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Directory talk:Jon Awbrey/Papers/Differential Logic : Introduction (view source)
Revision as of 03:50, 30 June 2009
, 03:50, 30 June 2009→Original Version
As it happens, the language of cacti is so abstract that it can bear at least two different interpretations as logical sentences denoting logical propositions. The two interpretations that I know about are descended from the ones that Charles Sanders Peirce called the ''entitative'' and the ''existential'' interpretations of his systems of graphical logics. For our present aims, I shall briefly introduce the alternatives and then quickly move to the existential interpretation of logical cacti.
As it happens, the language of cacti is so abstract that it can bear at least two different interpretations as logical sentences denoting logical propositions. The two interpretations that I know about are descended from the ones that Charles Sanders Peirce called the ''entitative'' and the ''existential'' interpretations of his systems of graphical logics. For our present aims, I shall briefly introduce the alternatives and then quickly move to the existential interpretation of logical cacti.
Table 13 illustrates the existential interpretation of cactus graphs and cactus expressions by providing English translations for a few of the most basic and commonly occurring forms.
Table A illustrates the existential interpretation of cactus graphs and cactus expressions by providing English translations for a few of the most basic and commonly occurring forms.
{| align="center" border="1" cellpadding="6" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
|+ <math>\text{Table A.}~~\text{Existential Interpretation}</math>
|- style="background:#f0f0ff"
| <math>\text{Cactus Graph}\!</math>
| <math>\text{Cactus Expression}\!</math>
| <math>\text{Interpretation}\!</math>
|-
|
<pre>
@
</pre>
| <math>{}^{\backprime\backprime}\texttt{~}{}^{\prime\prime}</math>
| <math>\operatorname{true}</math>
|-
|
<pre>
o
|
@
</pre>
| <math>\texttt{(~)}</math>
| <math>\operatorname{false}</math>
|}
<pre>
<pre>