There is a close correspondence between simplification of Boolean
expressions and simplifications of set expressions, with "not"
corresponding to "complement", "and" corresponding to "intersection", "or"
corresponding to "union", and "exclusive or" corresponding to "symmetric
difference".
This might be useful for your endeavors in at least four ways:
1. Notions from logic such as disjunctive subsumption, conjunctive
subsumption, conjunctive and disjunctive normal forms, prime implicants,
resolution, quantifiers, etc. might suggest transformations for simplifying
set expressions.
2. Vice versa for improving Maxima's simplification of Boolean expressions.
3. Implemented in sufficient generality, the two could share code.
4. In computer algebra, often the Boolean "atoms" are actually equations
and inequalities, which define subsets of the complex plane. Thus Boolean
algebra and set algebra are often intertwined, making it important to
consider them together.
-- best regards, david stoutemyer
On Thu, May 30, 2013 at 6:15 AM, Robert Dodier <robert.dodier at gmail.com>wrote:
> On 2013-05-30, Oliver Kullmann <O.Kullmann at swansea.ac.uk> wrote:
>
> > hopefully this wouldn't affect computations with simple sets (we are
> > highly dependent on sets constructed from lists, integers, and sets)?
>
> Right -- the general goal is to reinterpret some constructs which are
> now undefined. That probably implies that any expression which is now OK
> has to continue to yield the same result (except that some expressions
> no longer cause errors). However, some results seem to change depending
> on whether one considers arguments to be literal set elements or
> variables (this is about elementp specifically) -- it seems plausible
> that elementp(foo, bar) and 'elementp(foo, bar) could yield different
> results for the same foo and bar. I'd like to steer away from that, as
> it would be harder to comprehend, but I'm not sure how.
>
> best
>
> Robert Dodier
>
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