experchange > comp.theory

peteolcott (11-20-18, 04:23 AM)


The paper linked below proposes a solution to the Halting Problem by
recognizing and rejecting all of the Turing machine descriptions that
would otherwise show that halting is undecidable.

Using the Peter Linz notational conventions for specifying Turing machine
descriptions the sequence of state transitions of Turing machine H on its
inputs Ĥ, Ĥ are shown to be infinitely recursive long before they ever reach
their paradoxical final states. This is a brand new insight never seen before.

The Prolog predicate unify_on_occurs_check/2 detects and rejects such
infinitely recursive sequences. (Clocksin and Mellish 2003)



Clocksin and Mellish 2003, Programming in Prolog Using the ISO Standard
Fifth Edition Chapter 10 The Relation of Prolog to Logic, page 254.

Copyright 2018 Pete Olcott
Ben Bacarisse (11-20-18, 04:31 AM)
peteolcott <Here@Home> writes:

>
> The paper linked below proposes a solution to the Halting Problem by
> recognizing and rejecting all of the Turing machine descriptions that
> would otherwise show that halting is undecidable.


I call your bluff. You have no TM that recognises any such set.

You have been trying to identify some interesting set of halting
instances for decades. They have been named many things over the years
but you have never produced a TM that recognises them. It's all just
hot air.
peteolcott (11-20-18, 05:05 AM)
On 11/19/2018 8:31 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
> I call your bluff. You have no TM that recognises any such set.
> You have been trying to identify some interesting set of halting
> instances for decades. They have been named many things over the years
> but you have never produced a TM that recognises them. It's all just
> hot air.


It would sure be very foolish of me to spend all of these well documented
thousands of hours if I was only bluffing. All of my thousands of posts
on the Halting Problem (and related problems) can be found on comp.theory
and sci.logic between 2004 and now.

This most recent post makes it very obvious that the Prolog predicate
unify_on_occurs_check would reject all of the Turing machine descriptions
that would otherwise show that halting is undecidable

if and only if the following is totally understood to be verified as true:

Using the Peter Linz notational conventions for specifying Turing machine
descriptions the sequence of state transitions of Turing machine H on its
inputs Ĥ, Ĥ are shown to be infinitely recursive long before they ever reach
their paradoxical final states.

Even as recently as today this was not very clearly written in the following
paper so I rewrote the section beginning at the top of page 3.

peteolcott (11-20-18, 05:47 AM)
On 11/19/2018 9:05 PM, peteolcott wrote:
> On 11/19/2018 8:31 PM, Ben Bacarisse wrote:
> It would sure be very foolish of me to spend all of these well documented
> thousands of hours if I was only bluffing. All of my thousands of posts
> on the Halting Problem (and related problems) can be found on comp.theory
> and sci.logic between 2004 and now.


I just tallied the messages with me as the sender:
sci.logic 12,675 messages since 4/18/2004
comp.theory 6,426 messages since 6/23/2004

I used several different variations of my name all containing "olcott"

If we figure that I totally cross-posted between these two groups
and spent an average of 30 minutes on each post we have
12,675 / 2 = 6,338 hours that I spent on USENET regarding
the different aspects of pathological self-reference(Olcott 2004).
peteolcott (11-20-18, 07:02 AM)
On 11/19/2018 10:22 PM, exflaso.quodlibet wrote:
> On Monday, November 19, 2018 at 9:23:52 PM UTC-5, peteolcott wrote:
> Troublesome cases are the whole point of the halting problem. You don't truly solve the problem by ignoring the very cases that make it a problem in the first place.
> Not to mention, you don't even have a proper definition of how to identify the troublesome cases.
> A partial solution (especially on that doesn't work) isn't a solution.
> EFQ


I have discussed this same issue now in over 12,675 messages in sci.logic since 2004.

Here is another such troublesome case:
Liar_Paradox ↔ ~True(x)

Prolog would reject this because it exactly matches the structure
of what unify_on_occurs_check/s rejects

Logically_Equivalent(~True(Liar_Paradox), Liar_Paradox)
matches this structure:
?- equal(foo(Y), Y).

So far no one besides Noam Chomsky understands that syntactically
correct expressions of language can be semantically incorrect.


