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devel / comp.theory / Re: On recursion and infinite recursion (reprise)

SubjectAuthor
* On recursion and infinite recursion (reprise)Mr Flibble
+* On recursion and infinite recursion (reprise)olcott
|+* On recursion and infinite recursion (reprise)Ben
||`* On recursion and infinite recursion (reprise)olcott
|| `* On recursion and infinite recursion (reprise)Ben
||  `* H(P,P) == false is correctolcott
||   `* H(P,P) == false is correctBen
||    `* H(P,P) == false is correctolcott
||     `* H(P,P) == false is correctBen
||      `* H(P,P) == false is correctolcott
||       `* H(P,P) == false is correctBen
||        `* H(P,P) == false is correct [ verified facts ]olcott
||         +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         |`* H(P,P) == false is correct [ verified facts ]olcott
||         | +* H(P,P) == false is correct [ verified facts ]André G. Isaak
||         | |`* H(P,P) == false is correct [ verified facts ]olcott
||         | | `* H(P,P) == false is correct [ verified facts ]André G. Isaak
||         | |  `* H(P,P) == false is correct [ verified facts ]olcott
||         | |   +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |   |`* H(P,P) == false is correct [ verified facts ]olcott
||         | |   | `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |   |  `* H(P,P) == false is correct [ verified facts ]olcott
||         | |   |   `- H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |   `* H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |    `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |     `* H(P,P) == false is correct [ verified facts ]olcott
||         | |      `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |       `* H(P,P) == false is correct [ verified facts ]olcott
||         | |        `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |         `- H(P,P) == false is correct [ verified facts ]olcott
||         | +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |`* H(P,P) == false is correct [ verified facts ]olcott
||         | | `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |  `* H(P,P) == false is correct [ verified facts ]olcott
||         | |   +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |   |`* H(P,P) == false is correct [ verified facts ]olcott
||         | |   | +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |   | |`* H(P,P) == false is correct [ verified facts ]olcott
||         | |   | | `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |   | |  `- H(P,P) == false is correct [ verified facts ]olcott
||         | |   | `- H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |   `* H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |    `* H(P,P) == false is correct [ verified facts ]Malcolm McLean
||         | |     +* H(P,P) == false is correct [ verified facts ]Ben
||         | |     |`* H(P,P) == false is correct [ verified facts ]olcott
||         | |     | `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |     |  `* H(P,P) == false is correct [ verified facts ]olcott
||         | |     |   `- H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |     `* H(P,P) == false is correct [ verified facts ]olcott
||         | |      `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |       `* H(P,P) == false is correct [ verified facts ]olcott
||         | |        `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |         `* H(P,P) == false is correct [ verified facts ]olcott
||         | |          `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |           `* H(P,P) == false is correct [ verified facts ]olcott
||         | |            `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |             `* H(P,P) == false is correct [ verified facts ]olcott
||         | |              +* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |              |`* H(P,P) == false is correct [ verified facts ]olcott
||         | |              | `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |              |  +- H(P,P) == false is correct [ verified facts ]olcott
||         | |              |  `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |              |   +- H(P,P) == false is correct [ verified facts ]olcott
||         | |              |   `* H(P,P) == false is correct [ verified facts ]Dennis Bush
||         | |              |    `* H(P,P) == false is correct [ verified facts ]olcott
||         | |              |     `- H(P,P) == false is correct [ verified facts ]Richard Damon
||         | |              `* H(P,P) == false is correct [ verified facts ]André G. Isaak
||         | |               `* H(P,P) == false is correct [ verified facts ]olcott
||         | |                `* H(P,P) == false is correct [ verified facts ]André G. Isaak
||         | |                 `- H(P,P) == false is correct [ verified facts ]olcott
||         | `- H(P,P) == false is correct [ verified facts ]Richard Damon
||         `* H(P,P) == false is correct [ verified facts ]Ben
||          `* H(P,P) == false is correct [ verified facts ]olcott
||           +* H(P,P) == false is correct [ verified facts ]Python
||           |`* H(P,P) == false is correct [ verified facts ]olcott
||           | `- H(P,P) == false is correct [ verified facts ]Python
||           +* H(P,P) == false is correct [ verified facts ]Ben
||           |+- H(P,P) == false is correct [ verified facts ]olcott
||           |+* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           ||`* H(P,P) == false is correct [ Simple TM Interpreter ]Ben
||           || `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           ||  `* H(P,P) == false is correct [ Simple TM Interpreter ]Ben
||           ||   +* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           ||   |`* H(P,P) == false is correct [ Simple TM Interpreter ]Ben
||           ||   | `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           ||   |  `- H(P,P) == false is correct [ Simple TM Interpreter ]Ben
||           ||   `- H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |`* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           | `* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  +* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |`* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  | `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |  `* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  |   `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |    `* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  |     `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |      `* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  |       `* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |        `* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  |         +* H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           |  |         |`* H(P,P) == false is correct [ Simple TM Interpreter ]André G. Isaak
||           |  |         `* H(P,P) == false is correct [ Simple TM Interpreter ]Ben
||           |  `- H(P,P) == false is correct [ Simple TM Interpreter ]olcott
||           +- H(P,P) == false is correct [ verified facts ]Richard Damon
||           `* H(P,P) == false is correct [ verified facts ]Mikko
|`* On recursion and infinite recursion (reprise)Mikko
+* On recursion and infinite recursion (reprise)Richard Damon
+* On recursion and infinite recursion (reprise)Mikko
`* On recursion and infinite recursion (reprise)Mikko

