Hello!
I've read the paragraph about AI becoming a science and therefore more
formal. But somehow I'm having the impression that the informal
approach to problems in AI remains to be more common rather than
the rigorous/proof based style of other fields in computer science.
Don't get me wrong - that isn't meant as a criticism of the book, just
a general impression. (I've encountered other AI books/papers that
afirmed this.)

So where about can AI be found (considering a "formality hierarchy")?
Close to Formal Methods and Analysis of Algorithms, or rather near
fields like Software Engineering?
Maybe someone with more experience than me could comment on this?

regards

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Hi Bruce,

I think "this statement is definitely false" is more a paradox than a
contradiction, for when you decide it is false then it is true, and vice
versa. A contradiction is always false. And "consistently" has two
readings, one is the randomness you meant, and another reading common in
philosophical literature is that it is possible for a set of
propositions to all true. I'm just not sure which meaning the authors
seem to imply.

Paul

Tommy Gun wrote:

>     Sounds like sort of a contradiction.  The words "cannot
>     consistently" I think give it the flexability to sometimes be true
>     and sometimes not.  If the sentence was definate all of the time,
>     then it would just be a contradiction.   Take "this statement is
>     definately false" is a contradiction, but if it were, "this
>     statement is sometimes false" then there sometimes when it isn't a
>     contradiction.  "cannot  consistently" basically says that's it's
>     sorta random, so sometimes it could make sense.
>
>     Not sure if that helps, but it's just my $.02...
>
>      - Bruce
>
>
>     Message: 1
>     Date: Sun, 11 Sep 2005 23:08:35 +0800
>     From: Paul Hsueh-Min Chang
>     Subject: Problem about the J.R. Lucas sentence
>
>     Hi,
>
>     On page 950, the book argues that the sentence "J. R. Lucas cannot
>     consistently assert that this sentence is true." is necessarily true,
>     but Lucas cannot consistently assert it. There are two arguments
>     on that
>     page. I found no problem with the first argument, but could not
>     understand the second.
>
>     Here is the second argument.
>
>     "The sentence cannot be false, because if it were then Lucas could not
>     consistently assert it, so it would be true."
>
>     But, why couldn't Lucas consistently assert it /if it were false/? One
>     can of course assert a false sentence and be consistent at the same
>     time, because one is inconsistent if and only if it is
>     /impossible/ that
>     all his beliefs are true. If Lucas happens to believe a false
>     sentence,
>     he is still consistent.
>
>     Please help/correct me.
>
>     Paul
>
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To try and understand this equation I assumed the following:
number of possible percepts P = 3
lifetime of the agent (number of percepts it will receive) = 3
I the get an answer for the summation of 39.  However, if I manually
determine the number of possible ways in which the percepts can be
received I get 15 for the size of the lookup table.  Can somebody tell
me what I am not undestanding correctly?

Fred Kindl
fredkindl@...

I believe if you look at the "setup" on the previous
page you'll see the authors intended the term
"consistent" to be the logical definition. (see pages
137 and 353)  That is, for something to be consistent,
it cannot be contradictory.  Therefore, if the
sentance were false, he couldn't assert the sentance
and still be consistent, which therefore makes the
sentance true.

But the point of the paragraph is that because of the
construction of the sentance, the agent "J.R. Lucas"
cannot assert something that other agents can.
However the authors are pointing out that this doesn't
make him inferior.

Rob G.

