Undefinedness

#11

"JOG" <jog (AT) cs (DOT) nott.ac.uk> wrote

Quote:

On Nov 21, 2:22 pm, "David Cressey" <cresse... (AT) verizon (DOT) net> wrote:
"JOG" <j... (AT) cs (DOT) nott.ac.uk> wrote in message

news:84c11971-6500-48e4-ba0f-b8b659f390da (AT) d61g2000hsa (DOT) googlegroups.com...

Word up CDT. How the devil are you all? Well, I return with a question
that as ever highlights my complete lack of formal mathematical
training, and in light of knowing no logicians in my daily life (funny
that), I was hoping that one of you kind folks might be able to
advise:

Say I had a set of 3 encoded propositions:
R := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)}, {(Name,
Harry)} }

(note that Harry's Age is missing, so instead of adding a null, i've
intentionally just left the attribute out. Just ride with such oddness
for now if you would.)

What if I deigned to create a simple 'adults' subset of this set of
propositions, by creating a predicate that only returned the elements,
p, which contained an age attribute greater than 18. Could I state
this as (where E signifies set membership):

Adults := { p E R | EXISTSx ( x > 18 && (Age, x) E p ) }

My question obviously hinges around Harry's missing age attribute. In
this case would the EXISTSx (...) part of the set's intension simply
return a FALSE, or will I end up in the quagmire of 3VL with an
UNDEFINED? My instinct is that I am still in 2VL given there is no
null floating about, but since the recent, excellent discussions of
Jan's DEF operator, and having delved into beeson's logic of partial
terms, I am not at all confident.

Any comments are much appreciated, and regards to all, Jim.

I'm no mathematician or logician, but I'll answer anyway.

To me, it dpends on whether the relationship (Name, Age) follows the
open
world assumption or the closed world assumption.

While I was only really concerned about whether my logic statements
are sticking to 2VL internally, you've sent me off at a tangent here
because CWA is one of my bugbears. Imho its at best silly, and at
worst contradictory. Take relations such as:

Weather_is = { condition: Hot }
Weather_is_not = { condition: Cold }
Domain = {Hot, Cold}

Perfectly fine with full information, and a constraint that a
condition can't appear in both. And I can happily extrapolate from CWA
from the first relation that: !is(condition:cold)), and from the
second !is_not(condition:hot). Nice...

...until we're faced missing information. If both relations are empty
(because we just don't have the data say), then CWA tells me that:
!Weather_is(condition:Hot) and !Weather_is_not(condition:Hot). It is
both hot and not hot. Genius. I don't see how CWA based directly on
what propositions state can ever be justified for a system working in
the real world (TM).

In theory, you never have to be concerned about missing information. In
practice, you do.

In actual applications, missing information and the CWA are constantly
applied to make real world decisions.

"You don't have a reservation on this flight. You're not coming up on my
computer." People make decisions all the time based on what is not in the
database.

Quote:

Equally CWA would suggest that Harry is neither a child nor an adult
in the other example. Meh.

I am hence of the opinion that we should stick to OWA, or better still
a CWA that is aware it is only commenting on the _existence of
propositions_ themselves, and not the underlying truth of their
contents (preventing us asking questions with contradictory answers in
the first place).

If it's the closed world
assumption, then we would have to say that Harry is not included with
the
adults. However, if we defined another set, Children,

Children := { p E R | EXISTSx ( x < 19 && (Age, x) E p ) }

Please note that Harry is excluded from Children as well.

If we had a rule that says that every person mentioned in R is either a
child or an adult, that would be tantamount to requiring that the entry
for
Harry be rejected at time of insertion.

BTW, I see nothing odd about your notation.

Huzzah

NULLS are not needed. Hwever,
your proposition R actually contains two propositions: first that the
named
person exists, and second that the person named with an age has that
age.

True, and full decomposition to 6NF would be a valid approach. But one
that can add an unpleasant amount of joins. Theoretically no problem
of course, but who realistically fancies writing queries with n joins
just because you don't have complete information for a single entry
say... And lets be honest, when in the real world is any attribute
100% guaranteed to not going to have some missing data at some point?

In the real world, people use NULLS for a purpose. Sometimes that purpose
is theoretically valid. Sometimes, it's not. In the real world, people
make mistakes. Even when they are dealing with databases.