Pages:123456789
Re: H(P,P) == false is correct [ Simple TM Interpreter ]

<8735hkx5al.fsf@bsb.me.uk>

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https://www.novabbs.com/devel/article-flat.php?id=31905&group=comp.theory#31905

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From: ben.use...@bsb.me.uk (Ben)
Newsgroups: comp.theory
Subject: Re: H(P,P) == false is correct [ Simple TM Interpreter ]
Date: Sun, 08 May 2022 00:59:46 +0100
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 by: Ben - Sat, 7 May 2022 23:59 UTC

olcott <NoOne@NoWhere.com> writes:

> On 5/7/2022 6:01 PM, Ben wrote:
>> olcott <polcott2@gmail.com> writes:
>>
>>> On 5/6/2022 8:57 PM, Ben wrote:
>>>> olcott <polcott2@gmail.com> writes:
>>>>
>>>>> On 5/6/2022 6:36 AM, Ben wrote:
>>>>>> olcott <polcott2@gmail.com> writes:
>>>>>>
>>>>>>> On 5/5/2022 9:35 PM, Ben wrote:
>>>>>>>> olcott <polcott2@gmail.com> writes:
>>>>
>>>>>>>>> struct Quintuple
>>>>>>>>> {
>>>>>>>>> u32 state;
>>>>>>>>> u32 symbol;
>>>>>>>>> u32 write_symbol;
>>>>>>>>> u32 next_state;
>>>>>>>>> u8 Tape_Head_Move;
>>>>>>>>> }
>>>>>>>>>
>>>>>>>>> std::set<Quintuple> States;
>>>>>>>> Why is a set of objects that are not states called "States"?
>>>>>>>
>>>>>>> They are states, what did you think that states are?
>>>>
>>>>>> Not quintuples. There are lots of ways to represent a TM's states, but
>>>>>> states are not quintuples and quintuples are not states. This confusion
>>>>>> will (as you can see below) make lots of the code read badly.
>>>>>
>>>>> What did you think that states are?
>>>> Their only properties are that they are distinct and finite in number.
>>>
>>> Ah so you are only seeing the mathematical abstraction that uses
>>> directed graphs. That is not enough for an actual hardware machine to
>>> go on.
>> Nonsense. It's perfectly practical and entirely natiral to implement
>> this using a directed graph.
>
> A directed graph with labeled edges would seem to require all this
> (node and edge) info kept in a single struct when physically
> implemented as software. One node could have a list of edge data, yet
> that is cumbersome.

It's a few lines of C++.

>>>> I have written an interpreter in which the states are instances of a
>>>> class State, that holds all the information a TM might need when in that
>>>> state. But there are a hundreds of other ways to represent the states.
>>>
>>> In other words this:
>>> struct Quintuple
>>> {
>>> int state;
>>> int symbol;
>>> int write_symbol;
>>> int next_state;
>>> char tape_head_move;
>>> };
>> This is not a state. States are not quintuples and vice-versa. Please
>> don't pick this hill fight on.
>
> I want to grok this.

Grok what? Do you find the distinction between a state (a circle in the
graph of a TM) and a quintuple (one of the arrows in the graph) a
confusing one?

Or are you referring to groking my metaphor. All I meant is that this
distinction is so clear cut that digging your heels in over it is not a
wise move.

>>>> I think the best way to judge that will be to compare code. At the
>>>> moment you only have a very rough sketch.
>>>
>>> The "rough sketch" is fully operational code.
>
> More accurately the The "rough sketch" is my best estimate of is fully
> operational code.
>
>> That's very revealing. You've claimed to have other "fully operational
>> code" and since these sketches are clearly not operational, you must be
>> using the phrase in some rather loose way.
>
> I was trying to make it clear that it is not a more sketch with many
> missing pieces. All the pieces are there.