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

> Hi Bruce,
>
> I think "this statement is definitely false" is more
> a paradox than a
> contradiction, for when you decide it is false then
> it is true, and vice
> versa. A contradiction is always false. And
> "consistently" has two
> readings, one is the randomness you meant, and
> another reading common in
> philosophical literature is that it is possible for
> a set of
> propositions to all true. I'm just not sure which
> meaning the authors
> seem to imply.
>
> Paul
>
> Tommy Gun wrote:
>
> >     Sounds like sort of a contradiction.  The
> words "cannot
> >     consistently" I think give it the flexability
> to sometimes be true
> >     and sometimes not.  If the sentence was
> definate all of the time,
> >     then it would just be a contradiction.   Take
> "this statement is
> >     definately false" is a contradiction, but if
> it were, "this
> >     statement is sometimes false" then there
> sometimes when it isn't a
> >     contradiction.  "cannot  consistently"
> basically says that's it's
> >     sorta random, so sometimes it could make
> sense.
> >
> >     Not sure if that helps, but it's just my
> $.02...
> >
> >      - Bruce
> >
> >
> >     Message: 1
> >     Date: Sun, 11 Sep 2005 23:08:35 +0800
> >     From: Paul Hsueh-Min Chang
> >     Subject: Problem about the J.R. Lucas sentence
> >
> >     Hi,
> >
> >     On page 950, the book argues that the sentence
> "J. R. Lucas cannot
> >     consistently assert that this sentence is
> true." is necessarily true,
> >     but Lucas cannot consistently assert it. There
> are two arguments
> >     on that
> >     page. I found no problem with the first
> argument, but could not
> >     understand the second.
> >
> >     Here is the second argument.
> >
> >     "The sentence cannot be false, because if it
> were then Lucas could not
> >     consistently assert it, so it would be true."
> >
> >     But, why couldn't Lucas consistently assert it
> /if it were false/? One
> >     can of course assert a false sentence and be
> consistent at the same
> >     time, because one is inconsistent if and only
> if it is
> >     /impossible/ that
> >     all his beliefs are true. If Lucas happens to
> believe a false
> >     sentence,
> >     he is still consistent.
> >
> >     Please help/correct me.
> >
> >     Paul
> >
> > __________________________________________________
> > Do You Yahoo!?
> > Tired of spam? Yahoo! Mail has the best spam
> protection around
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> >
> >
>
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I'm not sure if you're being consistent in your
definition of P, the possible precepts, since I can't
figure out how you arrived at 15.  (I agree with 39).

To make life easy, assume you have a single sensor
which can return one of three values - A, B, or C.
The possible precept combinations can therefore be
enumerated as:

A
B
C
AA
AB
AC
BA
BB
BC
...
AAA
AAB
AAC
ABA
...

I think you'll find (as the formula implies) there are
3 possible combinations after the first input is
received (t=1), there are 3^3 = 9 additonal
combinations when the second input is received (t=2),
and 3^3^3 additional combinations once the 3rd input
is received (t=3).  Add them all together, and you can
see the agent would need a total of 39 table entries
to know what action to take based on it's precept
history.

Rob G.

--- kindlencotech <fredkindl@...> wrote:

> To try and understand this equation I assumed the
> following:
> number of possible percepts P = 3
> lifetime of the agent (number of percepts it will
> receive) = 3
> I the get an answer for the summation of 39.
> However, if I manually
> determine the number of possible ways in which the
> percepts can be
> received I get 15 for the size of the lookup table.
> Can somebody tell
> me what I am not undestanding correctly?
>
> Fred Kindl
> fredkindl@...
>
>
>
>
>
>


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But my question is that being false does *not* equal being contradictory
(i.e. necessarily false).  If the sentence were merely false but not
contradictory, he surely could consistently assert it.

So lets review the argument:

"The sentence cannot be false, because if it were then Lucas could not
consistently assert it, so it would be true."

Consider two conditions:
1. If the sentence were meant to be merely false, then Lucas could
consistently assert it, so the argument is invalid.
2. If the sentence were meant to be contradictory, then nobody could
consistently assert it, but then the argument would have a very strange
form: "if p were contradictory then A could not assert it, so p would be
true." Consider the following argument of the same form: "If 'Saddam
Hussein is the US President' were contradictory, then I could not assert
it, so he would be the US President". Clearly absurd.

Again, please correct me if I am wrong.

