Sunday, January 27, 2008

De Morgan's types 2

I'll try now to write down syllogisms contained in De Morgan's zodiac in modified spicular notation, where dot does not signify negation but particularity. I'll present each universal syllogism together with it's opposing particular syllogisms.

X))Y))Z=X))Z
Y((X(.(Z=Y(.(Z
X(.(Z((Y=X(.(Y

Z((Y((X=Z((X
Y))Z).)X=Y).)X
Z).)X))Y=Z).)Y

X))Y)(Z=X)(Z
Y((X(.)Z=Y(.)Z
X(.)Z)(Y=X(.(Y

Z)(Y((X=Z)(X
Y)(Z(.)X=Y).)X
Z(.)X))Y=Z(.)Y

X)(Y()Z=X))Z
Y)(X(.(Z=Y).(Z
X(.(Z()Y=X(.)Y

Z()Y)(X=Z((X
Y()Z).)X=Y(.)X
Z).)X)(Y=Z).(Y

X()Y))Z=X()Z
Y()X).(Z=Y(.(Z
X).(Z((Y=X).(Y

Z((Y()X=Z()X
Y))Z).(X=Y).(X
Z).(X()Y=Z).)Y

Now, this was a piece of cake. Iconicity of the spicular notation is a great help.