So saying "fully operational code" was what you have called "poetic
licence" in the past. Put a smiley in there next time you use this
level of poetic licence.

--
Ben.
"le génie humain a des limites, quand la bêtise humaine n’en a pas"
Alexandre Dumas (fils)

Re: On recursion and infinite recursion (reprise)

<t57tra$us8$1@dont-email.me>

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https://www.novabbs.com/devel/article-flat.php?id=31927&group=comp.theory#31927

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From: mikko.le...@iki.fi (Mikko)
Newsgroups: comp.theory
Subject: Re: On recursion and infinite recursion (reprise)
Date: Sun, 8 May 2022 11:09:14 +0300
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 by: Mikko - Sun, 8 May 2022 08:09 UTC

On 2022-05-04 18:09:44 +0000, olcott said:

> On 5/4/2022 2:31 AM, Mikko wrote:
>> On 2022-05-03 18:26:21 +0000, Mr Flibble said:
>>
>>> On Tue, 3 May 2022 12:31:44 +0300
>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>
>>>> On 2022-05-02 15:47:32 +0000, Mr Flibble said:
>>>>
>>>>> Not all infinitely recursive definitions are invalid however
>>>>> infinitely recursive definitions that arise out of a category error
>>>>> (as is the case with the halting problem) are invalid.
>>>>
>>>> An infinite recursion cannot arise out of a category error as the
>>>> recursion stops at the category error.
>>>
>>> Which is kind of my point: the category error is what makes the
>>> infinite recursion invalid thus rendering the halting problem
>>> definition itself invalid and any proofs predicated on it.
>>
>> Category error does not make the infinite recursion invalid, just
>> irrelevant. The sentence containing the category error wourld be
>> invalid even whithout the infinite recursion.
>>
>
> Infinite recursion prevents an expression of language from being a
> logic sentence.

Irrelevant if the expression is invalid for some more obvious reason
such as category error.

Mikko

Re: On recursion and infinite recursion (reprise)

<t57uhi$3nh$1@dont-email.me>

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https://www.novabbs.com/devel/article-flat.php?id=31928&group=comp.theory#31928

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From: mikko.le...@iki.fi (Mikko)
Newsgroups: comp.theory
Subject: Re: On recursion and infinite recursion (reprise)
Date: Sun, 8 May 2022 11:21:06 +0300
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 by: Mikko - Sun, 8 May 2022 08:21 UTC

On 2022-05-07 16:16:49 +0000, olcott said:

> On 5/7/2022 3:42 AM, Mikko wrote:
>> On 2022-05-06 19:14:24 +0000, olcott said:
>>
>>> On 5/6/2022 4:23 AM, Mikko wrote:
>>>> On 2022-05-05 17:52:48 +0000, olcott said:
>>>>
>>>>>>>>> On 5/3/2022 12:17 PM, Mikko wrote:
>>>>>>>>>> On 2022-05-03 14:38:57 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>> On 5/3/2022 4:36 AM, Mikko wrote:
>>>>
>>>>>>>>>>>> One of the rules that define Prolog language is
>>>>>>>>>>>>
>>>>>>>>>>>>  arguments ::= argument | argument "," arguments
>>>>>>>>>>>>
>>>>>>>>>>>> which is infinitely recursive. Is it invalid? Is Prolog invalid because
>>>>>>>>>>>> of this and other infinitely recursive rules?
>>>>>>>>>>>>
>>>>>>>>>>>> Mikko
>>>>
>>>>>>>>>>> If would have to be invalid because it can never be resolved.
>>>>
>>>>>>>>>> What would be invalid? Prolog? Definition of Prolog?
>>>>>>>>>> Why "would be" and not "is"?
>>>>
>>>>> I never retracted anything.
>>>>
>>>> So you still claim that Prolog is invalid?
>>>>
>>>> Mikko
>>>>
>>>
>>> I said exactly the opposite.
>>
>> As can be seen above:
>> You did not.
>> I asked: "Is Prolog invalid?"
>> You said "It would have to be invalid."
>> Here "It" apparently means "Prolog" but I wansn't quite sure
>> so I asked whether you meant something else. In your reply
>> you didn't say I was misinterpreting you so obviously I wasn't.
>> If you now say otherwise it can only mean that you have changed
>> your mind.
>>
>> Mikko
>>
>
> Prolog is valid, it is much valid, much more valid than symbolic or
> classical logic.

OK, now it is clear enough. You have said that an infinite recursion
in the definition makes Prolog invalid but it is valid anyway.
So we can see that your opinions are incoherent and not worth of attention.