Paul

The Geek wrote:

> I believe if you look at the "setup" on the previous
> page you'll see the authors intended the term
> "consistent" to be the logical definition. (see pages
> 137 and 353)  That is, for something to be consistent,
> it cannot be contradictory.  Therefore, if the
> sentance were false, he couldn't assert the sentance
> and still be consistent, which therefore makes the
> sentance true.
>
> But the point of the paragraph is that because of the
> construction of the sentance, the agent "J.R. Lucas"
> cannot assert something that other agents can.
> However the authors are pointing out that this doesn't
> make him inferior.
>
> Rob G.
>
> --- Paul Hsueh-Min Chang <avatar@...>
> wrote:
>
> > Hi Bruce,
> >
> > I think "this statement is definitely false" is more
> > a paradox than a
> > contradiction, for when you decide it is false then
> > it is true, and vice
> > versa. A contradiction is always false. And
> > "consistently" has two
> > readings, one is the randomness you meant, and
> > another reading common in
> > philosophical literature is that it is possible for
> > a set of
> > propositions to all true. I'm just not sure which
> > meaning the authors
> > seem to imply.
> >
> > Paul
> >
> > Tommy Gun wrote:
> >
> > >     Sounds like sort of a contradiction.  The
> > words "cannot
> > >     consistently" I think give it the flexability
> > to sometimes be true
> > >     and sometimes not.  If the sentence was
> > definate all of the time,
> > >     then it would just be a contradiction.   Take
> > "this statement is
> > >     definately false" is a contradiction, but if
> > it were, "this
> > >     statement is sometimes false" then there
> > sometimes when it isn't a
> > >     contradiction.  "cannot  consistently"
> > basically says that's it's
> > >     sorta random, so sometimes it could make
> > sense.
> > >
> > >     Not sure if that helps, but it's just my
> > $.02...
> > >
> > >      - Bruce
> > >
> > >
> > >     Message: 1
> > >     Date: Sun, 11 Sep 2005 23:08:35 +0800
> > >     From: Paul Hsueh-Min Chang
> > >     Subject: Problem about the J.R. Lucas sentence
> > >
> > >     Hi,
> > >
> > >     On page 950, the book argues that the sentence
> > "J. R. Lucas cannot
> > >     consistently assert that this sentence is
> > true." is necessarily true,
> > >     but Lucas cannot consistently assert it. There
> > are two arguments
> > >     on that
> > >     page. I found no problem with the first
> > argument, but could not
> > >     understand the second.
> > >
> > >     Here is the second argument.
> > >
> > >     "The sentence cannot be false, because if it
> > were then Lucas could not
> > >     consistently assert it, so it would be true."
> > >
> > >     But, why couldn't Lucas consistently assert it
> > /if it were false/? One
> > >     can of course assert a false sentence and be
> > consistent at the same
> > >     time, because one is inconsistent if and only
> > if it is
> > >     /impossible/ that
> > >     all his beliefs are true. If Lucas happens to
> > believe a false
> > >     sentence,
> > >     he is still consistent.
> > >
> > >     Please help/correct me.
> > >
> > >     Paul
> > >
>

Hi my name is mazhar & recently I join this group, coz I need
your/experts helps.
I m belonging from Pakistan & the student of MCS. Will u please tell me
the answer of exercise number 7.8 and 7.11 of AI A Modern Approach by
Russal.
Most important is Exercise 7.11 Minesweeper that will create more
problem from me so please any one of u solve this exercise & send it to
me, I m really thankful to u.
SYED ALI MAZHAR
MCS 2
FUAST University Karachi Pakistan
Mob: +92-333-2239246

I don't know if I'm explaining this very well.
Someone else should feel free to chime in if they've
got a better way of phrasing it...

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.

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.

The example is a little more complicated, since
they're violating a couple of normal rules for logic
systems - they have a sentance referring to the
assertability of sentances.  But if you reword the
sentance to say "Agent A cannot assert this sentance
without being wrong" I think it's a little more clear.

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.

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.

Rob G.

