  Constructing a fuzzy subset logic L with Boolean properties is notoriously
difficult because under a handful of "reasonable" conditions, we have the
following three debilitating constraints: (1) Bellman and Giertz in 1973 showed
that if L is distributive, then it must be idempotent. (2) Dubois and Padre in
1980 showed that if L has the excluded middle or the non-contradiction property
or both, then it must be non-idempotent. (3) Bellman and Giertz also
demonstrated in 1973 that even if L is idempotent, then the only choice
available for the (meet,join) logic operator pair is the (min,max) operator
pair. Thus it would seem impossible to construct a non-trivial fuzzy subset
logic with Boolean properties. However, this paper examines these three results
in detail, and shows that "hidden" in the hypotheses of the three is the
assumption that the operator pair (meet,join) is pointwise evaluated. It is
further demonstrated that removing this constraint yields the following
results: (A) It is indeed possible to construct fuzzy subset logics that have
all the Boolean properties, including that of idempotency, non-contradiction,
excluded middle, and distributivity. (B) Even if idempotency holds, (min,max)
is not the only choice for (meet,join).
