555Re: [aima-talk] Digest Number 303
- Sep 27, 2005I think the discussion all boils down to the
definition of "consistent" and "contradiction". I was
kind of hoping one of the authors would chime in at
some point to save me, but... :-) On page 137 they
define consistency in reference to CSP problems as "an
assignment that does not violate any constraints".
That was the reason for my A,B,C example - looking at
it as if it were a CSP.
Their argument assumes the sentance must either be
"true" or "false", (no quantuum physics or "unknown"
values allowed) and hinges on the
belief/assumption/fact one cannot "consistently"
assert that a sentance is true if it can be shown to
be false. If you buy into that, then their statement
follows naturally - if the sentance was false, then he
could not consistently assert it to be true, which
would therefore make the sentance true - a
contradiction since we assigned a value of "false" to
the sentance at the beginning. The only way you can
assign a value to the sentance and have everything
hold together is if you assume it's true, which then
implies that everyone else can assert it without a
problem, but he cannot.
But, at this point I don't think we're going to make
any headway. Since they didn't define the logic
system they're using, we can't really do anything
Thanks for the interesting discussion.
--- Paul Hsueh-Min Chang <avatar@...>
> I will try to make some clarifications below:__________________________________
> > While they haven't spelled it out in detail, I
> > they're using a simple logic system and definition
> > "consistent". In other words, they're not trying
> > allow for an "agent belief" representation where
> > acknowledge that beliefs might be wrong. Instead,
> > you assert a sentance it must be true or you've
> > introduced a contradiction.
> Maybe our sources are different. AFAIK a
> contradiction is the negation
> of a tautology (P. Tidman and H. Kahane, Logic and
> Philosophy: A Modern
> Introduction, 8th edition, p48). For example, p^~p
> is a contradiction.
> So when I assert a contingently false sentence whose
> truth depends on
> the world, I introduce no contradiction. But maybe
> our definitions of
> contradiction differ.
> > If we take 3 sentances:
> > A = B.
> > B = C.
> > A != C.
> > If we try to assert all three sentances, we cannot
> > it without creating a contradiction. Since this
> > the definition of "consistency", they would say
> > we cannot "consistently" assert all three
> > since doing so would introduce a contradiction.
> It is true that we would introduce inconsistency,
> but we would not
> introduce a contradiction. Of course, any set of
> sentences that contains
> any contradictory sentence is inconsistent, but not
> vice versa.
> > In this case, as an agent **I** can consistently
> > assert the sentance "Agent A cannot assert this
> > sentance without being wrong" without introducing
> > contradiction. However if Agent A tries to assert
> > same sentance, he runs into a problem. If he
> > it as true and is right, then the sentance is
> > so he's wrong.
> I know what you are trying to say, but that I don't
> think we are talking
> about the same thing. The authors clearly intend to
> show two things:
> 1. The sentence is a tautology (i.e. necessarily
> 2. Yet, J. R. Lucas cannot assert it.
> They offer two arguments to show (1). What I do not
> understand is the
> their second argument to show (1). You are talking
> about (2), which I
> find no problem.
> > But the whole point of the illustration is simply
> > show that **sometimes** one agent is unable to
> > assert/know/do things that another agent can, but
> > doesn't automatically imply that agent is
> > it's inability to assert/know/do may be related to
> > specific situation.
> I do understand the point; it is simply that
> particular argument (the
> one on p950 in parentheses) that confuses me. As a
> treatment, I think the chapter should reasonably be
> taken literally, but
> when I do so, I cannot make sense of that particular
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