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

> But my question is that being false does *not* equal
> being contradictory
> (i.e. necessarily false).  If the sentence were
> merely false but not
> contradictory, he surely could consistently assert
> it.
>
> So lets review the argument:
>
> "The sentence cannot be false, because if it were
> then Lucas could not
> consistently assert it, so it would be true."
>
> Consider two conditions:
> 1. If the sentence were meant to be merely false,
> then Lucas could
> consistently assert it, so the argument is invalid.
> 2. If the sentence were meant to be contradictory,
> then nobody could
> consistently assert it, but then the argument would
> have a very strange
> form: "if p were contradictory then A could not
> assert it, so p would be
> true." Consider the following argument of the same
> form: "If 'Saddam
> Hussein is the US President' were contradictory,
> then I could not assert
> it, so he would be the US President". Clearly
> absurd.
>
> Again, please correct me if I am wrong.
>
> Paul
>
> The Geek wrote:
>
> > I believe if you look at the "setup" on the
> previous
> > page you'll see the authors intended the term
> > "consistent" to be the logical definition. (see
> pages
> > 137 and 353)  That is, for something to be
> consistent,
> > it cannot be contradictory.  Therefore, if the
> > sentance were false, he couldn't assert the
> sentance
> > and still be consistent, which therefore makes the
> > sentance true.
> >
> > But the point of the paragraph is that because of
> the
> > construction of the sentance, the agent "J.R.
> Lucas"
> > cannot assert something that other agents can.
> > However the authors are pointing out that this
> doesn't
> > make him inferior.
> >
> > Rob G.
> >
> > --- Paul Hsueh-Min Chang
> <avatar@...>
> > wrote:
> >
> > > Hi Bruce,
> > >
> > > I think "this statement is definitely false" is
> more
> > > a paradox than a
> > > contradiction, for when you decide it is false
> then
> > > it is true, and vice
> > > versa. A contradiction is always false. And
> > > "consistently" has two
> > > readings, one is the randomness you meant, and
> > > another reading common in
> > > philosophical literature is that it is possible
> for
> > > a set of
> > > propositions to all true. I'm just not sure
> which
> > > meaning the authors
> > > seem to imply.
> > >
> > > Paul
> > >
> > > Tommy Gun wrote:
> > >
> > > >     Sounds like sort of a contradiction.  The
> > > words "cannot
> > > >     consistently" I think give it the
> flexability
> > > to sometimes be true
> > > >     and sometimes not.  If the sentence was
> > > definate all of the time,
> > > >     then it would just be a contradiction.
> Take
> > > "this statement is
> > > >     definately false" is a contradiction, but
> if
> > > it were, "this
> > > >     statement is sometimes false" then there
> > > sometimes when it isn't a
> > > >     contradiction.  "cannot  consistently"
> > > basically says that's it's
> > > >     sorta random, so sometimes it could make
> > > sense.
> > > >
> > > >     Not sure if that helps, but it's just my
> > > $.02...
> > > >
> > > >      - Bruce
> > > >
> > > >
> > > >     Message: 1
> > > >     Date: Sun, 11 Sep 2005 23:08:35 +0800
> > > >     From: Paul Hsueh-Min Chang
> > > >     Subject: Problem about the J.R. Lucas
> sentence
> > > >
> > > >     Hi,
> > > >
> > > >     On page 950, the book argues that the
> sentence
> > > "J. R. Lucas cannot
> > > >     consistently assert that this sentence is
> > > true." is necessarily true,
> > > >     but Lucas cannot consistently assert it.
> There
> > > are two arguments
> > > >     on that
> > > >     page. I found no problem with the first
> > > argument, but could not
> > > >     understand the second.
> > > >
> > > >     Here is the second argument.
> > > >
> > > >     "The sentence cannot be false, because if
> it
> > > were then Lucas could not
> > > >     consistently assert it, so it would be
> true."
> > > >
> > > >     But, why couldn't Lucas consistently
> assert it
> > > /if it were false/? One
> > > >     can of course assert a false sentence and
> be
> > > consistent at the same
> > > >     time, because one is inconsistent if and
> only
> > > if it is
> > > >     /impossible/ that
> > > >     all his beliefs are true. If Lucas happens
> to
> > > believe a false
> > > >     sentence,
> > > >     he is still consistent.
> > > >
> > > >     Please help/correct me.
> > > >
> > > >     Paul
> > > >
> >
>
>
>
>




__________________________________
Yahoo! Mail - PC Magazine Editors' Choice 2005
http://mail.yahoo.com

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

Hi,
   could anyone plz let me know the link to the answers of the
exercise
of this book

In page97, line 7:
The restriction is to choose an h function that never overestimates
the cost to reach the goal. Such an h is called an admissible
heuristic. Admissible heuristics are by nature optimistic, because
they think the cost of solving the problem is less than it actually is.

