Re: Tenth new law from the premises of syllogism


Jan Burse wrote:
A B C New (((A -> B) & (B -> C)) & (New -> A))) -> (New -> C)
0 0 0 0 1 1 1 1 1 1 1
0 0 0 1 1 1 1 0 0 1 0
0 0 1 0 1 1 1 1 1 1 1
0 0 1 1 1 1 1 0 0 1 1
0 1 0 0 1 0 0 0 1 1 1
0 1 0 1 1 0 0 0 0 1 0
0 1 1 0 1 1 1 1 1 1 1
0 1 1 1 1 1 1 0 0 1 1
1 0 0 0 0 0 1 0 1 1 1
1 0 0 1 0 0 1 0 1 1 0
1 0 1 0 0 0 1 0 1 1 1
1 0 1 1 0 0 1 0 1 1 1
1 1 0 0 1 0 0 0 1 1 1
1 1 0 1 1 0 0 0 1 1 0
1 1 1 0 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1

Gosh, its indeed one of the many tautologies.

I remember that you wrote a posting that
shows that you can embed boolean algebra
in your system.

Then it MUST generate all tautologies, supposed
the & and -> belongs to the aforementioned
boolean algebra.

Your particular formula that is a tautology,
is in fact a gulash of syllogistic reasoning
and weakening, i.e. of (A->B)&(B->C)->(A->C)
and D->(N->D).

Bye

Conbra wrote:
Tenth new law from the premises of syllogism is as follows

(((a → b) & (b → c)) & (New → a))) → (New → c)

The meaning of the sign ↕ is “be independent of”, “→” is
implication, “&” is logic and. “υ” is a constant of “Concept
Algebra”.

More messages see http://groups.google.com/group/Concept-Algebra/

The tenth law
(((a → b) & (b → c)) & (New → a))) → (New → c)
is transferred from formula
((a → b) & (b → c)) → ((New → a) → (New → c))
this formula is calculated after solving following logic equation
((a → b) & (b → c)) → X = υ
the constant can be explained as Tautology on logic or Universe on Set.
this equation also can be transferred to set algebra using compound
operation as follows

X / ((a ⊂ b) ∩ (b ⊂ c)) = υ

operation / is "get from",⊂is "be included by", "belong to" or "is",
∩ is conjunction. This is a equation on set algebra. This equation is
to ask "What will be got from the condition of set a belongs to set b
and set b belongs to set c", Here the conjunction is read as "and".
One of the result from these conditions is
(New ⊂ c) / (New ⊂ a)
That is to say if set a belongs to set b and set b belongs to set c,
then "if New belongs to set a, then New must belong to set c". This is
a law fit on Set algebra.

Bye

.