Mikko

Re: On recursion and infinite recursion (reprise)

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 by: olcott - Mon, 9 May 2022 15:39 UTC

On 5/8/2022 3:09 AM, Mikko wrote:
> On 2022-05-04 18:09:44 +0000, olcott said:
>
>> On 5/4/2022 2:31 AM, Mikko wrote:
>>> On 2022-05-03 18:26:21 +0000, Mr Flibble said:
>>>
>>>> On Tue, 3 May 2022 12:31:44 +0300
>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>
>>>>> On 2022-05-02 15:47:32 +0000, Mr Flibble said:
>>>>>
>>>>>> Not all infinitely recursive definitions are invalid however
>>>>>> infinitely recursive definitions that arise out of a category error
>>>>>> (as is the case with the halting problem) are invalid.
>>>>>
>>>>> An infinite recursion cannot arise out of a category error as the
>>>>> recursion stops at the category error.
>>>>
>>>> Which is kind of my point: the category error is what makes the
>>>> infinite recursion invalid thus rendering the halting problem
>>>> definition itself invalid and any proofs predicated on it.
>>>
>>> Category error does not make the infinite recursion invalid, just
>>> irrelevant. The sentence containing the category error wourld be
>>> invalid even whithout the infinite recursion.
>>>
>>
>> Infinite recursion prevents an expression of language from being a
>> logic sentence.
>
> Irrelevant if the expression is invalid for some more obvious reason
> such as category error.
>
> Mikko
>

That <is> the category error.
Is this sentence true: "What time is it?"
It is a category error only delclarative sentences can be true.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

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 by: olcott - Mon, 9 May 2022 15:41 UTC

On 5/8/2022 3:21 AM, Mikko wrote:
> On 2022-05-07 16:16:49 +0000, olcott said:
>
>> On 5/7/2022 3:42 AM, Mikko wrote:
>>> On 2022-05-06 19:14:24 +0000, olcott said:
>>>
>>>> On 5/6/2022 4:23 AM, Mikko wrote:
>>>>> On 2022-05-05 17:52:48 +0000, olcott said:
>>>>>
>>>>>>>>>> On 5/3/2022 12:17 PM, Mikko wrote:
>>>>>>>>>>> On 2022-05-03 14:38:57 +0000, olcott said:
>>>>>>>>>>>
>>>>>>>>>>>> On 5/3/2022 4:36 AM, Mikko wrote:
>>>>>
>>>>>>>>>>>>> One of the rules that define Prolog language is
>>>>>>>>>>>>>
>>>>>>>>>>>>>  arguments ::= argument | argument "," arguments
>>>>>>>>>>>>>
>>>>>>>>>>>>> which is infinitely recursive. Is it invalid? Is Prolog
>>>>>>>>>>>>> invalid because
>>>>>>>>>>>>> of this and other infinitely recursive rules?
>>>>>>>>>>>>>
>>>>>>>>>>>>> Mikko
>>>>>
>>>>>>>>>>>> If would have to be invalid because it can never be resolved.
>>>>>
>>>>>>>>>>> What would be invalid? Prolog? Definition of Prolog?
>>>>>>>>>>> Why "would be" and not "is"?
>>>>>
>>>>>> I never retracted anything.
>>>>>
>>>>> So you still claim that Prolog is invalid?
>>>>>
>>>>> Mikko
>>>>>
>>>>
>>>> I said exactly the opposite.
>>>
>>> As can be seen above:
>>> You did not.
>>> I asked: "Is Prolog invalid?"
>>> You said "It would have to be invalid."
>>> Here "It" apparently means "Prolog" but I wansn't quite sure
>>> so I asked whether you meant something else. In your reply
>>> you didn't say I was misinterpreting you so obviously I wasn't.
>>> If you now say otherwise it can only mean that you have changed
>>> your mind.
>>>
>>> Mikko
>>>
>>
>> Prolog is valid, it is much valid, much more valid than symbolic or
>> classical logic.
>
> OK, now it is clear enough. You have said that an infinite recursion
> in the definition makes Prolog invalid but it is valid anyway.

I never said anything like that. An expression of the language of Prolog
is invalid, Prolog itself is valid.

> So we can see that your opinions are incoherent and not worth of attention.

If you only glance at ten percent of the words that I say before
artificially contriving a rebuttal your rebuttals are going to be pretty
shitty.

