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Directory:Jon Awbrey/Papers/Propositional Equation Reasoning Systems (view source)
Revision as of 17:20, 10 August 2009
, 17:20, 10 August 2009→Praeclarum theorema: del unnec specs
====Praeclarum theorema====
====Praeclarum theorema====
An illustrious example of a propositional theorem is the ''praeclarum theorema'', the ''admirable'', ''shining'', or ''splendid'' theorem of [[Leibniz]].
An illustrious example of a propositional theorem is the ''praeclarum theorema'', the ''admirable'', ''shining'', or ''splendid'' theorem of Leibniz.
{| align="center" cellpadding="8" width="90%"
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<p>If ''a'' is ''b'' and ''d'' is ''c'', then ''ad'' will be ''bc''.</p>
<p>If ''a'' is ''b'' and ''d'' is ''c'', then ''ad'' will be ''bc''.</p>
<p>''ad'' is ''bd'', and ''bd'' is ''bc'', therefore ''ad'' is ''bc''. Q.E.D.</p>
<p>''ad'' is ''bd'', and ''bd'' is ''bc'', therefore ''ad'' is ''bc''. Q.E.D.</p>
<p>([[Leibniz]], ''Logical Papers'', p. 41).</p>
<p>(Leibniz, ''Logical Papers'', p. 41).</p>
|}
Under the existential interpretation, the praeclarum theorema is represented by means of the following logical graph.
Under the existential interpretation, the praeclarum theorema is represented by means of the following logical graph.
{| align="center" border="0" cellpadding="10" cellspacing="0"
{| align="center" cellpadding="10"
| [[Image:PERS_Figure_14.jpg|500px]] || (14)
| [[Image:PERS_Figure_14.jpg|500px]] || (14)
|}
|}
And here's a neat proof of that nice theorem.
And here's a neat proof of that nice theorem.
{| align="center" border="0" cellpadding="10" cellspacing="0"
{| align="center" cellpadding="10"
| [[Image:PERS_Figure_15.jpg|500px]] || (15)
| [[Image:PERS_Figure_15.jpg|500px]] || (15)
|}
|}