I have a project

an input validator

tautologies are valid, e.g. a=a
and contradictions are not valid, e.g. !(a=a)

other than that we have to record things and prohibit contradictions. whatever was entered first takes precedence unless the entry is forced.

e.g.
a=1
OK
b=2
OK
a+b=4
not ok
c+d=4
OK
c=1
ok (d=3)
d=2
not ok

so it uses relations instead of operations and through the various rules it prevents new relations from entering the db if they contradict the old ones

I have a cookie. It's burnt on the bottom, just slightly, and it hits with the contradiction of flavors.