>
> Mikko
>

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

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 by: Mikko - Mon, 9 May 2022 16:45 UTC

On 2022-05-09 15:41:50 +0000, olcott said:

> On 5/8/2022 3:21 AM, Mikko wrote:
>> On 2022-05-07 16:16:49 +0000, olcott said:
>>
>>> On 5/7/2022 3:42 AM, Mikko wrote:
>>>> On 2022-05-06 19:14:24 +0000, olcott said:
>>>>
>>>>> On 5/6/2022 4:23 AM, Mikko wrote:
>>>>>> On 2022-05-05 17:52:48 +0000, olcott said:
>>>>>>
>>>>>>>>>>> On 5/3/2022 12:17 PM, Mikko wrote:
>>>>>>>>>>>> On 2022-05-03 14:38:57 +0000, olcott said:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 5/3/2022 4:36 AM, Mikko wrote:
>>>>>>
>>>>>>>>>>>>>> One of the rules that define Prolog language is
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>  arguments ::= argument | argument "," arguments
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> which is infinitely recursive. Is it invalid? Is Prolog invalid because
>>>>>>>>>>>>>> of this and other infinitely recursive rules?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Mikko
>>>>>>
>>>>>>>>>>>>> If would have to be invalid because it can never be resolved.
>>>>>>
>>>>>>>>>>>> What would be invalid? Prolog? Definition of Prolog?
>>>>>>>>>>>> Why "would be" and not "is"?
>>>>>>
>>>>>>> I never retracted anything.
>>>>>>
>>>>>> So you still claim that Prolog is invalid?
>>>>>>
>>>>>> Mikko
>>>>>>
>>>>>
>>>>> I said exactly the opposite.
>>>>
>>>> As can be seen above:
>>>> You did not.
>>>> I asked: "Is Prolog invalid?"
>>>> You said "It would have to be invalid."
>>>> Here "It" apparently means "Prolog" but I wansn't quite sure
>>>> so I asked whether you meant something else. In your reply
>>>> you didn't say I was misinterpreting you so obviously I wasn't.
>>>> If you now say otherwise it can only mean that you have changed
>>>> your mind.
>>>>
>>>> Mikko
>>>>
>>>
>>> Prolog is valid, it is much valid, much more valid than symbolic or
>>> classical logic.
>>
>> OK, now it is clear enough. You have said that an infinite recursion
>> in the definition makes Prolog invalid but it is valid anyway.
>
> I never said anything like that. An expression of the language of
> Prolog is invalid, Prolog itself is valid.

Yes, you did. See above.

Mikko

Re: On recursion and infinite recursion (reprise)

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 by: Mikko - Mon, 9 May 2022 16:48 UTC

On 2022-05-09 15:39:00 +0000, olcott said:

> On 5/8/2022 3:09 AM, Mikko wrote:
>> On 2022-05-04 18:09:44 +0000, olcott said:
>>
>>> On 5/4/2022 2:31 AM, Mikko wrote:
>>>> On 2022-05-03 18:26:21 +0000, Mr Flibble said:
>>>>
>>>>> On Tue, 3 May 2022 12:31:44 +0300
>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>>
>>>>>> On 2022-05-02 15:47:32 +0000, Mr Flibble said:
>>>>>>
>>>>>>> Not all infinitely recursive definitions are invalid however
>>>>>>> infinitely recursive definitions that arise out of a category error
>>>>>>> (as is the case with the halting problem) are invalid.
>>>>>>
>>>>>> An infinite recursion cannot arise out of a category error as the
>>>>>> recursion stops at the category error.
>>>>>
>>>>> Which is kind of my point: the category error is what makes the
>>>>> infinite recursion invalid thus rendering the halting problem
>>>>> definition itself invalid and any proofs predicated on it.
>>>>
>>>> Category error does not make the infinite recursion invalid, just
>>>> irrelevant. The sentence containing the category error wourld be
>>>> invalid even whithout the infinite recursion.
>>>>
>>>
>>> Infinite recursion prevents an expression of language from being a
>>> logic sentence.
>>
>> Irrelevant if the expression is invalid for some more obvious reason
>> such as category error.
>>
>> Mikko
>>
>
> That <is> the category error.
> Is this sentence true: "What time is it?"
> It is a category error only delclarative sentences can be true.

Irrelevant as Mr Flibble did not discuss questions.

Mikko

Re: On recursion and infinite recursion (reprise)

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 by: Mikko - Mon, 9 May 2022 16:58 UTC

On 2022-05-03 18:13:05 +0000, olcott said:

> Expressions of language can only be correctly construed as true:
> (a) if they are defined to be true
> (b) have no contradictory elements in (a)
> (c) are derived by applying true preserving operations to (a) or (c)

You forgot: an expression is true if it is a tautology.
E.g., a sentence of the form (A ∧ (A → B)) → B is true.