The best we can hope for is that database will not amplify the mistakes
people make, at least not very often.

#12

On 23 nov, 12:31, "David Cressey" <cresse... (AT) verizon (DOT) net> wrote:

Quote:

"JOG" <j... (AT) cs (DOT) nott.ac.uk> wrote in message

news:ea3deb47-3697-4eb5-8b4f-34cf2ef2ec25 (AT) t47g2000hsc (DOT) googlegroups.com...> On Nov 21, 2:22 pm, "David Cressey" <cresse... (AT) verizon (DOT) net> wrote:
"JOG" <j... (AT) cs (DOT) nott.ac.uk> wrote in message

news:84c11971-6500-48e4-ba0f-b8b659f390da (AT) d61g2000hsa (DOT) googlegroups.com...

Word up CDT. How the devil are you all? Well, I return with a question
that as ever highlights my complete lack of formal mathematical
training, and in light of knowing no logicians in my daily life (funny
that), I was hoping that one of you kind folks might be able to
advise:

Say I had a set of 3 encoded propositions:
R := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)}, {(Name,
Harry)} }

(note that Harry's Age is missing, so instead of adding a null, i've
intentionally just left the attribute out. Just ride with such oddness
for now if you would.)

What if I deigned to create a simple 'adults' subset of this set of
propositions, by creating a predicate that only returned the elements,
p, which contained an age attribute greater than 18. Could I state
this as (where E signifies set membership):

Adults := { p E R | EXISTSx ( x > 18 && (Age, x) E p ) }

My question obviously hinges around Harry's missing age attribute. In
this case would the EXISTSx (...) part of the set's intension simply
return a FALSE, or will I end up in the quagmire of 3VL with an
UNDEFINED? My instinct is that I am still in 2VL given there is no
null floating about, but since the recent, excellent discussions of
Jan's DEF operator, and having delved into beeson's logic of partial
terms, I am not at all confident.

Any comments are much appreciated, and regards to all, Jim.

I'm no mathematician or logician, but I'll answer anyway.

To me, it dpends on whether the relationship (Name, Age) follows the
open
world assumption or the closed world assumption.

While I was only really concerned about whether my logic statements
are sticking to 2VL internally, you've sent me off at a tangent here
because CWA is one of my bugbears. Imho its at best silly, and at
worst contradictory. Take relations such as:

Weather_is = { condition: Hot }
Weather_is_not = { condition: Cold }
Domain = {Hot, Cold}

Perfectly fine with full information, and a constraint that a
condition can't appear in both. And I can happily extrapolate from CWA
from the first relation that: !is(condition:cold)), and from the
second !is_not(condition:hot). Nice...

...until we're faced missing information. If both relations are empty
(because we just don't have the data say), then CWA tells me that:
!Weather_is(condition:Hot) and !Weather_is_not(condition:Hot). It is
both hot and not hot. Genius. I don't see how CWA based directly on
what propositions state can ever be justified for a system working in
the real world (TM).

In theory, you never have to be concerned about missing information. In
practice, you do.

I know that's not how you meant "in theory", but in current research
in database theory this is actually a hot topic, especially in
connection with missing or uncertain information (including null
values) and also with data integration where the classical CWA almost
never fully applies. There's a whole spectrum between the full CWA and
the OWA that go from stronger assumption to weaker assumptions. It can
for example be that the CWA applies only to certain selections or
projections of the relation.

Quote:

The best we can hope for is that database will not amplify the mistakes
people make, at least not very often.

That seems to me almost unavoidable. Any system that enhances your
power is likely to amplify the magnitude of your mistakes. The best we
can do is to make the people that deal with these systems aware of
these dangers and train them well. They should hire more database
professors. ;-)

-- Jan Hidders

#13

On Nov 23, 10:06 am, Jan Hidders <hidd... (AT) gmail (DOT) com> wrote:

Quote:

That seems to me almost unavoidable. Any system that enhances your
power is likely to amplify the magnitude of your mistakes.

"To err is human, but to really screw things up you need a computer."

