettivo logico indicato con '.') di proposizioni atomiche, come ad esempio la proposizione 'Ma.Yb' che sta ad indicare come l'abitante 'a' sia un maschio e l'abitante 'b' sia giovane. Inoltre è opportuno definire il <strong>state-description </strong>come la congiunzione di proposizione atomiche che coinvolgono tutte le costanti individuali; gli state-description sono una possibile rappresentazione del mondo.</p> <p style="text-align: justify;">La tabella di tutti gli state-description è la seguente e sarà fondamentale per compiere i calcoli pratici al fine di ottenere l'informazione associata alle proposizioni. L'insieme di tutti gli state-description è chiamato '<strong>spazio logico</strong>'.</p> <table style="height: 158px;" width="550"> <tbody> <tr style="height: 13px;"> <td style="width: 49.6894px; background-color: yellow; text-align: center; height: 13px;">State</td> <td style="width: 49.6894px; background-color: yellow; text-align: center; height: 13px;">M,Y</td> <td style="width: 49.6894px; background-color: yellow; text-align: center; height: 13px;">M,!Y</td> <td style="width: 49.6894px; background-color: yellow; text-align: center; height: 13px;">!M,Y</td> <td style="width: 49.6894px; background-color: yellow; text-align: center; height: 13px;">!M,!Y</td> <td style="width: 49.6894px; background-color: yellow; text-align: center; height: 13px;">State</td> <td style="width: 49.6894px; background-color: yellow; text-align: center; height: 13px;">M,Y</td> <td style="width: 49.6894px; background-color: yellow; text-align: center; height: 13px;">M,!Y</td> <td style="width: 49.6894px; background-color: yellow; text-align: center; height: 13px;">!M,Y</td> <td style="width: 49.7082px; background-color: yellow; text-align: center; height: 13px;">!M,!Y</td> </tr> <tr style="text-align: center; height: 13.6273px;"> <td style="width: 49.6894px; height: 13.6273px;">Z1</td> <td style="width: 49.6894px; height: 13.6273px;">a,b,c </td> <td style="width: 49.6894px; height: 13.6273px;">- </td> <td style="width: 49.6894px; height: 13.6273px;">- </td> <td style="width: 49.6894px; height: 13.6273px;">- </td> <td style="width: 49.6894px; height: 13.6273px;">Z33</td> <td style="width: 49.6894px; height: 13.6273px;">b </td> <td style="width: 49.6894px; height: 13.6273px;">- </td> <td style="width: 49.6894px; height: 13.6273px;">-</td> <td style="width: 49.7082px; height: 13.6273px;">a,c </td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 49.6894px; height: 13px;">Z2</td> <td style="width: 49.6894px; height: 13px;"> -</td> <td style="width: 49.6894px; height: 13px;">a,b,c </td> <td style="width: 49.6894px; height: 13px;">-</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">Z34</td> <td style="width: 49.6894px; height: 13px;">a </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.7082px; height: 13px;">b,c </td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 49.6894px; height: 13px;">Z3</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">a,b,c </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">Z35</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">c </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.7082px; height: 13px;">a,b </td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 49.6894px; height: 13px;">Z4</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">a,b,c </td> <td style="width: 49.6894px; height: 13px;">Z36</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">b </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.7082px; height: 13px;">a,c </td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 49.6894px; height: 13px;">Z5</td> <td style="width: 49.6894px; height: 13px;">a,b</td> <td style="width: 49.6894px; height: 13px;">c</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">-</td> <td style="width: 49.6894px; height: 13px;">Z37</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">a </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.7082px; height: 13px;">b,c </td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 49.6894px; height: 13px;">Z6</td> <td style="width: 49.6894px; height: 13px;">a,c </td> <td style="width: 49.6894px; height: 13px;">b </td> <td style="width: 49.6894px; height: 13px;">-</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">Z38</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">c </td> <td style="width: 49.7082px; height: 13px;">a,b </td> </tr> <tr style="text-align: center; height: 14px;"> <td style="width: 49.6894px; height: 14px;">Z7</td> <td style="width: 49.6894px; height: 14px;">b,c</td> <td style="width: 49.6894px; height: 14px;">a </td> <td style="width: 49.6894px; height: 14px;">- </td> <td style="width: 49.6894px; height: 14px;">- </td> <td style="width: 49.6894px; height: 14px;">Z39</td> <td style="width: 49.6894px; height: 14px;">- </td> <td style="width: 49.6894px; height: 14px;">- </td> <td style="width: 