Mikko

Re: On recursion and infinite recursion (reprise)

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 by: olcott - Mon, 9 May 2022 17:11 UTC

On 5/9/2022 11:45 AM, Mikko wrote:
> On 2022-05-09 15:41:50 +0000, olcott said:
>
>> On 5/8/2022 3:21 AM, Mikko wrote:
>>> On 2022-05-07 16:16:49 +0000, olcott said:
>>>
>>>> On 5/7/2022 3:42 AM, Mikko wrote:
>>>>> On 2022-05-06 19:14:24 +0000, olcott said:
>>>>>
>>>>>> On 5/6/2022 4:23 AM, Mikko wrote:
>>>>>>> On 2022-05-05 17:52:48 +0000, olcott said:
>>>>>>>
>>>>>>>>>>>> On 5/3/2022 12:17 PM, Mikko wrote:
>>>>>>>>>>>>> On 2022-05-03 14:38:57 +0000, olcott said:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 5/3/2022 4:36 AM, Mikko wrote:
>>>>>>>
>>>>>>>>>>>>>>> One of the rules that define Prolog language is
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>  arguments ::= argument | argument "," arguments
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> which is infinitely recursive. Is it invalid? Is Prolog
>>>>>>>>>>>>>>> invalid because
>>>>>>>>>>>>>>> of this and other infinitely recursive rules?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Mikko
>>>>>>>
>>>>>>>>>>>>>> If would have to be invalid because it can never be resolved.
>>>>>>>
>>>>>>>>>>>>> What would be invalid? Prolog? Definition of Prolog?
>>>>>>>>>>>>> Why "would be" and not "is"?
>>>>>>>
>>>>>>>> I never retracted anything.
>>>>>>>
>>>>>>> So you still claim that Prolog is invalid?
>>>>>>>
>>>>>>> Mikko
>>>>>>>
>>>>>>
>>>>>> I said exactly the opposite.
>>>>>
>>>>> As can be seen above:
>>>>> You did not.
>>>>> I asked: "Is Prolog invalid?"
>>>>> You said "It would have to be invalid."
>>>>> Here "It" apparently means "Prolog" but I wansn't quite sure
>>>>> so I asked whether you meant something else. In your reply
>>>>> you didn't say I was misinterpreting you so obviously I wasn't.
>>>>> If you now say otherwise it can only mean that you have changed
>>>>> your mind.
>>>>>
>>>>> Mikko
>>>>>
>>>>
>>>> Prolog is valid, it is much valid, much more valid than symbolic or
>>>> classical logic.
>>>
>>> OK, now it is clear enough. You have said that an infinite recursion
>>> in the definition makes Prolog invalid but it is valid anyway.
>>
>> I never said anything like that. An expression of the language of
>> Prolog is invalid, Prolog itself is valid.
>
> Yes, you did. See above.
>
> Mikko
>

Prolog is not invalid.
Prolog is able to detect expressions of the Prolog language that are
invalid using unify_with_occurs_check.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

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 by: olcott - Mon, 9 May 2022 17:12 UTC

On 5/9/2022 11:48 AM, Mikko wrote:
> On 2022-05-09 15:39:00 +0000, olcott said:
>
>> On 5/8/2022 3:09 AM, Mikko wrote:
>>> On 2022-05-04 18:09:44 +0000, olcott said:
>>>
>>>> On 5/4/2022 2:31 AM, Mikko wrote:
>>>>> On 2022-05-03 18:26:21 +0000, Mr Flibble said:
>>>>>
>>>>>> On Tue, 3 May 2022 12:31:44 +0300
>>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>>>
>>>>>>> On 2022-05-02 15:47:32 +0000, Mr Flibble said:
>>>>>>>
>>>>>>>> Not all infinitely recursive definitions are invalid however
>>>>>>>> infinitely recursive definitions that arise out of a category error
>>>>>>>> (as is the case with the halting problem) are invalid.
>>>>>>>
>>>>>>> An infinite recursion cannot arise out of a category error as the
>>>>>>> recursion stops at the category error.
>>>>>>
>>>>>> Which is kind of my point: the category error is what makes the
>>>>>> infinite recursion invalid thus rendering the halting problem
>>>>>> definition itself invalid and any proofs predicated on it.
>>>>>
>>>>> Category error does not make the infinite recursion invalid, just
>>>>> irrelevant. The sentence containing the category error wourld be
>>>>> invalid even whithout the infinite recursion.
>>>>>
>>>>
>>>> Infinite recursion prevents an expression of language from being a
>>>> logic sentence.
>>>
>>> Irrelevant if the expression is invalid for some more obvious reason
>>> such as category error.
>>>
>>> Mikko
>>>
>>
>> That <is> the category error.
>> Is this sentence true: "What time is it?"
>> It is a category error only delclarative sentences can be true.
>
> Irrelevant as Mr Flibble did not discuss questions.
>
> Mikko
>

