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human approch

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  • Maithreebhanu Wimalasekare
    Is acting human approch to AI it usefull orpractical except for simulation and games. ( robotics exculded ) Are there new avenues for reserch in this area and
    Message 1 of 9 , Jun 12, 2006
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      Is acting human approch to AI it usefull orpractical except for simulation and games. ( robotics exculded )

      Are there new avenues for reserch in this area and what promise do they offers to reserchers?


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    • cedricstjl
      Why does it matter? I m quantifying over objects that behave exactly like FOL functions instead of quantifying directly over FOL functions. I could write a
      Message 2 of 9 , Jun 13, 2006
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        Why does it matter? I'm quantifying over "objects that behave exactly
        like FOL functions" instead of quantifying directly over FOL functions.

        I could write a program, which takes as input a second-order logic
        sentence, does inference in FOL with the conversion from my first
        post, and translates back into second-order logic. Or are there SOL
        sentences that wouldn't be translatable?

        Thank you for your time,

        Cedric

        --- In aima-talk@yahoogroups.com, "Peter Norvig" <peter@...> wrote:
        >
        > You could do that, and that could be a way of expressing reflexivity,
        > but it wouldn't be quantifying over FOL functions -- it would be
        > quantifying over objects that you happen to call "functions" but are
        > regular objects as far as the logic is concerned.
        >
        > -Peter
        >
        > On 6/8/06, cedricstjl <cedricstjl@...> wrote:
        > > I have some difficulty seeing the difference in expressiveness between
        > > first-order logic and higher-order logics. Wikipedia (as well as AIMA,
        > > AFAICT) says that F-O logic cannot quantify over functions. But
        > > couldn't it be achieved equivalently by reifying functions and
        > > predicates? I.e.:
        > >
        > > x = fun(var)
        > >
        > > becomes
        > >
        > > x = call_function(fun, var)
        > >
        > > and then one can express reflexivity:
        > >
        > > for all fun, a, b: reflexive(fun) <=> call_function(fun, a, b) =
        > > call_function(fun, b, a)
        > >
        > > Cedric
      • Peter Norvig
        I agree that for most of what you would reasonably want to do, it wouldn t matter. But the point is that when you quantify over all functions/relations
        Message 3 of 9 , Jun 13, 2006
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          I agree that for most of what you would reasonably want to do, it
          wouldn't matter. But the point is that when you quantify over all
          functions/relations (represented as objects), you wouldn't be
          quantifying over "call_function" nor "reflexive".

          -Peter

          On 6/13/06, cedricstjl <cedricstjl@...> wrote:
          > Why does it matter? I'm quantifying over "objects that behave exactly
          > like FOL functions" instead of quantifying directly over FOL functions.
          >
          > I could write a program, which takes as input a second-order logic
          > sentence, does inference in FOL with the conversion from my first
          > post, and translates back into second-order logic. Or are there SOL
          > sentences that wouldn't be translatable?
          >
          > Thank you for your time,
          >
          > Cedric
          >
          > --- In aima-talk@yahoogroups.com, "Peter Norvig" <peter@...> wrote:
          > >
          > > You could do that, and that could be a way of expressing reflexivity,
          > > but it wouldn't be quantifying over FOL functions -- it would be
          > > quantifying over objects that you happen to call "functions" but are
          > > regular objects as far as the logic is concerned.
          > >
          > > -Peter
          > >
          > > On 6/8/06, cedricstjl <cedricstjl@...> wrote:
          > > > I have some difficulty seeing the difference in expressiveness between
          > > > first-order logic and higher-order logics. Wikipedia (as well as AIMA,
          > > > AFAICT) says that F-O logic cannot quantify over functions. But
          > > > couldn't it be achieved equivalently by reifying functions and
          > > > predicates? I.e.:
          > > >
          > > > x = fun(var)
          > > >
          > > > becomes
          > > >
          > > > x = call_function(fun, var)
          > > >
          > > > and then one can express reflexivity:
          > > >
          > > > for all fun, a, b: reflexive(fun) <=> call_function(fun, a, b) =
          > > > call_function(fun, b, a)
          > > >
          > > > Cedric
          >
          >
          >
          >
          >
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          >
          > Yahoo! Groups Links
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        • cedricstjl
          I don t see why one would ever want to quantify over call_function. I don t think that there is an equivalent to that in regular logic. I can quantify over
          Message 4 of 9 , Jun 14, 2006
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            I don't see why one would ever want to quantify over call_function. I
            don't think that there is an equivalent to that in "regular" logic.