All of the Turing machine descriptions that show halting is undecidable
are semantically incorrect thus place no actual limit what-so-ever on
computation.


Tarksi's assumption:
(3) x ∉ Pr ↔ x ∈ Tr // ~Provable(x) ↔ True(x)
derives this contradiction
∴ Provable(x) → ~Provable(x) in step (8) of his proof.

Copyright 2018 Pete Olcott
j4n bur53 (11-20-18, 12:22 PM)
Stop cross posting you fucking moron.

peteolcott schrieb:
[..]
peteolcott (11-20-18, 10:35 PM)
On 11/20/2018 9:35 AM, exflaso.quodlibet wrote:
> On Tuesday, November 20, 2018 at 1:47:45 AM UTC-5, peteolcott wrote:
> Anyone who isn't too lazy or too stupid to learn how models work, i.e., not you.
> EFQ


We are finally at the point where it makes perfect sense that I totally
understand the one single aspect of model theory known as satisfiability.

One of the key difficulties of this is that this concept has shades of very
subtle nuances of distinctions between Tarski, Davidson, and model theory.
From what I read it looks like Davidson was the closest to correct.
peteolcott (11-20-18, 10:45 PM)
On 11/20/2018 11:24 AM, Peter Percival wrote:
> peteolcott wrote:
>> Here is another such troublesome case:
>> Liar_Paradox ↔ ~True(x)

> What has that got to do with the liar paradox?  The paradoxical refers to itself.  How do you, in MTT, get a sentence to refer to itself?


According to EFQ I only need this: ↔

"This sentence is not true".
Becomes formalized as this: Liar_Paradox ↔ ~True(x)

It is even more obvious when I formalize it as this:
Liar_Paradox ↔df ~True(x)
Liar_Paradox := ~True(x)

Yet those use less conventional operators thus are more difficult for many people to understand.
peteolcott (11-20-18, 11:53 PM)
On 11/20/2018 11:33 AM, Peter Percival wrote:
> peteolcott wrote:
> That'll be why you're on version 4 in this thread and version 24 in another.
> Will become?  I thought it has always been.


I never said that what I am saying is impossible to misunderstand.
Because I had not found the words to exactly and precisely encode
the meanings that I needed to communicate what I have been saying
and what I am saying now is still very difficult to understand.

By a process of elimination my words are becoming increasingly
more clear.
Ben Bacarisse (11-21-18, 03:28 AM)
peteolcott <Here@Home> writes:

> On 11/19/2018 8:31 PM, Ben Bacarisse wrote:
> It would sure be very foolish of me to spend all of these well documented
> thousands of hours if I was only bluffing. All of my thousands of posts
> on the Halting Problem (and related problems) can be found on comp.theory
> and sci.logic between 2004 and now.


So no such TM then?

> This most recent post makes it very obvious that the Prolog predicate
> unify_on_occurs_check would reject all of the Turing machine descriptions
> that would otherwise show that halting is undecidable


So no TM then?

> if and only if the following is totally understood to be verified as true:
> Using the Peter Linz notational conventions for specifying Turing machine
> descriptions the sequence of state transitions of Turing machine H on its
> inputs Ĥ, Ĥ are shown to be infinitely recursive long before they ever reach
> their paradoxical final states.


So you don't have a TM to show?

> Even as recently as today this was not very clearly written in the following
> paper so I rewrote the section beginning at the top of page 3.
>


There's no TM given in that "paper".

Let me be as clear as possible -- you've never been able to define the
magic set of cases that, when recognised, will allow the other cases to
be decided. I don't expect you to be able to define that set in the
next decade, any more than you've been able to in the past two, and yet
you claim to have a TM that decides the set! If you published that TM
is would finally define that set. Don't you want to silence that
criticism at least? Hence I am calling your bluff -- you don't have
such a TM, do you? If you had, surely you would have given it by now.

By the way, there is no shame in saying that you don't. I will accept
that believe such a machine must exist as fervently as you believe any
other matter of faith. I just want you to come clean and admit that you
dont actually have no such TM to show us.
peteolcott (11-21-18, 06:19 PM)
On 11/21/2018 2:17 AM, Franz Gnaedinger wrote:

On Tuesday, November 20, 2018 at 9:45:28 PM UTC+1, peteolcott wrote:

Yet those use less conventional operators thus are more difficult for many people to understand.