49.6894px; height: 14px;">b </td> <td style="width: 49.7082px; height: 14px;">a,c </td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 49.6894px; height: 13px;">Z8</td> <td style="width: 49.6894px; height: 13px;">a,b</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">c </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">Z40</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">a </td> <td style="width: 49.7082px; height: 13px;">b,c </td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 49.6894px; height: 13px;">Z9</td> <td style="width: 49.6894px; height: 13px;">a,c</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">b</td> <td style="width: 49.6894px; height: 13px;">- </td> <td style="width: 49.6894px; height: 13px;">Z41</td> <td style="width: 49.6894px; height: 13px;">a </td> <td style="width: 49.6894px; height: 13px;">b </td> <td style="width: 49.6894px; height: 13px;">c </td> <td style="width: 49.7082px; height: 13px;">- </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z10</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b,c</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z42</td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.7082px; height: 13px; text-align: center;"> -</td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z11</td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z43</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.7082px; height: 13px; text-align: center;">- </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z12</td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,c</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z44</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.7082px; height: 13px; text-align: center;">- </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z13</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b,c</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z45</td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.7082px; height: 13px; text-align: center;">- </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z14</td> <td style="width: 49.6894px; text-align: center; height: 13px;">c</td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z46</td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.7082px; height: 13px; text-align: center;">- </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z15</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b</td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,c</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z47</td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.7082px; height: 13px; text-align: center;"> c</td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z16</td> <td style="width: 49.6894px; text-align: center; height: 13px;">a</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b,c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z48</td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.7082px; height: 13px; text-align: center;">b </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z17</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,b</td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z49</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.7082px; height: 13px; text-align: center;">c </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z18</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,c</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z50</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.7082px; height: 13px; text-align: center;">a </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z19</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b,c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z51</td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.7082px; height: 13px; text-align: center;">b </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z20</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z52</td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.7082px; height: 13px; text-align: center;">a </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z21</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z53</td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.7082px; height: 13px; text-align: center;">c </td> </tr> <tr style="height: 15px;"> <td style="width: 49.6894px; text-align: center; height: 15px;">Z22</td> <td style="width: 49.6894px; text-align: center; height: 15px;">- </td> <td style="width: 49.6894px; text-align: center; height: 15px;">b,c</td> <td style="width: 49.6894px; text-align: center; height: 15px;">- </td> <td style="width: 49.6894px; text-align: center; height: 15px;">a</td> <td style="width: 49.6894px; text-align: center; height: 15px;">Z54</td> <td style="width: 49.6894px; text-align: center; height: 15px;">a </td> <td style="width: 49.6894px; text-align: center; height: 15px;">- </td> <td style="width: 49.6894px; text-align: center; height: 15px;">c </td> <td style="width: 49.7082px; height: 15px; text-align: center;">b </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z23</td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z55</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.7082px; height: 13px; text-align: center;">c </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z24</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z56</td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.7082px; height: 13px; text-align: center;">a </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z25</td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b,c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z57</td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.7082px; height: 13px; text-align: center;">b </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z26</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z58</td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.7082px; height: 13px; text-align: center;">a </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z27</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z59</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.7082px; height: 13px; text-align: center;">c </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z28</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b,c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z60</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.7082px; height: 13px; text-align: center;">b </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z29</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c</td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z61</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.7082px; height: 13px; text-align: center;">c </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z30</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z62</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.7082px; height: 13px; text-align: center;">a </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z31</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b,c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z63</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a </td> <td style="width: 49.7082px; height: 13px; text-align: center;">b </td> </tr> <tr style="height: 13px;"> <td style="width: 49.6894px; text-align: center; height: 13px;">Z32</td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">a,b</td> <td style="width: 49.6894px; text-align: center; height: 13px;">Z64</td> <td style="width: 49.6894px; text-align: center; height: 13px;">- </td> <td style="width: 49.6894px; text-align: center; height: 13px;">c </td> <td style="width: 49.6894px; text-align: center; height: 13px;">b </td> <td style="width: 49.7082px; height: 13px; text-align: center;">a </td> </tr> </tbody> </table> <p style="text-align: justify;">Un esempio di lettura dello state-description della tabella è il caso Z15 che corriponde alla proposizione</p> <p style="text-align: center;">Z15 = [M.Y]b.[M.!Y]a,c = Mb.Yb.Ma.!Ya.Mc.!Yc</p> <p style="text-align: justify;">Se si indica con il termine Range di una proposizione il numero di state-description in cui la proposizione si presenta, si ha ad esempio che per la proposizione s =Ma il Range è:</p> <p style="text-align: center;">Range(Ma)= 32</p> <p style="text-align: justify;">in quanto 'Ma' compare in Z1 ... Z60.</p> <p style="text-align: justify;">Una volta noto lo spazio logico del linguaggio considerato Carnap introduce la misura m(-) di probabilità, cha ha il compito di assegnare la probabilità 'logica' ai vari stati (atomici, molecolari e state-description). Tale funzione deve soddisfare alcune proprietà che abbiamo presentato in altra nota ed in special modo vale la proprietà seguente che stabilisce quando due state-description sono fra loro isomorfi:</p> <p style="text-align: justify;">Se <img title="Z_j" src="https://latex.codecogs.com/gif.latex?Z_j" /> è ottenuto da <img title="Z_i" src="https://latex.codecogs.com/gif.latex?Z_i" /> con una permutazione delle costanti individuali allora i due stati sono <em>isomorfi</em> e <img title="m(Z_j)=m(Z_i)" src="https://latex.codecogs.com/gif.latex?m(Z_j)=m(Z_i)" />. Per fare un esempio relativo al nostro spazio logico, i due state-description Z5 = 'Ma.Ya.Mb.Yb.Mc.!Yc' e Z6='Ma.Ya.Mc.Yc.Mb.!Yb' sono fra loro isomorfi in quanto Z6 si ottiene da Z5 permutando la costante individuale 'b' con la costante individuale 'c'. Questa proprietà sta ad indicare che gli elementi individuali sono considerati 'alla pari'.