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Very interesting ...
What would be the difference if we think it in this way:
p -> q
q ^ p -> ~r
q ^ ~p -> r
p -> s
and s is ~r.
or think it in a probabilistic way, if we let:
p: born in New York
q: born in United States
r: born in New Jersey
then we have:
P(q|p) = 1
P(r|q) = v
P(r|p) = 0
P(
[EMAIL PROTECTED] wrote:
> Consider the following line of reasoning. Let p be the proposition
> "Ronald was born in New York." From p, we can infer q: Ronald was
> born in the United States. From q, we can infer r: It is possible
> that Ronald was born in New Jersey. On the other hand, from p we ca
On Jul 13, 2005, at 12:48 AM, [EMAIL PROTECTED] wrote:
> Consider the following line of reasoning. Let p be the proposition
> "Ronald was born in New York." From p, we can infer q: Ronald was
> born in the United States. From q, we can infer r: It is possible
> that Ronald was born in New J
On Tue, 12 Jul 2005 [EMAIL PROTECTED] wrote:
> Consider the following line of reasoning. Let p be the proposition
> "Ronald was born in New York." From p, we can infer q: Ronald was born
> in the United States.
> From q, we can infer r: It is possible that Ronald
> was born in New Jersey.
That's
[EMAIL PROTECTED] wrote:
> Consider the following line of reasoning. Let p be the proposition
> "Ronald was born in New York." From p, we can infer q: Ronald was born
> in the United States. From q, we can infer r: It is possible that
> Ronald was born in New Jersey. On the other hand, from p w
There is no contradiction. There is no paradox.
I would argue that a proposition (a) of the form "It is possible
that X" is logically equivalent to "X or not X". Note that
a proposition (b) of the form "It is not possible that X" is
logically equivalent to "not X". Propositions (a) and (b) are
no
I think that this paradox is due that some information is lost during inference.
The process of information losing may be a big problem for machine decision
making
and other interesting topics.
Thanks a lot.
Best regards,
Chenghui Cai
Ph.D. Student
Lab for Intelligent Systems & Controls (LISC)
D
In terms of logic, there is no contradiction here. Whatever contradiction
there may appear to be is due to the use of the word "possible" in these
statements. "It is not possible that Q" is equivalent simply to "not Q".
"It is possible that Q" is equivalent simply to "Q or not Q". "Not Q" and
[EMAIL PROTECTED] writes:
> Consider the following line of reasoning. Let p be the proposition "Ronald
> was born in New York." From p, we can infer q: Ronald was born in the United
> States. From q, we can infer r: It is possible that Ronald was born in New
> Jersey. On the other hand, from p
> Consider the following line of reasoning. Let p be the proposition
> "Ronald was born in New York." From p, we can infer q: Ronald was born
> in the United States. From q, we can infer r: It is possible that
> Ronald was born in New Jersey. On the other hand, from p we can infer
> s: It is not p
FIRST CALL FOR PAPERS
Ninth International Symposium on Artificial Intelligence and Mathematics
http://anytime.cs.umass.edu/aimath06/
January 4-6, 2006
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Paper Submission Deadline: October 2, 2005
The International Symposium on Artificial Intelligence and Mathematics is a
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