Classical Logic – Square of Opposition – an Aristotelian AI?

J. M. K. Walkow

“A Nonstandard Graph, Elements and Operations, a Card Game Dialect A combination of the Mold dialects and Sandwich graphs, backed by axiomatic math, creates a unique space of science and fantasy.”

– J.M.K. Walkow, Naturalistic Fantasy

D5_Square_of_Opposition_-_the_square_of_logic_small
The Four Aristotelian Propositions and Square of Opposition

S-P=0              S-P=S

S-P<S              S-P>0

– weak minus
= equal
> weak ordering
0 empty
S any
P any

Blue Earth Islands
SaP All S is P
SeP No S is P
SiP Some S is P
SoP Some S is not P

images square

Universal affirmative A
Universal negative E
Particular affirmative I
Particular negative O

Happy Portal Cove
EXAMPLES:

Barbara (AAA)
All men are mortal. (MaP)
All Greeks are men. (SaM)
All Greeks are mortal. (SaP)

M-P=0 and S-M=0 then S-P=0

Celarent (EAE)
Similar: Cesare (EAE)

No reptiles have fur. (MeP)
All snakes are reptiles. (SaM)
No snakes have fur. (SeP)

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