</p> <p style="text-align: justify;">Notando che gli stati con la stessa probabilità (quindi isomorfi) portano la stessa quantità di informazione, possiamo immaginare di suddividere lo spazio logico in apposite strutture composte da state-description isomorfi. Operando in questo modo abbiamo le strutture seguenti:</p> <table style="height: 192px; width: 528px;"> <tbody> <tr> <td style="width: 102.227px; background-color: yellow; text-align: center;">Struttura</td> <td style="width: 411.773px; background-color: yellow; text-align: center;">Insieme di description State</td> </tr> <tr> <td style="width: 102.227px;">T1</td> <td style="width: 411.773px;">Z1</td> </tr> <tr> <td style="width: 102.227px;">T2</td> <td style="width: 411.773px;">Z2</td> </tr> <tr> <td style="width: 102.227px;">T3</td> <td style="width: 411.773px;">Z3</td> </tr> <tr> <td style="width: 102.227px;">T4</td> <td style="width: 411.773px;">Z4</td> </tr> <tr> <td style="width: 102.227px;">T5</td> <td style="width: 411.773px;">Z5vZ6vZ7</td> </tr> <tr> <td style="width: 102.227px;">T6</td> <td style="width: 411.773px;">Z8vZ9vZ10</td> </tr> <tr> <td style="width: 102.227px;">T7</td> <td style="width: 411.773px;">Z11vZ12vZ13</td> </tr> <tr> <td style="width: 102.227px;">T8</td> <td style="width: 411.773px;">Z14vZ15vZ16</td> </tr> <tr> <td style="width: 102.227px;">T9</td> <td style="width: 411.773px;">Z17vZ18vZ19</td> </tr> <tr> <td style="width: 102.227px;">T10</td> <td style="width: 411.773px;">Z20vZ21vZ22</td> </tr> <tr> <td style="width: 102.227px;">T11</td> <td style="width: 411.773px;">Z23vZ24vZ5</td> </tr> <tr> <td style="width: 102.227px;">T12</td> <td style="width: 411.773px;">Z26vZ27vZ28</td> </tr> <tr> <td style="width: 102.227px;">T13</td> <td style="width: 411.773px;">Z29vZ30vZ31</td> </tr> <tr> <td style="width: 102.227px;">T14</td> <td style="width: 411.773px;">Z32vZ33vZ34</td> </tr> <tr> <td style="width: 102.227px;">T15</td> <td style="width: 411.773px;">Z35vZ36vZ37</td> </tr> <tr> <td style="width: 102.227px;">T16</td> <td style="width: 411.773px;">Z38vZ39vZ40</td> </tr> <tr> <td style="width: 102.227px;">T17</td> <td style="width: 411.773px;">Z41vZ42vZ43vZ44vZ45vZ46</td> </tr> <tr> <td style="width: 102.227px;">T18</td> <td style="width: 411.773px;">Z47vZ48vZ49vZ50vZ51vZ52</td> </tr> <tr> <td style="width: 102.227px;">T19</td> <td style="width: 411.773px;">Z53vZ54vZ55vZ56vZ57vZ58</td> </tr> <tr> <td style="width: 102.227px;">T20</td> <td style="width: 411.773px;">Z59vZ60vZ61vZ62vZ63vZ64</td> </tr> </tbody> </table> <p style="text-align: justify;">dove il simbolo 'v' sta ad indicare l'operatore logico 'or'. La misura di probabilità basata sulle strutture appena indicate viene chiamata da Carnap m* e permette di associare all'insieme di strutture la stessa probablilità; nel nostro caso abbiamo</p> <p style="text-align: center;">m*(Ti) = 1/20</p> <p style="text-align: justify;">Siamo ora in grado di associare una misura di probablilità ad ogni singolo state-description, partendo proprio dalla misura di probabilità delle strutture a cui gli state-description appartengono. </p> <p style="text-align: center;"><img title="m^*(Z_i)=\frac{m^*(T_i)}{n_{T_{i}}(Z_i)}" src="https://latex.codecogs.com/gif.latex?m^*(Z_i)=\frac{m^*(T_i)}{n_{T_{i}}(Z_i)}" /></p> <p style="text-align: justify;">dove <img title="n_{T_{i}}(Z_i)" src="https://latex.codecogs.com/gif.latex?n_{T_{i}}(Z_i)" /> rappresenta il numero di Zi presenti nella struttura Ti. In questo modo abbiamo ad esempio che m*(Z1) = 1/20, m(Z5) = 1/20*1/3= 1/60 ed infine m(Z64) = 1/20* 1/6=1/120.</p> <p style="text-align: justify;">Riproducendo la tabella degli state-description, possiamo inserire anche la misura di probabilità per ognuno di essi.</p> <table style="height: 158px; width: 550px;"> <tbody> <tr style="height: 13px;"> <td style="width: 45px; background-color: yellow; text-align: center; height: 13px;">State</td> <td style="width: 52px; background-color: yellow; text-align: center; height: 13px;">M,Y</td> <td style="width: 49px; background-color: yellow; text-align: center; height: 13px;">M,!Y</td> <td style="width: 49px; background-color: yellow; text-align: center; height: 13px;">!M,Y</td> <td style="width: 49px; background-color: yellow; text-align: center; height: 13px;">!M,!Y</td> <td style="width: 49px; background-color: yellow; text-align: center; height: 13px;">m*</td> <td style="width: 44.3886px; background-color: yellow; text-align: center; height: 13px;">State</td> <td style="width: 53.6114px; background-color: yellow; text-align: center; height: 13px;">M,Y</td> <td style="width: 49px; background-color: yellow; text-align: center; height: 13px;">M,!Y</td> <td style="width: 49px; background-color: yellow; text-align: center; height: 13px;">!M,Y</td> <td style="width: 49px; background-color: yellow; text-align: center; height: 13px;">!M,!Y</td> <td style="width: 49px; background-color: yellow; text-align: center; height: 13px;">m*</td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 45px; height: 13px;">Z1</td> <td style="width: 52px; height: 13px;">a,b,c </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">1/20</td> <td style="width: 44.3886px; height: 13px;">Z33</td> <td