In the article, Quantum Theory Derived from Logic, a
logical expression was derived for
n parallel paths of m steps each.
This is equation [7] shown again below.
(q0 qn)
= ni1,i2,i3,i4...im=0 (q0
qi1)(qi1 qi2)(qi2 qi3)(qi3 qi4)...(qim qn).
To gain some confidence that this expression is true, you can
cut and paste the text into this
truth-table generator. This is an expression for when n=4 and
m=3. Altogether there are (n+1)m=53=125
different terms of 4 implications each.
(q0
=> q4)
<=>
((q0
=> q0)
/\ (q0
=> q0)
/\ (q0
=> q0)
/\ (q0
=> q4))
\/ ((q0
=> q0)
/\ (q0
=> q0)
/\ (q0
=> q1)
/\ (q1
=> q4))
\/ ((q0
=> q0)
/\ (q0
=> q0)
/\ (q0
=> q2)
/\ (q2
=> q4))
\/ ((q0
=> q0)
/\ (q0
=> q0)
/\ (q0
=> q3)
/\ (q3
=> q4))
\/ ((q0
=> q0)
/\ (q0
=> q0)
/\ (q0
=> q4)
/\ (q4
=> q4))
\/ ((q0
=> q0)
/\ (q0
=> q1)
/\ (q1
=> q0)
/\ (q0
=> q4))
\/ ((q0
=> q0)
/\ (q0
=> q1)
/\ (q1
=> q1)
/\ (q1
=> q4))
\/ ((q0
=> q0)
/\ (q0
=> q1)
/\ (q1
=> q2)
/\ (q2
=> q4))
\/ ((q0
=> q0)
/\ (q0
=> q1)
/\ (q1
=> q3)
/\ (q3
=> q4))
\/ ((q0
=> q0)
/\ (q0
=> q1)
/\ (q1
=> q4)
/\ (q4
=> q4))
\/ ((q0
=> q0)
/\ (q0
=> q2)
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=> q0)
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=> q4))
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=> q1)
/\ (q1
=> q4))
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=> q2)
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=> q2)
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=> q4))
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=> q2)
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=> q3)
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=> q4))
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=> q4))
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=> q4))
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=> q1)
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=> q2)
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=> q4))
\/ ((q0
=> q1)
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=> q0)
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=> q3)
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=> q4))
\/ ((q0
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=> q4))
\/ ((q0
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