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Directory:Jon Awbrey/Papers/Propositional Equation Reasoning Systems (view source)
Revision as of 17:57, 10 August 2009
, 17:57, 10 August 2009→Exemplary proofs: del unnec specs
====Peirce's law====
====Peirce's law====
: ''Main article : [[Peirce's law]]
: ''Main article'' : [[Peirce's law]]
Peirce's law is commonly written in the following form:
Peirce's law is commonly written in the following form:
{| align="center" cellpadding="10"
| <math>((p \Rightarrow q) \Rightarrow p) \Rightarrow p</math>
|}
The existential graph representation of Peirce's law is shown in Figure 12.
The existential graph representation of Peirce's law is shown in Figure 12.
{| align="center" border="0" cellpadding="10" cellspacing="0"
{| align="center" cellpadding="10"
| [[Image:PERS_Figure_12.jpg|500px]] || (12)
| [[Image:PERS_Figure_12.jpg|500px]] || (12)
|}
|}
A graphical proof of Peirce's law is shown in Figure 13.
A graphical proof of Peirce's law is shown in Figure 13.
{| align="center" border="0" cellpadding="10" cellspacing="0"
{| align="center" cellpadding="10"
| [[Image:PERS_Figure_13.jpg|500px]] || (13)
| [[Image:PERS_Figure_13.jpg|500px]] || (13)
|}
|}
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%"
{| align="center" cellpadding="10" width="90%"
|
|
<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>