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Re: [aima-talk] Digest Number 303

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  • Paul Hsueh-Min Chang
    ... Maybe our sources are different. AFAIK a contradiction is the negation of a tautology (P. Tidman and H. Kahane, Logic and Philosophy: A Modern
    Message 1 of 10 , Sep 24, 2005
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      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
    • The Geek
      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
      Message 2 of 10 , 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
        formal.

        Thanks for the interesting discussion.

        Rob G.


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

        > 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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      • shivam shukla
        hey everybody am doing a project on image processing n am using the convolution theorem given in chapter 25.in tht am not able to get an image function. it
        Message 3 of 10 , Sep 27, 2005
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          hey everybody am doing a project on image processing n am using the convolution theorem given in chapter 25.in tht am not able to get an image function.

           it would be a great help for me if anyone could tell wat sort of a function is this image function.

                    thanx.


          Yahoo! India Matrimony: Find your partner now.
        • Robin
          The index in my edition (2nd) gives only two mentions of convolution: pg 869 and pg 899. These are in chapter 24, not ch. 25. So I m not sure what you re
          Message 4 of 10 , Sep 28, 2005
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            The index in my edition (2nd) gives only two mentions
            of convolution: pg 869 and pg 899. These are in chapter
            24, not ch. 25. So I'm not sure what you're looking at.
            But in general, when you apply a convolution to an image,
            the "image function" is just the pixel value at each
            (x,y) location. The value you use will depend on context
            - what you want to do. A commonly used value is pixel
            brightness. A white pixel has brightness 255, and a black
            one has brightness 0. If you're starting from a color
            image, you can calculate brightness by averaging the red,
            blue, and green values at pixel (x,y).

            Here's a good explanation of convolution in an image-
            processing context:
            http://www.cee.hw.ac.uk/hipr/html/convolve.html

            - Robin


            --- In aima-talk@yahoogroups.com, shivam shukla <shirohin@y...> wrote:
            >
            > hey everybody am doing a project on image processing n am using the
            convolution theorem given in chapter 25.in tht am not able to get an
            image function.
            >
            > it would be a great help for me if anyone could tell wat sort of a
            function is this image function.
            >
            > thanx.
            >
            >
            > ---------------------------------
            > Yahoo! India Matrimony: Find your partner now.
          • Paul Hsueh-Min Chang
            I doubt if I can make the issues more clear, but I ll try. I still think the main problem lies in the phrase if it were false . If a proposition in a set is
            Message 5 of 10 , Sep 29, 2005
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              I doubt if I can make the issues more clear, but I'll try.

              I still think the main problem lies in the phrase "if it were false". If
              a proposition in a set is "shown" to be false from observation rather
              than through logical proof, the proposition does not make the set
              inconsistent, because it *could* be true in some other possible world.
              If I recall correctly, that is how logical possibility is defined. Your
              ABC example is indeed inconsistent because it can be proved without
              observing the world state that the set contains at least one false sentence.

              So, according to the defintion of consistency, the authors mostly likely
              do not mean "if it were provably false". Otherwise, the argument would
              be employing a tautologus sentence: "if the sentence were provably
              false, then he (or in fact, anyone) could not consistently assert it to
              be true". One derives nothing from a tautology

              But, without the word "provably", I don't see how the contingent truth
              or falsity of a sentence have anything to do with consistency, for
              reasons above. Furthermore, it seems to me that J. R. Lucas just cannot
              consistently assert the sentence anyway, whether it is true or false.

              I do agree that we can do nothing formal without identifying the
              underlying logic system. Perhaps somebody can enlighten us?

              > Thanks for the interesting discussion.
              Thank you.

              Paul



              The Geek wrote:

              > 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
              > formal.
              >
              > Thanks for the interesting discussion.
              >
              > Rob G.
              >
              >
              > --- Paul Hsueh-Min Chang <avatar@...>
              > wrote:
              >
              > > 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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