Marshall

#14

On 21 nov, 14:34, JOG <j... (AT) cs (DOT) nott.ac.uk> wrote:

Quote:

Word up CDT. How the devil are you all? Well, I return with a question
that as ever highlights my complete lack of formal mathematical
training, and in light of knowing no logicians in my daily life (funny
that), I was hoping that one of you kind folks might be able to
advise:

Say I had a set of 3 encoded propositions:
R := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)}, {(Name,
Harry)} }

(note that Harry's Age is missing, so instead of adding a null, i've
intentionally just left the attribute out. Just ride with such oddness
for now if you would.)

What if I deigned to create a simple 'adults' subset of this set of
propositions, by creating a predicate that only returned the elements,
p, which contained an age attribute greater than 18. Could I state
this as (where E signifies set membership):

Adults := { p E R | EXISTSx ( x > 18 && (Age, x) E p ) }

My question obviously hinges around Harry's missing age attribute. In
this case would the EXISTSx (...) part of the set's intension simply
return a FALSE, or will I end up in the quagmire of 3VL with an
UNDEFINED? My instinct is that I am still in 2VL given there is no
null floating about, but since the recent, excellent discussions of
Jan's DEF operator, and having delved into beeson's logic of partial
terms, I am not at all confident.

Any comments are much appreciated, and regards to all, Jim.
I do not understand how you can already go to any form of subtyping

without a valid proposition allowing to establish relation R? I
suggest decomposing R before attempting to constitute Adults such
as...

R := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)}, {(Name,
Harry)} }
into ....(I assume Name as being a unique identifier)
RName:= { {(Name, Tom)}, {(Name, Dick)}, {(Name,
Harry)} } -->p1
and
RAges := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)} } -->
p2
You may then constitute....

Adults := { p1 E R1 | EXISTSx ( x > 18 && (Age, x) E p1 ) }

#15

"Jan Hidders" <hidders (AT) gmail (DOT) com> wrote

Quote:

On 23 nov, 12:31, "David Cressey" <cresse... (AT) verizon (DOT) net> wrote:
"JOG" <j... (AT) cs (DOT) nott.ac.uk> wrote in message

news:ea3deb47-3697-4eb5-8b4f-34cf2ef2ec25 (AT) t47g2000hsc (DOT) googlegroups.com...

On Nov 21, 2:22 pm, "David Cressey" <cresse... (AT) verizon (DOT) net> wrote:

Quote:

"JOG" <j... (AT) cs (DOT) nott.ac.uk> wrote in message

news:84c11971-6500-48e4-ba0f-b8b659f390da (AT) d61g2000hsa (DOT) googlegroups.com...

Word up CDT. How the devil are you all? Well, I return with a
question
that as ever highlights my complete lack of formal mathematical
training, and in light of knowing no logicians in my daily life
(funny
that), I was hoping that one of you kind folks might be able to
advise:

Say I had a set of 3 encoded propositions:
R := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)},
{(Name,
Harry)} }

(note that Harry's Age is missing, so instead of adding a null,
i've
intentionally just left the attribute out. Just ride with such
oddness
for now if you would.)

What if I deigned to create a simple 'adults' subset of this set
of
propositions, by creating a predicate that only returned the
elements,
p, which contained an age attribute greater than 18. Could I state
this as (where E signifies set membership):

Adults := { p E R | EXISTSx ( x > 18 && (Age, x) E p ) }

My question obviously hinges around Harry's missing age attribute.
In
this case would the EXISTSx (...) part of the set's intension
simply
return a FALSE, or will I end up in the quagmire of 3VL with an
UNDEFINED? My instinct is that I am still in 2VL given there is
no
null floating about, but since the recent, excellent discussions
of
Jan's DEF operator, and having delved into beeson's logic of
partial
terms, I am not at all confident.

Any comments are much appreciated, and regards to all, Jim.

I'm no mathematician or logician, but I'll answer anyway.

To me, it dpends on whether the relationship (Name, Age) follows
the
open
world assumption or the closed world assumption.

While I was only really concerned about whether my logic statements
are sticking to 2VL internally, you've sent me off at a tangent here
because CWA is one of my bugbears. Imho its at best silly, and at
worst contradictory. Take relations such as:

Weather_is = { condition: Hot }
Weather_is_not = { condition: Cold }
Domain = {Hot, Cold}

Perfectly fine with full information, and a constraint that a
condition can't appear in both. And I can happily extrapolate from CWA
from the first relation that: !is(condition:cold)), and from the
second !is_not(condition:hot). Nice...