Can anyone give me more explanation why it always gets the optimial
result when it never overestimates the total cost.

In page97, line 7:
The restriction is to choose an h function that never overestimates
the cost to reach the goal. Such an h is called an admissible
heuristic. Admissible heuristics are by nature optimistic, because
they think the cost of solving the problem is less than it actually is.

Can anyone give me more explanation why it always gets the optimial
result when it never overestimates the total cost.

I think my version is different from yours, but I
assume you're talking about the A* search algorithm.

The proof is in the book a page or so later, but  look
at it the other way for a second - if the path
estimate were sometimes too high, then based on the
inflated estimate you might ignore a path that would
have turned out to have a "short cut" in it.  But by
guaranteeing that the actual cost will always be more
than your estimate, you're guaranteed never to ignore
a short cut.

To put it another way, with an admissible heuristic
any unexplored path is guaranteed to be worse than or
equal to it's estimate - never better.  Thus when you
actually explore a path, you're guaranteed that it's
cost will only get worse.  So if you've found an
actual path solution that's equal to or better than
the best unexplored path estimates, the actual path
you've found is guaranteed to be the best because the
unexplored paths can only get more costly when they're
explored.

I hope that made sense.

Rob G.

--- lwudong <wudongs@...> wrote:

> In page97, line 7:
> The restriction is to choose an h function that
> never overestimates
> the cost to reach the goal. Such an h is called an
> admissible
> heuristic. Admissible heuristics are by nature
> optimistic, because
> they think the cost of solving the problem is less
> than it actually is.
>
> Can anyone give me more explanation why it always
> gets the optimial
> result when it never overestimates the total cost.
>
>
>
>
>




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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
>
>
>





__________________________________
Yahoo! Mail - PC Magazine Editors' Choice 2005
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---

From: aima-talk@yahoogroups.com [mailto:aima-talk@yahoogroups.com] On Behalf Of The Geek
Sent: Monday, September 26, 2005 6:03 PM
To: aima-talk@yahoogroups.com
Subject: Re: [aima-talk] about A* search

I think my version is different from yours, but I
assume you're talking about the A* search algorithm.

The proof is in the book a page or so later, but  look
at it the other way for a second - if the path
estimate were sometimes too high, then based on the
inflated estimate you might ignore a path that would
have turned out to have a "short cut" in it.  But by
guaranteeing that the actual cost will always be more
than your estimate, you're guaranteed never to ignore
a short cut. 

To put it another way, with an admissible heuristic
any unexplored path is guaranteed to be worse than or
equal to it's estimate - never better.  Thus when you
actually explore a path, you're guaranteed that it's
cost will only get worse.  So if you've found an
actual path solution that's equal to or better than
the best unexplored path estimates, the actual path
you've found is guaranteed to be the best because the
unexplored paths can only get more costly when they're
explored.

I hope that made sense.

Rob G.

--- lwudong <wudongs@...> wrote:

> In page97, line 7:
> The restriction is to choose an h function that
> never overestimates
> the cost to reach the goal. Such an h is called an
> admissible
> heuristic. Admissible heuristics are by nature
> optimistic, because
> they think the cost of solving the problem is less
> than it actually is.
>
> Can anyone give me more explanation why it always
> gets the optimial
> result when it never overestimates the total cost.
>
>
>
>
>



           
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Yahoo! Mail - PC Magazine Editors' Choice 2005
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---

From: savastinuk [mailto:minnie@...]
Sent: Tuesday, September 27, 2005 7:04 AM
To: 'aima-talk@yahoogroups.com'
Subject: RE: [aima-talk] about A* search

This makes sense. : )

 

Can you also explain consistent? Or, better yet, INconsistent?

Still talking A*.

 

thanks....