            I can quantify over reflexive by adding another level of indirection.
            reflexive(f) becomes call_function_2(reflexive, f). As long as all
            functions have a clearly defined level, it should work. Furthermore,
            using levels is, from what I've read, a common way of avoiding
            Russell's paradox in SOL. Does the "SOL is strictly more expressive
            than FOL" claim apply only to SOL without levels?

            Cedric

            --- In aima-talk@yahoogroups.com, "Peter Norvig" <peter@...> wrote:
            >
            > I agree that for most of what you would reasonably want to do, it
            > wouldn't matter. But the point is that when you quantify over all
            > functions/relations (represented as objects), you wouldn't be
            > quantifying over "call_function" nor "reflexive".
            >
            > -Peter
            >
            > On 6/13/06, cedricstjl <cedricstjl@...> wrote:
            > > Why does it matter? I'm quantifying over "objects that behave exactly
            > > like FOL functions" instead of quantifying directly over FOL
            functions.
            > >
            > > I could write a program, which takes as input a second-order logic
            > > sentence, does inference in FOL with the conversion from my first
            > > post, and translates back into second-order logic. Or are there SOL
            > > sentences that wouldn't be translatable?
            > >
            > > Thank you for your time,
            > >
            > > Cedric
            > >
            > > --- In aima-talk@yahoogroups.com, "Peter Norvig" <peter@> wrote:
            > > >
            > > > You could do that, and that could be a way of expressing
            reflexivity,
            > > > but it wouldn't be quantifying over FOL functions -- it would be
            > > > quantifying over objects that you happen to call "functions" but are
            > > > regular objects as far as the logic is concerned.
            > > >
            > > > -Peter
            > > >
            > > > On 6/8/06, cedricstjl <cedricstjl@> wrote:
            > > > > I have some difficulty seeing the difference in expressiveness
            between
            > > > > first-order logic and higher-order logics. Wikipedia (as well
            as AIMA,
            > > > > AFAICT) says that F-O logic cannot quantify over functions. But
            > > > > couldn't it be achieved equivalently by reifying functions and
            > > > > predicates? I.e.:
            > > > >
            > > > > x = fun(var)
            > > > >
            > > > > becomes
            > > > >
            > > > > x = call_function(fun, var)
            > > > >
            > > > > and then one can express reflexivity:
            > > > >
            > > > > for all fun, a, b: reflexive(fun) <=> call_function(fun, a, b) =
            > > > > call_function(fun, b, a)
            > > > >
            > > > > Cedric
          • cedricstjl
            Actually, I think that I don t even need levels. for all fun, a, b: call_function(reflexive, fun) call_function(fun, a, b) = call_function(fun, b, a) seems
            Message 5 of 9 , Jun 14, 2006
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              Actually, I think that I don't even need levels.

              for all fun, a, b: call_function(reflexive, fun) <=>
              call_function(fun, a, b) = call_function(fun, b, a)

              seems to work fine to me.