style="width: 53.6114px; height: 13px;">b </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">-</td> <td style="width: 49px; height: 13px;">a,c </td> <td style="width: 49px; height: 13px;">1/60</td> </tr> <tr style="text-align: center; height: 13.313px;"> <td style="width: 45px; height: 13.313px;">Z2</td> <td style="width: 52px; height: 13.313px;"> -</td> <td style="width: 49px; height: 13.313px;">a,b,c </td> <td style="width: 49px; height: 13.313px;">-</td> <td style="width: 49px; height: 13.313px;">- </td> <td style="width: 49px; height: 13.313px;">1/20</td> <td style="width: 44.3886px; height: 13.313px;">Z34</td> <td style="width: 53.6114px; height: 13.313px;">a </td> <td style="width: 49px; height: 13.313px;">- </td> <td style="width: 49px; height: 13.313px;">- </td> <td style="width: 49px; height: 13.313px;">b,c </td> <td style="width: 49px; height: 13.313px;">1/60</td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 45px; height: 13px;">Z3</td> <td style="width: 52px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">a,b,c </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">1/20</td> <td style="width: 44.3886px; height: 13px;">Z35</td> <td style="width: 53.6114px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">c </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">a,b </td> <td style="width: 49px; height: 13px;">1/60</td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 45px; height: 13px;">Z4</td> <td style="width: 52px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">a,b,c </td> <td style="width: 49px; height: 13px;">1/20</td> <td style="width: 44.3886px; height: 13px;">Z36</td> <td style="width: 53.6114px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">b </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">a,c </td> <td style="width: 49px; height: 13px;">1/60</td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 45px; height: 13px;">Z5</td> <td style="width: 52px; height: 13px;">a,b</td> <td style="width: 49px; height: 13px;">c</td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">-</td> <td style="width: 49px; height: 13px;">1/60</td> <td style="width: 44.3886px; height: 13px;">Z37</td> <td style="width: 53.6114px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">a </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">b,c </td> <td style="width: 49px; height: 13px;">1/60</td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 45px; height: 13px;">Z6</td> <td style="width: 52px; height: 13px;">a,c </td> <td style="width: 49px; height: 13px;">b </td> <td style="width: 49px; height: 13px;">-</td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">1/60</td> <td style="width: 44.3886px; height: 13px;">Z38</td> <td style="width: 53.6114px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">c </td> <td style="width: 49px; height: 13px;">a,b </td> <td style="width: 49px; height: 13px;">1/60</td> </tr> <tr style="text-align: center; height: 14px;"> <td style="width: 45px; height: 14px;">Z7</td> <td style="width: 52px; height: 14px;">b,c</td> <td style="width: 49px; height: 14px;">a </td> <td style="width: 49px; height: 14px;">- </td> <td style="width: 49px; height: 14px;">- </td> <td style="width: 49px; height: 14px;">1/60</td> <td style="width: 44.3886px; height: 14px;">Z39</td> <td style="width: 53.6114px; height: 14px;">- </td> <td style="width: 49px; height: 14px;">- </td> <td style="width: 49px; height: 14px;">b </td> <td style="width: 49px; height: 14px;">a,c </td> <td style="width: 49px; height: 14px;">1/60</td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 45px; height: 13px;">Z8</td> <td style="width: 52px; height: 13px;">a,b</td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">c </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">1/60</td> <td style="width: 44.3886px; height: 13px;">Z40</td> <td style="width: 53.6114px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">a </td> <td style="width: 49px; height: 13px;">b,c </td> <td style="width: 49px; height: 13px;">1/60</td> </tr> <tr style="text-align: center; height: 13px;"> <td style="width: 45px; height: 13px;">Z9</td> <td style="width: 52px; height: 13px;">a,c</td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">b</td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">1/60</td> <td style="width: 44.3886px; height: 13px;">Z41</td> <td style="width: 53.6114px; height: 13px;">a </td> <td style="width: 49px; height: 13px;">b </td> <td style="width: 49px; height: 13px;">c </td> <td style="width: 49px; height: 13px;">- </td> <td style="width: 49px; height: 13px;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z10</td> <td style="width: 52px; text-align: center; height: 13px;">b,c</td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z42</td> <td style="width: 53.6114px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; height: 13px; text-align: center;"> -</td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z11</td> <td style="width: 52px; text-align: center; height: 13px;">a,b </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z43</td> <td style="width: 53.6114px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; height: 13px; text-align: center;">- </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z12</td> <td style="width: 52px; text-align: center; height: 13px;">a,c</td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z44</td> <td style="width: 53.6114px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; height: 13px; text-align: center;">- </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z13</td> <td style="width: 52px; text-align: center; height: 13px;">b,c</td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z45</td> <td style="width: 53.6114px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; height: 13px; text-align: center;">- </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z14</td> <td style="width: 52px; text-align: center; height: 13px;">c</td> <td style="width: 49px; text-align: center; height: 13px;">a,b </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z46</td> <td style="width: 53.6114px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; height: 13px; text-align: center;">- </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z15</td> <td style="width: 52px; text-align: center; height: 13px;">b</td> <td style="width: 49px; text-align: center; height: 13px;">a,c</td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z47</td> <td style="width: 53.6114px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; height: 13px; text-align: center;"> c</td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z16</td> <td style="width: 52px; text-align: center; height: 13px;">a</td> <td style="width: 49px; text-align: center; height: 13px;">b,c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z48</td> <td style="width: 53.6114px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; height: 13px; text-align: center;">b </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z17</td> <td style="width: 52px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a,b</td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z49</td> <td style="width: 53.6114px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; height: 13px; text-align: center;">c </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z18</td> <td style="width: 52px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a,c</td> <td style="width: 49px; text-align: center; height: 13px;">b</td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z50</td> <td style="width: 53.6114px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; height: 13px; text-align: center;">a </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z19</td> <td style="width: 52px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">b,c </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z51</td> <td style="width: 53.6114px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; height: 13px; text-align: center;">b </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z20</td> <td style="width: 52px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a,b </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z52</td> <td style="width: 53.6114px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; height: 13px; text-align: center;">a </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z21</td> <td style="width: 52px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a,c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z53</td> <td style="width: 53.6114px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; height: 13px; text-align: center;">c </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 15px;"> <td style="width: 45px; text-align: center; height: 15px;">Z22</td> <td style="width: 52px; text-align: center; height: 15px;">- </td> <td style="width: 49px; text-align: center; height: 15px;">b,c</td> <td style="width: 49px; text-align: center; height: 15px;">- </td> <td style="width: 49px; text-align: center; height: 15px;">a</td> <td style="width: 49px; text-align: center; height: 15px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 15px;">Z54</td> <td style="width: 53.6114px; text-align: center; height: 15px;">a </td> <td style="width: 49px; text-align: center; height: 15px;">- </td> <td style="width: 49px; text-align: center; height: 15px;">c </td> <td style="width: 49px; height: 15px; text-align: center;">b </td> <td style="width: 49px; height: 15px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z23</td> <td style="width: 52px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a,b </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z55</td> <td style="width: 53.6114px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; height: 13px; text-align: center;">c </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z24</td> <td style="width: 52px; text-align: center; height: 13px;">b</td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a,c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z56</td> <td style="width: 53.6114px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; height: 13px; text-align: center;">a </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z25</td> <td style="width: 52px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">b,c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z57</td> <td style="width: 53.6114px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; height: 13px; text-align: center;">b </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z26</td> <td style="width: 52px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">a,b </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z58</td> <td style="width: 53.6114px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; height: 13px; text-align: center;">a </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z27</td> <td style="width: 52px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">a,c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z59</td> <td style="width: 53.6114px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; height: 13px; text-align: center;">c </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z28</td> <td style="width: 52px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">b,c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z60</td> <td style="width: 53.6114px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; height: 13px; text-align: center;">b </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z29</td> <td style="width: 52px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a,b </td> <td style="width: 49px; text-align: center; height: 13px;">c</td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z61</td> <td style="width: 53.6114px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; height: 13px; text-align: center;">c </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z30</td> <td style="width: 52px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a,c </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z62</td> <td style="width: 53.6114px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; height: 13px; text-align: center;">a </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z31</td> <td style="width: 52px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">b,c </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z63</td> <td style="width: 53.6114px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">a </td> <td style="width: 49px; height: 13px; text-align: center;">b </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> <tr style="height: 13px;"> <td style="width: 45px; text-align: center; height: 13px;">Z32</td> <td style="width: 52px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">a,b</td> <td style="width: 49px; text-align: center; height: 13px;">1/60</td> <td style="width: 44.3886px; text-align: center; height: 13px;">Z64</td> <td style="width: 53.6114px; text-align: center; height: 13px;">- </td> <td style="width: 49px; text-align: center; height: 13px;">c </td> <td style="width: 49px; text-align: center; height: 13px;">b </td> <td style="width: 49px; height: 13px; text-align: center;">a </td> <td style="width: 49px; height: 13px; text-align: center;">1/120</td> </tr> </tbody> </table> <p>La misura di probabilità induce sullo spazio logico una funzione di conferma c(-,-) che è definita nel modo seguente:</p> <p style="text-align: center;"><img title="c^*(h,e)=\frac{m^*(h.e)}{m^*(e)}" src="https://latex.codecogs.com/gif.latex?c^*(h,e)=\frac{m^*(h.e)}{m^*(e)}" /></p> <p style="text-align: justify;">dove 'h' è l'ipotesi che si fa sullo spazio logico ed 'e' l'evidenza empirica che si ha a disposizione. Così ad esempio se h='Mc' e l'evidenza empirica e='Ma.Mb' possiamo calcolare il grado di conferma dell'ipotesi 'Mc' in base all'evidenza 'Ma.Mb', dato dalla funzione c*('Mc', ''Ma.Mb). Iniziamo con il calcolare m*(e)=m*('Ma.Mb') = 2*1/20 + 10*1/60 + 4*1/120 = 1/10 + 1/6 + 1/30 = 0.10 + 0.16 + 0.03 = 0.29. Tocca ora all'ipotesi h e quindi calcoliamo m*('Ma.Mb.Mc') = 2*1/20 + 6*1/60 + 0*1/120 = 1/10 + 1/10 = 0.2. A questo punto possiamo calcolare il grado di conferma:</p> <p style="text-align: center;"><img title="c^*(h,e)=C^*(Mc, Ma.Mb)=\frac{m^*(Ma.Mb.Mc)}{m^*(Ma.Mb)}=\frac{0.2}{0.29}=0.68" src="https://latex.codecogs.com/gif.latex?c^*(h,e)=C^*(Mc,&space;Ma.Mb)=\frac{m^*(Ma.Mb.Mc)}{m^*(Ma.Mb)}=\frac{0.2}{0.29}=0.68" /></p> <p style="text-align: justify;">Gli ulteriori calcoli legati all'informazione di proposizioni legate allo spazio logico costruito in questa nota, saranno analizzati in un momento successivo</p>
Some notes on Relativity and other arguments