...until we're faced missing information. If both relations are empty
(because we just don't have the data say), then CWA tells me that:
!Weather_is(condition:Hot) and !Weather_is_not(condition:Hot). It is
both hot and not hot. Genius. I don't see how CWA based directly on
what propositions state can ever be justified for a system working in
the real world (TM).

In theory, you never have to be concerned about missing information. In
practice, you do.

I know that's not how you meant "in theory", but in current research
in database theory this is actually a hot topic, especially in
connection with missing or uncertain information (including null
values) and also with data integration where the classical CWA almost
never fully applies. There's a whole spectrum between the full CWA and
the OWA that go from stronger assumption to weaker assumptions. It can
for example be that the CWA applies only to certain selections or
projections of the relation.

I accept the correction.

While I have no handle on the theoretical aspects of uncertainty (other
than a certain minimal experience with Shannon's entropy model), I'd like
to suggest that, in practice, people deal with uncertain or inadequate
iinformation all the time. Their coping mechanisms may rely on intuition or
educated intuition more than on formalisms, but their responses are
extraordinarily adapted.

Contrast the folowing:

"You don't have a reservation on this flight. Your name isn't coming up on
my computer."

"When I bring your name up on my screen, the date of birth is blank. You
were obviously never born."

Except in jest, you would never expect the second response from an ordinary
person.

Quote:

The best we can hope for is that database will not amplify the mistakes
people make, at least not very often.

That seems to me almost unavoidable. Any system that enhances your
power is likely to amplify the magnitude of your mistakes. The best we
can do is to make the people that deal with these systems aware of
these dangers and train them well. They should hire more database
professors. ;-)

While some amplification is unavoidable, I claim that there are systems
that amplify people's correct thinking relatively more, and amplify
people's mistakes relatively less than other systems. I think this is one
measure of a system's "goodness". While I wouldn't want to take this to an
extreme, and claim that any system is "idiot proof", there are some
systems that go further than others in this direction.

I don't think ordinary people need database professors. They need
information age kindergarten teachers. It's not the same skill.

Quote:

-- Jan Hidders

#16

David Cressey wrote:

Quote:

"Jan Hidders" <hidders (AT) gmail (DOT) com> wrote in message
news:46b18d2e-3a66-457d-b4ab-b7c98753cd2b (AT) l1g2000hsa (DOT) googlegroups.com...

On 23 nov, 12:31, "David Cressey" <cresse... (AT) verizon (DOT) net> wrote:

"JOG" <j... (AT) cs (DOT) nott.ac.uk> wrote in message

news:ea3deb47-3697-4eb5-8b4f-34cf2ef2ec25 (AT) t47g2000hsc (DOT) googlegroups.com...
On Nov 21, 2:22 pm, "David Cressey" <cresse... (AT) verizon (DOT) net> wrote:

"JOG" <j... (AT) cs (DOT) nott.ac.uk> wrote in message

news:84c11971-6500-48e4-ba0f-b8b659f390da (AT) d61g2000hsa (DOT) googlegroups.com...

Word up CDT. How the devil are you all? Well, I return with a

question

that as ever highlights my complete lack of formal mathematical
training, and in light of knowing no logicians in my daily life

(funny

that), I was hoping that one of you kind folks might be able to
advise:

Say I had a set of 3 encoded propositions:
R := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)},

{(Name,

Harry)} }

(note that Harry's Age is missing, so instead of adding a null,

i've

intentionally just left the attribute out. Just ride with such

oddness

for now if you would.)

What if I deigned to create a simple 'adults' subset of this set

of

propositions, by creating a predicate that only returned the

elements,

p, which contained an age attribute greater than 18. Could I state
this as (where E signifies set membership):

Adults := { p E R | EXISTSx ( x > 18 && (Age, x) E p ) }

My question obviously hinges around Harry's missing age attribute.

In

this case would the EXISTSx (...) part of the set's intension

simply

return a FALSE, or will I end up in the quagmire of 3VL with an
UNDEFINED? My instinct is that I am still in 2VL given there is

no

null floating about, but since the recent, excellent discussions

of

Jan's DEF operator, and having delved into beeson's logic of

partial

terms, I am not at all confident.