              Cedric

              --- In aima-talk@yahoogroups.com, "cedricstjl" <cedricstjl@...> wrote:
              >
              > I don't see why one would ever want to quantify over call_function. I
              > don't think that there is an equivalent to that in "regular" logic.
              >
              > I can quantify over reflexive by adding another level of indirection.
              > reflexive(f) becomes call_function_2(reflexive, f). As long as all
              > functions have a clearly defined level, it should work. Furthermore,
              > using levels is, from what I've read, a common way of avoiding
              > Russell's paradox in SOL. Does the "SOL is strictly more expressive
              > than FOL" claim apply only to SOL without levels?
              >
              > Cedric
              >
              > --- In aima-talk@yahoogroups.com, "Peter Norvig" <peter@> wrote:
              > >
              > > I agree that for most of what you would reasonably want to do, it
              > > wouldn't matter. But the point is that when you quantify over all
              > > functions/relations (represented as objects), you wouldn't be
              > > quantifying over "call_function" nor "reflexive".
              > >
              > > -Peter
              > >
              > > On 6/13/06, cedricstjl <cedricstjl@> wrote:
              > > > Why does it matter? I'm quantifying over "objects that behave
              exactly
              > > > like FOL functions" instead of quantifying directly over FOL
              > functions.
              > > >
              > > > I could write a program, which takes as input a second-order logic
              > > > sentence, does inference in FOL with the conversion from my first
              > > > post, and translates back into second-order logic. Or are there SOL
              > > > sentences that wouldn't be translatable?
              > > >
              > > > Thank you for your time,
              > > >
              > > > Cedric
              > > >
              > > > --- In aima-talk@yahoogroups.com, "Peter Norvig" <peter@> wrote:
              > > > >
              > > > > You could do that, and that could be a way of expressing
              > reflexivity,
              > > > > but it wouldn't be quantifying over FOL functions -- it would be
              > > > > quantifying over objects that you happen to call "functions"
              but are
              > > > > regular objects as far as the logic is concerned.
              > > > >
              > > > > -Peter
              > > > >
              > > > > On 6/8/06, cedricstjl <cedricstjl@> wrote:
              > > > > > I have some difficulty seeing the difference in expressiveness
              > between
              > > > > > first-order logic and higher-order logics. Wikipedia (as well
              > as AIMA,
              > > > > > AFAICT) says that F-O logic cannot quantify over functions. But
              > > > > > couldn't it be achieved equivalently by reifying functions and
              > > > > > predicates? I.e.:
              > > > > >
              > > > > > x = fun(var)
              > > > > >
              > > > > > becomes
              > > > > >
              > > > > > x = call_function(fun, var)
              > > > > >
              > > > > > and then one can express reflexivity:
              > > > > >
              > > > > > for all fun, a, b: reflexive(fun) <=> call_function(fun, a, b) =
              > > > > > call_function(fun, b, a)
              > > > > >
              > > > > > Cedric
              >
            • Joe Hendrix
              ... This is a useful technique. I ve also seen it called currifying in other papers, however it doesn t let you achieve the full power of second-order logic,
              Message 6 of 9 , Jun 14, 2006
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                > On 6/8/06, cedricstjl <cedricstjl@> wrote:
                > couldn't it be achieved equivalently by reifying functions and
                > predicates?

                This is a useful technique. I've also seen it called currifying in
                other papers, however it doesn't let you achieve the full power of
                second-order logic, much less higher-order logic.

                A basic first-order logic result is that finiteness is not
                expressible. That is there is no sentence P such that M is a model of
                P iff. M is finite. However, in second order logic one can express
                finiteness. Specifically, if P is the statement that all injective
                functions are surjective, then M is a model of P iff. M is finite.

                The wikipedia article on second-order logic discusses some of the
                differences between first-order and second-order logic at more length
                than this email.

                Joe
              • cedricstjl
                Hmmm, I ve got a hard time translating your example, or those from the Wikipedia article into logical sentences (I have no idea how to express that a model is
                Message 7 of 9 , Jun 15, 2006
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                  Hmmm, I've got a hard time translating your example, or those from the
                  Wikipedia article into logical sentences (I have no idea how to
                  express that a model is finite, for instance). I guess I should pick
                  up a book on the subject; my only background in logic is from AIMA and
                  Hofstadter's book.

                  Thanks for the info!

                  Cedric

                  --- In aima-talk@yahoogroups.com, Joe Hendrix <jhendrix@...> wrote:
                  >
                  > > On 6/8/06, cedricstjl <cedricstjl@> wrote:
                  > > couldn't it be achieved equivalently by reifying functions and
                  > > predicates?
                  >
                  > This is a useful technique. I've also seen it called currifying in
                  > other papers, however it doesn't let you achieve the full power of
                  > second-order logic, much less higher-order logic.
                  >
                  > A basic first-order logic result is that finiteness is not
                  > expressible. That is there is no sentence P such that M is a model of
                  > P iff. M is finite. However, in second order logic one can express
                  > finiteness. Specifically, if P is the statement that all injective
                  > functions are surjective, then M is a model of P iff. M is finite.
                  >
                  > The wikipedia article on second-order logic discusses some of the
                  > differences between first-order and second-order logic at more length
                  > than this email.
                  >
                  > Joe
                  >
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