He discussed category error, I provided an example of a category error.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

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 by: olcott - Mon, 9 May 2022 17:16 UTC

On 5/9/2022 11:58 AM, Mikko wrote:
> On 2022-05-03 18:13:05 +0000, olcott said:
>
>> Expressions of language can only be correctly construed as true:
>> (a) if they are defined to be true
>> (b) have no contradictory elements in (a)
>> (c) are derived by applying true preserving operations to (a) or (c)
>
> You forgot: an expression is true if it is a tautology.
> E.g., a sentence of the form (A ∧ (A → B)) → B is true.
>
> Mikko
>

Logical implication
p q p ⇒ q
T T T
T F F
F T T
F F T

The forth row is not truth preserving.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: On recursion and infinite recursion (reprise)

<mmheK.59313$XU1.13300@fx09.iad>

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 by: Richard Damon - Mon, 9 May 2022 23:21 UTC

On 5/9/22 1:11 PM, olcott wrote:
> On 5/9/2022 11:45 AM, Mikko wrote:
>> On 2022-05-09 15:41:50 +0000, olcott said:
>>
>>> On 5/8/2022 3:21 AM, Mikko wrote:
>>>> On 2022-05-07 16:16:49 +0000, olcott said:
>>>>
>>>>> On 5/7/2022 3:42 AM, Mikko wrote:
>>>>>> On 2022-05-06 19:14:24 +0000, olcott said:
>>>>>>
>>>>>>> On 5/6/2022 4:23 AM, Mikko wrote:
>>>>>>>> On 2022-05-05 17:52:48 +0000, olcott said:
>>>>>>>>
>>>>>>>>>>>>> On 5/3/2022 12:17 PM, Mikko wrote:
>>>>>>>>>>>>>> On 2022-05-03 14:38:57 +0000, olcott said:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 5/3/2022 4:36 AM, Mikko wrote:
>>>>>>>>
>>>>>>>>>>>>>>>> One of the rules that define Prolog language is
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>  arguments ::= argument | argument "," arguments
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> which is infinitely recursive. Is it invalid? Is Prolog
>>>>>>>>>>>>>>>> invalid because
>>>>>>>>>>>>>>>> of this and other infinitely recursive rules?
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Mikko
>>>>>>>>
>>>>>>>>>>>>>>> If would have to be invalid because it can never be
>>>>>>>>>>>>>>> resolved.
>>>>>>>>
>>>>>>>>>>>>>> What would be invalid? Prolog? Definition of Prolog?
>>>>>>>>>>>>>> Why "would be" and not "is"?
>>>>>>>>
>>>>>>>>> I never retracted anything.
>>>>>>>>
>>>>>>>> So you still claim that Prolog is invalid?
>>>>>>>>
>>>>>>>> Mikko
>>>>>>>>
>>>>>>>
>>>>>>> I said exactly the opposite.
>>>>>>
>>>>>> As can be seen above:
>>>>>> You did not.
>>>>>> I asked: "Is Prolog invalid?"
>>>>>> You said "It would have to be invalid."
>>>>>> Here "It" apparently means "Prolog" but I wansn't quite sure
>>>>>> so I asked whether you meant something else. In your reply
>>>>>> you didn't say I was misinterpreting you so obviously I wasn't.
>>>>>> If you now say otherwise it can only mean that you have changed
>>>>>> your mind.
>>>>>>
>>>>>> Mikko
>>>>>>
>>>>>
>>>>> Prolog is valid, it is much valid, much more valid than symbolic or
>>>>> classical logic.
>>>>
>>>> OK, now it is clear enough. You have said that an infinite recursion
>>>> in the definition makes Prolog invalid but it is valid anyway.
>>>
>>> I never said anything like that. An expression of the language of
>>> Prolog is invalid, Prolog itself is valid.
>>
>> Yes, you did. See above.
>>
>> Mikko
>>
>
> Prolog is not invalid.
> Prolog is able to detect expressions of the Prolog language that are
> invalid using unify_with_occurs_check.
>

But the key is that just because they are valid Prolog, doesn't mean
they aren't valid logic in a more powerful logic system.

If you want to limit the logic you use to just what Prolog offers, fine,
but realize that you are leaving a LOT of Logic Theory outside your
ability to deal with.

This includes things like Computation Theory and systems for which
Godel's incompleteness theory hold.