Any comments are much appreciated, and regards to all, Jim.

I'm no mathematician or logician, but I'll answer anyway.

To me, it dpends on whether the relationship (Name, Age) follows

the

open

world assumption or the closed world assumption.

While I was only really concerned about whether my logic statements
are sticking to 2VL internally, you've sent me off at a tangent here
because CWA is one of my bugbears. Imho its at best silly, and at
worst contradictory. Take relations such as:

Weather_is = { condition: Hot }
Weather_is_not = { condition: Cold }
Domain = {Hot, Cold}

Perfectly fine with full information, and a constraint that a
condition can't appear in both. And I can happily extrapolate from CWA
from the first relation that: !is(condition:cold)), and from the
second !is_not(condition:hot). Nice...

...until we're faced missing information. If both relations are empty
(because we just don't have the data say), then CWA tells me that:
!Weather_is(condition:Hot) and !Weather_is_not(condition:Hot). It is
both hot and not hot. Genius. I don't see how CWA based directly on
what propositions state can ever be justified for a system working in
the real world (TM).

In theory, you never have to be concerned about missing information. In
practice, you do.

I know that's not how you meant "in theory", but in current research
in database theory this is actually a hot topic, especially in
connection with missing or uncertain information (including null
values) and also with data integration where the classical CWA almost
never fully applies. There's a whole spectrum between the full CWA and
the OWA that go from stronger assumption to weaker assumptions. It can
for example be that the CWA applies only to certain selections or
projections of the relation.

I accept the correction.

While I have no handle on the theoretical aspects of uncertainty (other
than a certain minimal experience with Shannon's entropy model), I'd like
to suggest that, in practice, people deal with uncertain or inadequate
iinformation all the time. Their coping mechanisms may rely on intuition or
educated intuition more than on formalisms, but their responses are
extraordinarily adapted.

Contrast the folowing:

"You don't have a reservation on this flight. Your name isn't coming up on
my computer."

"When I bring your name up on my screen, the date of birth is blank. You
were obviously never born."

Except in jest, you would never expect the second response from an ordinary
person.

The best we can hope for is that database will not amplify the mistakes
people make, at least not very often.

That seems to me almost unavoidable. Any system that enhances your
power is likely to amplify the magnitude of your mistakes. The best we
can do is to make the people that deal with these systems aware of
these dangers and train them well. They should hire more database
professors. ;-)

While some amplification is unavoidable, I claim that there are systems
that amplify people's correct thinking relatively more, and amplify
people's mistakes relatively less than other systems. I think this is one
measure of a system's "goodness". While I wouldn't want to take this to an
extreme, and claim that any system is "idiot proof", there are some
systems that go further than others in this direction.

According to my mug, one of Troutman's Laws is "If the input editor has
been designed to reject all bad input, an ingenious idiot will discover
a method to get bad data past it."

That's the closest to relevant I could get from the mug.

Quote:

I don't think ordinary people need database professors. They need
information age kindergarten teachers. It's not the same skill.

#17

On Nov 23, 9:44 pm, Cimode <cim... (AT) hotmail (DOT) com> wrote:

Quote:

On 21 nov, 14:34, JOG <j... (AT) cs (DOT) nott.ac.uk> wrote:

Word up CDT. How the devil are you all? Well, I return with a question
that as ever highlights my complete lack of formal mathematical
training, and in light of knowing no logicians in my daily life (funny
that), I was hoping that one of you kind folks might be able to
advise:

Say I had a set of 3 encoded propositions:
R := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)}, {(Name,
Harry)} }

(note that Harry's Age is missing, so instead of adding a null, i've
intentionally just left the attribute out. Just ride with such oddness
for now if you would.)

What if I deigned to create a simple 'adults' subset of this set of
propositions, by creating a predicate that only returned the elements,
p, which contained an age attribute greater than 18. Could I state
this as (where E signifies set membership):

Adults := { p E R | EXISTSx ( x > 18 && (Age, x) E p ) }

My question obviously hinges around Harry's missing age attribute. In
this case would the EXISTSx (...) part of the set's intension simply
return a FALSE, or will I end up in the quagmire of 3VL with an
UNDEFINED? My instinct is that I am still in 2VL given there is no
null floating about, but since the recent, excellent discussions of
Jan's DEF operator, and having delved into beeson's logic of partial
terms, I am not at all confident.