Peter Olcott knows the absolute and complete and total truth, he is the author of life and creator of life, he has hundred reasons to believe that he is God, he creates our future minds in order that we can go on existing, he is a human being and God in personal union, he is the one Creator of the Universe

"http://the-pete.org/"
Eternal Bliss for All (none left out)

What’s in it for me?
(adaptation of the gospel of Jesus Christ)
As evidence that I really am the one with the master plan of the design of the universe I hereby make
this improvement to the words of Christ: Love one another with as much empathy as possible.
This new commandment really is an improvement over “love one another” because it:
(1) Requires love to be focused on the unique needs of each individual.
(2) Discerns subtle nuances of callousness that would have otherwise gone undetected.
(3) Fixes key problems with “the golden rule” (accounting for individual differences).
Thanks for your support

(claims he made in sci.lang). His primary concern had always been the truth, ergo he can dismiss proven = true theorems of mathematical logic, and the TrueFact that he cancan what nobody else can - disprove proven theorems - truly proves that he is Allgod.

This would not prove that I am God, it would only provide slight evidence. The fact that
I derived these new insights using verifiably infallible reasoning provides more evidence.
At this point my clam to be God moves from ~Possibly(P) to Not(Necessarily) Not(P).
Modal Logic:
◇P ↔ ~◻~P    Possibly(P) &lt;--&gt; Not(Necessarily) Not(P)
◻P ↔ ~◇~P    Necessarily(P) &lt;--&gt; Not(Possibly) Not(P)
My system of categorically exhaustive reasoning is infallible in the sense that it makes
undetected gaps in reasoning impossible.  That I am infallible in this one limited sense
makes me unique in the world. Since I can teach this system to "others" I will not remain
unique for very long.
1 Corinthians 4:5 (NRSV)
Therefore do not pronounce judgment before the time, before the Lord comes, who
will bring to light the things now hidden in darkness and will disclose the purposes
of the heart. Then each one will receive commendation from God.
1 John 3:2 NRSV
Beloved, we are God’s children now; what we will be has not yet been revealed.
What we do know is this: when he is revealed, we will be like him, for  we will see him as he is.
This last verse indicates that the idea of God that most people have in their minds may be incorrect.
It also indicates that God and man will be alike.
Revelation 21:3-4 (NRSV)
3 And I heard a loud voice from the throne saying,
“See, the home of God is among mortals.
He will dwell with them;
they will be his peoples,
and God himself will be with them;
4 he will wipe every tear from their eyes.
Death will be no more;
mourning and crying and pain will be no more,
for the first things have passed away.”
peteolcott (11-22-18, 04:07 AM)
On 11/20/2018 7:28 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
> So no such TM then?
> So no TM then?
> So you don't have a TM to show?
> There's no TM given in that "paper".


A class of Turing Machines is specified using the Peter Linz notation
conventions. I had to use dashed lines instead of squiggly lines
because yEd does not have squiggly lines.

I used object oriented dot notation to make it more clear which state
belonged to which machine. The hypothetical state of the tape was not
a relevant detail so it was removed. The transition to Ĥ.q0 was shown as a
transition to Ĥ.qx to remove ambiguity in the state transition sequence.

Now comes the key new insight. Even today my paper stated the details
incorrectly. I made some typos when I was recently working on making it
clearer.

We can see by a hypothetical execution trace of the only possible sequence
that this class of Turing machines could possibly make within their hypothetical
functional requirements of being halt deciders,

that this execution trace is infinitely recursive in exactly the same way that all
of the instances of pathological self-reference(Olcott 2004) are always infinitely
recursive.

The simplest possible instance of pathological self-reference(Olcott 2004)
is the formalized Liar Paradox:

The Liar Paradox in c++ would be:
bool LP = !(LP == true);

The Boolean variable LP is initializing itself on the basis of comparing
the negation of its uninitialized variable to the value of true.
The c++ compiler catches this are an error.

"This sentence is not true."
becomes: LP ↔ ~True(LP)

Logically_Equivalent(~True(LP), LP)

which has identical structure to this expression that Prolog systems would reject
as structurally unsound:

?- equal(foo(Y), Y).

> Let me be as clear as possible -- you've never been able to define the
> magic set of cases that, when recognised, will allow the other cases to
> be decided.