Re: On recursion and infinite recursion (reprise)

<YtheK.30797$kgsb.15667@fx97.iad>

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 by: Richard Damon - Mon, 9 May 2022 23:30 UTC

On 5/9/22 1:16 PM, olcott wrote:
> On 5/9/2022 11:58 AM, Mikko wrote:
>> On 2022-05-03 18:13:05 +0000, olcott said:
>>
>>> Expressions of language can only be correctly construed as true:
>>> (a) if they are defined to be true
>>> (b) have no contradictory elements in (a)
>>> (c) are derived by applying true preserving operations to (a) or (c)
>>
>> You forgot: an expression is true if it is a tautology.
>> E.g., a sentence of the form (A ∧ (A → B)) → B is true.
>>
>> Mikko
>>
>
> Logical implication
> p    q    p ⇒ q
> T    T    T
> T    F    F
> F    T    T
> F    F    T
>
> The forth row is not truth preserving.
>

So, is the implication that if x is a cat then x is an animal isn't true
because my actual x is a office building, so an office building is NOT a
cat (!p), and an office building is NOT an animal (!q), so I guess you
can't say that "if x is a cat then x is an animal" (p[ -> q) ?

That IS what you seem to be saying.

Or, but "fourth line" do you meen the F T T line, in which case if my x
was a dog, then I have

a dog is NOT a cat (!p), but a dog IS an animal (q), so are you saying
the implication that "if x is a cat then x is an animal" (p[ -> q)?

Re: On recursion and infinite recursion (reprise)

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 by: Mikko - Tue, 10 May 2022 07:34 UTC

On 2022-05-09 17:11:24 +0000, olcott said:

> On 5/9/2022 11:45 AM, Mikko wrote:
>> On 2022-05-09 15:41:50 +0000, olcott said:
>>
>>> On 5/8/2022 3:21 AM, Mikko wrote:
>>>> On 2022-05-07 16:16:49 +0000, olcott said:
>>>>
>>>>> On 5/7/2022 3:42 AM, Mikko wrote:
>>>>>> On 2022-05-06 19:14:24 +0000, olcott said:
>>>>>>
>>>>>>> On 5/6/2022 4:23 AM, Mikko wrote:
>>>>>>>> On 2022-05-05 17:52:48 +0000, olcott said:
>>>>>>>>
>>>>>>>>>>>>> On 5/3/2022 12:17 PM, Mikko wrote:
>>>>>>>>>>>>>> On 2022-05-03 14:38:57 +0000, olcott said:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 5/3/2022 4:36 AM, Mikko wrote:
>>>>>>>>
>>>>>>>>>>>>>>>> One of the rules that define Prolog language is
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>  arguments ::= argument | argument "," arguments
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> which is infinitely recursive. Is it invalid? Is Prolog invalid because
>>>>>>>>>>>>>>>> of this and other infinitely recursive rules?
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Mikko
>>>>>>>>
>>>>>>>>>>>>>>> If would have to be invalid because it can never be resolved.
>>>>>>>>
>>>>>>>>>>>>>> What would be invalid? Prolog? Definition of Prolog?
>>>>>>>>>>>>>> Why "would be" and not "is"?
>>>>>>>>
>>>>>>>>> I never retracted anything.
>>>>>>>>
>>>>>>>> So you still claim that Prolog is invalid?
>>>>>>>>
>>>>>>>> Mikko
>>>>>>>>
>>>>>>>
>>>>>>> I said exactly the opposite.
>>>>>>
>>>>>> As can be seen above:
>>>>>> You did not.
>>>>>> I asked: "Is Prolog invalid?"
>>>>>> You said "It would have to be invalid."
>>>>>> Here "It" apparently means "Prolog" but I wansn't quite sure
>>>>>> so I asked whether you meant something else. In your reply
>>>>>> you didn't say I was misinterpreting you so obviously I wasn't.
>>>>>> If you now say otherwise it can only mean that you have changed
>>>>>> your mind.
>>>>>>
>>>>>> Mikko
>>>>>>
>>>>>
>>>>> Prolog is valid, it is much valid, much more valid than symbolic or
>>>>> classical logic.
>>>>
>>>> OK, now it is clear enough. You have said that an infinite recursion
>>>> in the definition makes Prolog invalid but it is valid anyway.
>>>
>>> I never said anything like that. An expression of the language of
>>> Prolog is invalid, Prolog itself is valid.
>>
>> Yes, you did. See above.
>>
>> Mikko
>>
>
> Prolog is not invalid.
> Prolog is able to detect expressions of the Prolog language that are
> invalid using unify_with_occurs_check.

So now you have retracted your
> If would have to be invalid because it can never be resolved.

Mikko

Re: On recursion and infinite recursion (reprise)

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 by: wij - Tue, 10 May 2022 15:40 UTC

>...[cut]
> Logical implication
> p q p ⇒ q
> T T T
> T F F
> F T T
> F F T
>
> The forth row is not truth preserving.

Even now, you know how to copy/paste. You don't seem to understand logic.

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