Susan

---

From: aima-talk@yahoogroups.com [mailto:aima-talk@yahoogroups.com] On Behalf Of The Geek
Sent: Monday, September 26, 2005 6:03 PM
To: aima-talk@yahoogroups.com
Subject: Re: [aima-talk] about A* search

I think my version is different from yours, but I
assume you're talking about the A* search algorithm.

The proof is in the book a page or so later, but  look
at it the other way for a second - if the path
estimate were sometimes too high, then based on the
inflated estimate you might ignore a path that would
have turned out to have a "short cut" in it.  But by
guaranteeing that the actual cost will always be more
than your estimate, you're guaranteed never to ignore
a short cut. 

To put it another way, with an admissible heuristic
any unexplored path is guaranteed to be worse than or
equal to it's estimate - never better.  Thus when you
actually explore a path, you're guaranteed that it's
cost will only get worse.  So if you've found an
actual path solution that's equal to or better than
the best unexplored path estimates, the actual path
you've found is guaranteed to be the best because the
unexplored paths can only get more costly when they're
explored.

I hope that made sense.

Rob G.

--- lwudong <wudongs@...> wrote:

> In page97, line 7:
> The restriction is to choose an h function that
> never overestimates
> the cost to reach the goal. Such an h is called an
> admissible
> heuristic. Admissible heuristics are by nature
> optimistic, because
> they think the cost of solving the problem is less
> than it actually is.
>
> Can anyone give me more explanation why it always
> gets the optimial
> result when it never overestimates the total cost.
>
>
>
>
>



           
__________________________________
Yahoo! Mail - PC Magazine Editors' Choice 2005
http://mail.yahoo.com

I think my version is different from yours, but I
assume you're talking about the A* search algorithm.

The proof is in the book a page or so later, but  look
at it the other way for a second - if the path
estimate were sometimes too high, then based on the
inflated estimate you might ignore a path that would
have turned out to have a "short cut" in it.  But by
guaranteeing that the actual cost will always be more
than your estimate, you're guaranteed never to ignore
a short cut. 

To put it another way, with an admissible heuristic
any unexplored path is guaranteed to be worse than or
equal to it's estimate - never better.  Thus when you
actually explore a path, you're guaranteed that it's
cost will only get worse.  So if you've found an
actual path solution that's equal to or better than
the best unexplored path estimates, the actual path
you've found is guaranteed to be the best because the
unexplored paths can only get more costly when they're
explored.

I hope that made sense.

Rob G.

--- lwudong <wudongs@...> wrote:

> In page97, line 7:
> The restriction is to choose an h function that
> never overestimates
> the cost to reach the goal. Such an h is called an
> admissible
> heuristic. Admissible heuristics are by nature
> optimistic, because
> they think the cost of solving the problem is less
> than it actually is.
>
> Can anyone give me more explanation why it always
> gets the optimial
> result when it never overestimates the total cost.
>
>
>
>
>



           
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__________________________________________________
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Tired of spam? Yahoo! Mail has the best spam protection around
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Consistency of heuristics is a little more tricky to
explain, since every consistent one is also
admissible.

If you're not from the U.S., I'll apologize in advance
for the following example....

Lets say you're trying to get from New York to L.A. by
car - forget the fact that it would now cost you a
small fortune to do so.  A consistent heuristic is one
where the estimate to get from New York to L.A. must
be equal to or smaller than the actual cost to get
from New York to any other city **plus** the estimate
to get from that city to L.A.  In other words, if you
drive from New York to Chicago, then estimate the
distance from Chicago to L.A. you're not supposed to
get a smaller answer than your original estimate.  If
you use straight-line distance, it's easy to see this
is consistent.

Admissible heurstics must guarantee the estimate is no
larger than the actual cost turns out to be.
Consistent heuristics must also guarantee the "revised
estimate" (the sum of the actual distance traveled so
far plus the estimate of what you've got remaining)
never goes down as you explore the path.

