In this segment we're gonna take a look at box logic. Unfortunately, we cannot do
that here on the studio so we're gonna have to take a road trip. Today we're
headed for Stanford University's renowned logic laboratory. Follow me. And here we
are. This is the logic laboratory. It may not look like much at least not
superficially but this is where we investigate some of the latest innovations
in logic technology. Today our goal was to look at box logic. Now the language of box
logic is pretty simple. There are really just three constants. There is large box,
there is medium box, and there is small box and they are all oriented one way or
the other. Forming compound sentences from our consonants is easy. If we want to
negate a sentence, we just invert. Not medium box, medium box. If you want this
form of this junction from our constants, we stack them up. So here we have small
box or medium box. And a conjunction is formed simply by placing multiple boxes or
stacks of boxes on our table. So it's effectively colossal for. Okay. Now, let's
try to use our logic to solve some problems. How about the problem case of
Mary Patton Quincy? We call that. If it's Monday, Mary loves Pat or Quincy and
Quincy, if Mary loves Pat, Mary loves Quincy. Let's see how we can represent
that information using our new language. So first of all, if Mary loves Pat, Mary
loves Quincy let's, let this medium sized box represent the fact that Mary loves
Pat. This one represents Mary loves Quincy and the large one is going to be Monday.
So we wanna say, if Mary loves Pat, Mary loves Quincy. How do we do that? Recalling
the rules for converting to colossal form, we know that p implies q as equivalent to
not p or q. So if you wanted to write that, we would write not Mary loves Pat or
Mary loves Quincy. So, not Mary loves Pat or Mary loves Quincy. If Mary loves Pat,
Mary loves Quincy. How about our other sentence? If it's Monday, then Mary loves
Pat or Quincy. It's Monday, let's see. We need to say not Monday or Pat or Quincy.
So it's not Monday mo re quick copies. Or Pat or Quincy. So there we have it. If
it's Monday, Mary loves Pat or Quincy. If Mary loves Pat, Mary loves Quincy,
represented, representing the premises of the problem. Now you may recall that the
object of the problem was to show that if it's Monday then Mary loves Quincy. So how
could we do that? What we have done is representing but we can also do
computation, deduction with box logic. Any rules are pretty simple. If we ever have
one stack which has a constant. Literal which is the complement of literal on
another stack, we can do resolution on them. So here we have one stack with
medium box down, here one stack with medium box up. We can combine the two
stacks and eliminate the complementary literals and form these answers and since
it's a duplicate, we can throw that one away and we're left with our conclusion.
If it's Monday, Mary loves Quincy, nifty. Okay, what's the point? The point is that
the language of logic is not about particular sets of symbols. And the active
deduction doesn't mean necessarily that we're operating upon those particular
symbols. Logic is an abstraction. Any instantiation of the symbols is equally
good and any operations on them is equally good provided that it respects that basic
abstraction. Okay. That's it for our visit to the logic laboratory today. We'll be
back again later in the course with some additional demonstrations and we'll see
you then.