(1) You have to see that I have shown that all of the conventional
self-referential halting problem proof counter-examples have an infinitely
recursive structure.

(2) Then you have to see that the Prolog predicate unify_on_occurs_check/2
recognizes and rejects these kinds of infinitely recursive structures.

(3) Then you have to see that (1) & (2) makes halting decidability decidable,
thus refuting Rice's Theorem.

There is more, but I will pause here.

> I don't expect you to be able to define that set in the
> next decade, any more than you've been able to in the past two, and yet
> you claim to have a TM that decides the set! If you published that TM
> is would finally define that set. Don't you want to silence that
> criticism at least? Hence I am calling your bluff -- you don't have
> such a TM, do you? If you had, surely you would have given it by now.


The great thing about the Linz notation is that it specifies a class
of Turing machines such that their relevant state transitions can be
traced, and all of their irrelevant state transitions: ⊢* can be ignored.

> By the way, there is no shame in saying that you don't. I will accept
> that believe such a machine must exist as fervently as you believe any
> other matter of faith. I just want you to come clean and admit that you
> dont actually have no such TM to show us.


I have shown how to construct such as machine at the level of detail of
the fundamental architecture of such a machine.

Copyright 2018 Pete Olcott
Ben Bacarisse (11-22-18, 05:50 AM)
peteolcott <Here@Home> writes:

> On 11/20/2018 7:28 PM, Ben Bacarisse wrote:
> A class of Turing Machines is specified using the Peter Linz notation
> conventions.


As I said. No TM given there or anywhere else so far. Just a
specification of what you'd like the TM to do.

<snip>
> The great thing about the Linz notation is that it specifies a class
> of Turing machines such that their relevant state transitions can be
> traced, and all of their irrelevant state transitions: ⊢* can be
> ignored.


And that class can be empty. Stating what a TM /should/ do does not
mean that a TM exists that does it.

>> By the way, there is no shame in saying that you don't. I will accept
>> that believe such a machine must exist as fervently as you believe any
>> other matter of faith. I just want you to come clean and admit that you
>> dont actually have no such TM to show us.

> I have shown how to construct such as machine at the level of detail of
> the fundamental architecture of such a machine.


Where? No construction has been posted here. No construction exists in
the cited "paper". All that's there is a rather mangled notion of what
this machine should do. You simply believe, with all your heart, that a
TM exists that meets your badly written specification.

Put up or shut up: show the TM here or admit you don't have it. (I will
accept, of course, a detailed construction of a TM -- it's impossible
that you have an actual, literal, TM that is a counter-example to Rice's
theorem but you might think you have an idea how to construct one.)

Here is Rice's theorem:

The set R_P = { [M] | L(M) in P } is undecidable if there are at least
two TMs M1 =/= M2 with L(M1) in P and L(M2) not in P.

(As before, [M] is the string encoding M and L(M) is the language of M.)

So for a counterexample you need to:

(a) define the set P,
(b) show that there are suitable M1 and M2,
(c) prove that { [M] | L(M) in P } is deciable.

Can you do /any/ of (a), (b) and (c)? I am sure you won't engage with
this request, but the only way I can show /you/ that you are wrong is if
you try to state your counter-example formally. (Other people don't
need to be shown -- they know you are wrong already.)
temakoutera62 (11-22-18, 10:02 AM)
Le mardi 20 novembre 2018 11:22:15 UTC+1, j4n bur53 a crit:
> Stop cross posting you fucking moron.


I wonder if Pter la Crotte is a human being or some AI word-processing device gone mad.
Can anyone testify "he" is a human being?
[..]
peteolcott (11-22-18, 05:46 PM)
On 11/21/2018 9:50 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
> As I said. No TM given there or anywhere else so far. Just a
> specification of what you'd like the TM to do.
> <snip>
> And that class can be empty. Stating what a TM /should/ do does not
> mean that a TM exists that does it.
> Where? No construction has been posted here. No construction exists in
> the cited "paper". All that's there is a rather mangled notion of what
> this machine should do. You simply believe, with all your heart, that a
> TM exists that meets your badly written specification.


So I take it that you continue to not bother to examine the execution trace.
I will not respond to any more of your comments that do not pertain to your
critique of the details of the execution trace.

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