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555Re: [aima-talk] Digest Number 303

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  • The Geek
    Sep 27, 2005
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      I 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.

      Rob G.

      --- Paul Hsueh-Min Chang <avatar@...>

      > I will try to make some clarifications below:
      > > While they haven't spelled it out in detail, I
      > think
      > > they're using a simple logic system and definition
      > of
      > > "consistent". In other words, they're not trying
      > to
      > > allow for an "agent belief" representation where
      > we
      > > acknowledge that beliefs might be wrong. Instead,
      > if
      > > 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
      > do
      > > it without creating a contradiction. Since this
      > is
      > > the definition of "consistency", they would say
      > that
      > > we cannot "consistently" assert all three
      > sentances,
      > > 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
      > a
      > > contradiction. However if Agent A tries to assert
      > the
      > > same sentance, he runs into a problem. If he
      > asserts
      > > it as true and is right, then the sentance is
      > false,
      > > 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
      > true).
      > 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
      > to
      > > show that **sometimes** one agent is unable to
      > > assert/know/do things that another agent can, but
      > that
      > > doesn't automatically imply that agent is
      > inferior,
      > > it's inability to assert/know/do may be related to
      > the
      > > specific situation.
      > I do understand the point; it is simply that
      > particular argument (the
      > one on p950 in parentheses) that confuses me. As a
      > philosophical
      > treatment, I think the chapter should reasonably be
      > taken literally, but
      > when I do so, I cannot make sense of that particular
      > argument.
      > Paul

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