You have to get kind of goofy to find things that are
admissible but not consistent - taking the
straight-line distance divided by the number of
letters in the city name for example.  The estimate is
guaranteed to be low (since it's always less than the
straight-line distance), and thus is admissible.  When
you start at New York your estimate would be 2400/7 =
342.86.  If you drove 95 miles to Philadelphia, you're
estimate from Philadelphia to L.A. would be 2320 / 12
= 193.33.  Adding that back to the 95 miles you drove
from New York we see that we now think we can get from
New York to L.A. by way of Philadelphia for an
estimated cost of 193.33 + 95 = 288.33, less than our
original estimate of 342.86, thus demonstrating that
the heuristic is not consistent.

Rob G.

--- savastinuk <minnie@...> wrote:

> This makes sense. : )
>
> Can you also explain consistent? Or, better yet,
> INconsistent?
> Still talking A*.
>
> thanks....
> Susan
>
>
>   _____
>
> From: aima-talk@yahoogroups.com
> [mailto:aima-talk@yahoogroups.com] On Behalf
> Of The Geek
> Sent: Monday, September 26, 2005 6:03 PM
> To: aima-talk@yahoogroups.com
> Subject: Re: [aima-talk] about A* search
>
>
> I think my version is different from yours, but I
> assume you're talking about the A* search algorithm.
>
> The proof is in the book a page or so later, but
> look
> at it the other way for a second - if the path
> estimate were sometimes too high, then based on the
> inflated estimate you might ignore a path that would
> have turned out to have a "short cut" in it.  But by
> guaranteeing that the actual cost will always be
> more
> than your estimate, you're guaranteed never to
> ignore
> a short cut.
>
> To put it another way, with an admissible heuristic
> any unexplored path is guaranteed to be worse than
> or
> equal to it's estimate - never better.  Thus when
> you
> actually explore a path, you're guaranteed that it's
> cost will only get worse.  So if you've found an
> actual path solution that's equal to or better than
> the best unexplored path estimates, the actual path
> you've found is guaranteed to be the best because
> the
> unexplored paths can only get more costly when
> they're
> explored.
>
> I hope that made sense.
>
> Rob G.
>
> --- lwudong <wudongs@...> wrote:
>
> > In page97, line 7:
> > The restriction is to choose an h function that
> > never overestimates
> > the cost to reach the goal. Such an h is called an
> > admissible
> > heuristic. Admissible heuristics are by nature
> > optimistic, because
> > they think the cost of solving the problem is less
> > than it actually is.
> >
> > Can anyone give me more explanation why it always
> > gets the optimial
> > result when it never overestimates the total cost.
> >
> >
> >
> >
> >
>
>
>
>
> __________________________________
> Yahoo! Mail - PC Magazine Editors' Choice 2005
> http://mail.yahoo.com
>
>
>
>
>
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> YAHOO! GROUPS LINKS
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> <http://groups.yahoo.com/group/aima-talk> " on the
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---

From: aima-talk@yahoogroups.com [mailto:aima-talk@yahoogroups.com] On Behalf Of The Geek
Sent: Tuesday, September 27, 2005 1:46 PM
To: aima-talk@yahoogroups.com
Subject: RE: [aima-talk] about A* search

Consistency of heuristics is a little more tricky to
explain, since every consistent one is also
admissible.

If you're not from the U.S., I'll apologize in advance
for the following example....

Lets say you're trying to get from New York to L.A. by
car - forget the fact that it would now cost you a
small fortune to do so.  A consistent heuristic is one
where the estimate to get from New York to L.A. must
be equal to or smaller than the actual cost to get
from New York to any other city **plus** the estimate
to get from that city to L.A.  In other words, if you
drive from New York to Chicago, then estimate the
distance from Chicago to L.A. you're not supposed to
get a smaller answer than your original estimate.  If
you use straight-line distance, it's easy to see this
is consistent.

Admissible heurstics must guarantee the estimate is no
larger than the actual cost turns out to be.
Consistent heuristics must also guarantee the "revised
estimate" (the sum of the actual distance traveled so
far plus the estimate of what you've got remaining)
never goes down as you explore the path.

