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>>q p
q
So formally, ''q'' is true, whatever it is :) If this sounds overly theoretic, here's a tricky practical example in puzzle solving, Lewis Carroll's last sorites (pp. 123f.). The task is to conclude
something from the following premises:
1. The only animals in this house are cats
1. Every animal is suitable for a pet, that loves to gaze at the moon
1. When I detest an animal, I avoid it
1. No animals are carnivorous, unless they prowl at night
1. No cat fail to kill mice
1. No animals ever take to me, except what are in this house
1. Kangaroos are not suitable for pets
1. None but carnivora kill mice
1. I detest animals that do not take to me
1. Animals that prowl at night always love to gaze at the moon
These are encoded to the following one-letter predicates:
* a - avoided by me
* c - cat
* d - detested by me
* h - house, in this
* k - kill mice
* m - moon, love to gaze at
* n - night, prowl at
* p - pet, suitable for
* r - (kanga)roo
* t - take to me
* v - (carni)vorous
So the problem set can be restated, in Spencer-Brown's terms, as