[FOM] Why inclusive disjunction?
Timothy Y. Chow
tchow at alum.mit.edu
Fri Jan 12 09:47:42 EST 2007
Arguments about natural language, and about the choice of OR vs. XOR *in
isolation*, are kind of fun but are doomed to be inconclusive, and I don't
think they address the right question anyway. A better question is, given
that we're interested in the AND operation, should we pair it with OR or
with XOR?
The answer is, we pair AND with OR if we're interested in the duality
between them---de Morgan's laws; series vs. parallel circuits; the analogy
with intersection/union, meet/join, for all/there exists, etc.; the fact
that each is distributive over the other; and so on. We pair AND with XOR
if we're interested in arithmetic/algebra/geometry over F_2, where AND is
multiplication and XOR is addition.
Tim
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