You have to get kind of goofy to find things that are
admissible but not consistent - taking the
straight-line distance divided by the number of
letters in the city name for example.  The estimate is
guaranteed to be low (since it's always less than the
straight-line distance), and thus is admissible.  When
you start at New York your estimate would be 2400/7 =
342.86.  If you drove 95 miles to Philadelphia, you're
estimate from Philadelphia to L.A. would be 2320 / 12
= 193.33.  Adding that back to the 95 miles you drove
from New York we see that we now think we can get from
New York to L.A. by way of Philadelphia for an
estimated cost of 193.33 + 95 = 288.33, less than our
original estimate of 342.86, thus demonstrating that
the heuristic is not consistent.

Rob G.

--- savastinuk <minnie@...> wrote:

> This makes sense. : )
> 
> Can you also explain consistent? Or, better yet,
> INconsistent?
> Still talking A*.
> 
> thanks....
> Susan
>
>
>   _____ 
>
> From: aima-talk@yahoogroups.com
> [mailto:aima-talk@yahoogroups.com] On Behalf
> Of The Geek
> Sent: Monday, September 26, 2005 6:03 PM
> To: aima-talk@yahoogroups.com
> Subject: Re: [aima-talk] about A* search
>
>
> I think my version is different from yours, but I
> assume you're talking about the A* search algorithm.
>
> The proof is in the book a page or so later, but
> look
> at it the other way for a second - if the path
> estimate were sometimes too high, then based on the
> inflated estimate you might ignore a path that would
> have turned out to have a "short cut" in it.  But by
> guaranteeing that the actual cost will always be
> more
> than your estimate, you're guaranteed never to
> ignore
> a short cut. 
>
> To put it another way, with an admissible heuristic
> any unexplored path is guaranteed to be worse than
> or
> equal to it's estimate - never better.  Thus when
> you
> actually explore a path, you're guaranteed that it's
> cost will only get worse.  So if you've found an
> actual path solution that's equal to or better than
> the best unexplored path estimates, the actual path
> you've found is guaranteed to be the best because
> the
> unexplored paths can only get more costly when
> they're
> explored.
>
> I hope that made sense.
>
> Rob G.
>
> --- lwudong <wudongs@...> wrote:
>
> > In page97, line 7:
> > The restriction is to choose an h function that
> > never overestimates
> > the cost to reach the goal. Such an h is called an
> > admissible
> > heuristic. Admissible heuristics are by nature
> > optimistic, because
> > they think the cost of solving the problem is less
> > than it actually is.
> >
> > Can anyone give me more explanation why it always
> > gets the optimial
> > result when it never overestimates the total cost.
> >
> >
> >
> >
> >
>
>
>
>            
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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.

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.

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

anyone can give me some clues about the up-to-date info about expert
system? Seems this topic has been being faded?

Thanks in advance.

"oldatum" <oldatum@...> writes:

> anyone can give me some clues about the up-to-date info about expert
> system? Seems this topic has been being faded?

I wondered this myself, and posted some notes to my blog:

   Expert systems: what happened in the past decade?
   http://www.paoloamoroso.it/log/050309.html


Paolo
--
Lisp Propulsion Laboratory log - http://www.paoloamoroso.it/log

Hello ML,
I'm the guy who's doing an alternative implementation of the algorithms in the
book in Java. I've done a long break but now I've decided to continue with the
project, even with no help :-(

I've just finished the package related to chapter 7.

You can see the documentation in:
http://www.artificialidea.com/my_programs/docs/index.html

If you would like to download all I have done until now:
http://www.artificialidea.com/index.php?page=my_programs

I'd more than appreciate any comment.

Regards,
--
Ivan F. Villanueva B.
The dream of intelligent machines: www.artificialidea.com
Encrypted mail preferred.
GPG Key Id: 3FDBF85F 2004-10-18 Ivan-Fernando Villanueva Barrio

Dear everyone:

Could anyone please tell me if I would like to do research on Automatic Music Composition Generator, who is the professor in this area and what is the website to focus on?

Thank you for all answers.

Best regards,

Jaidee, Mr.

Yahoo! Music Unlimited - Access over 1 million songs. Try it free.

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