Any comments are much appreciated, and regards to all, Jim.

I do not understand how you can already go to any form of subtyping
without a valid proposition allowing to establish relation R?

Well first, I'm not sure that I'd refer to specifying a subset of
propositions as 'subtyping', second, all the propositions are valid as
far as I can tell (their pretty simple ones after all), and third, R
isn't a relation. Regards, J.

Quote:

I suggest decomposing R before attempting to constitute Adults such
as...

R := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)}, {(Name,
Harry)} }
into ....(I assume Name as being a unique identifier)
RName:= { {(Name, Tom)}, {(Name, Dick)}, {(Name,
Harry)} } -->p1
and
RAges := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)} } --
p2
You may then constitute....

Adults := { p1 E R1 | EXISTSx ( x > 18 && (Age, x) E p1 ) }

#18

On 24 nov, 02:03, JOG <j... (AT) cs (DOT) nott.ac.uk> wrote:

Quote:

On Nov 23, 9:44 pm, Cimode <cim... (AT) hotmail (DOT) com> wrote:

On 21 nov, 14:34, JOG <j... (AT) cs (DOT) nott.ac.uk> wrote:

Word up CDT. How the devil are you all? Well, I return with a question
that as ever highlights my complete lack of formal mathematical
training, and in light of knowing no logicians in my daily life (funny
that), I was hoping that one of you kind folks might be able to
advise:

Say I had a set of 3 encoded propositions:
R := { {(Name, Tom), (Age, 42)}, {(Name, Dick), (Age, 16)}, {(Name,
Harry)} }

(note that Harry's Age is missing, so instead of adding a null, i've
intentionally just left the attribute out. Just ride with such oddness
for now if you would.)

What if I deigned to create a simple 'adults' subset of this set of
propositions, by creating a predicate that only returned the elements,
p, which contained an age attribute greater than 18. Could I state
this as (where E signifies set membership):

Adults := { p E R | EXISTSx ( x > 18 && (Age, x) E p ) }

My question obviously hinges around Harry's missing age attribute. In
this case would the EXISTSx (...) part of the set's intension simply
return a FALSE, or will I end up in the quagmire of 3VL with an
UNDEFINED? My instinct is that I am still in 2VL given there is no
null floating about, but since the recent, excellent discussions of
Jan's DEF operator, and having delved into beeson's logic of partial
terms, I am not at all confident.

Any comments are much appreciated, and regards to all, Jim.

I do not understand how you can already go to any form of subtyping
without a valid proposition allowing to establish relation R?

Well first, I'm not sure that I'd refer to specifying a subset of
propositions as 'subtyping'
It's true that when one assumes that a set of valid propositions ought

to respect a close world assumption, one tends to attempt to seek a
matching relation. I apologize for this relational bias. Given the
fact that I do have this bias I obviously tend to perceive Adults as a
subtype of decomposed relation RAges.

Quote:

, second, all the propositions are valid as
far as I can tell (their pretty simple ones after all),
Depends what you imply by *valid*...

In the relational perspective, the fact that they respond to binary
logic is a necessary but not sufficient criteria to consider them as
valid.

Quote:

and third, R
isn't a relation. Regards, J.
Yep...I got this one...I think the problem is easy solved once you

embrace relational framework...Answers have been brought to this
problem.. I am curious as to what xactly you are trying to
establish...

Regard...

Regards...

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Undefinedness

comp.databases.theory comp.databases.theory

Re: Undefinedness - 11-23-2007 , 05:31 AM

Re: Undefinedness - 11-23-2007 , 12:06 PM

Re: Undefinedness - 11-23-2007 , 02:25 PM

Re: Undefinedness - 11-23-2007 , 03:44 PM

Re: Undefinedness - 11-23-2007 , 04:27 PM

Re: Undefinedness - 11-23-2007 , 04:59 PM

Re: Undefinedness - 11-23-2007 , 07:03 PM

Re: Undefinedness - 11-28-2007 , 06:00 PM