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Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this)

Subject Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this)
Newsgroups comp.lang.lisp, comp.lang.c++, comp.lang.c, comp.lang.prolog
References (3 earlier) <20190426104732.755@kylheku.com> <rsqdnaWxiMopGV7BnZ2dnUU7-KvNnZ2d@giganews.com> <20190426174714.286@kylheku.com> <SIOdnf4c_uZsHFnBnZ2dnUU7-QfNnZ2d@giganews.com> <polzE.414$fq3.286@fx07.iad>
From peteolcott <Here@Home>
Date 2019-05-04 15:07 -0500
Message-ID <97WdnZYZv9mHbFDBnZ2dnUU7-RvNnZ2d@giganews.com> (permalink)

Cross-posted to 4 groups.

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On 5/4/2019 2:05 PM, Richard Damon wrote:
> On 4/27/19 12:23 PM, peteolcott wrote:
>> Truth cannot possibly be unprovable in the sound deductive inference model.
>>
>> Within the sound deductive inference model there is a (connected
>> sequence of
>> valid deductions from true premises to a true conclusion)  thus unlike the
>> formal proofs of symbolic logic provability cannot diverge from truth.
> 
> I will admit that I haven't followed this thread closely, but to me this
> seems to imply that this 'sound deductive inference model' must be
> somewhat weak in what it can express to be able to make such a claim.
> 

Deductively Sound Formal Proofs
https://www.researchgate.net/publication/332864362_Deductively_Sound_Formal_Proofs

It simply filters out semantically incoherent expressions of language.
These expressions were not filtered out previously because formal systems
ignored semantic constraints.

> Yes, there are many statements which are provable true, and this can be
> shown with a valid proof from true premises and valid inferences leading
> to the conclusion. There are also many statements which are provable
> false, as you can prove their converse.
> 

Every closed WFF left over is semantically incoherent.

> If the logic system is sufficiently rich in capability, it would seem
> like, in general, proving that something can not be proven true or false
> is not easy, so it would seem hard to determine that something is
> 'unsound'. 

Its all in my linked one page paper.

> The issue is that there can be an incredibly large number of
> possible paths to combine known true premises with valid deductions to
> get more statements that are provably true, which can be combined with
> each other to get even more provably true statement. To be able to say
> that it will be impossible to find a path to the specified statement
> seems hard, unless the logic system is naturally weak and able to prove
> only a very limited set of statements.
> 

If we simply leap to the chase:
∃F ∈ Formal_System ∃G ∈ Closed_WFF(F) (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G)))
The above logic sentence asserts that there are some closed WFF that
are neither true or false.

Axiom Schema(3) Deductively_Sound_Consequence(x) ↔ (True(x) ∨ False(x))
excludes expressions of language that do not evaluate to true or false
as not belonging to the set of deductively sound consequences.

> A great example of this would be the Four Color Map Theorem. For a very
> long time it was 'Unproved' and thus would seem to be declared 'Unsound'
> by this logic, but was eventually proved true.
> 


-- 
Copyright 2019 Pete Olcott All rights reserved

"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

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Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-26 09:58 -0500
  Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Siri Cruise <chine.bleu@yahoo.com> - 2019-04-26 08:20 -0700
    Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-26 10:48 -0500
      Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) paul wallich <pw@panix.com> - 2019-04-26 13:40 -0400
        Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 15:10 -0500
  Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Siebe de Vos <siebe@de-vos.de> - 2019-04-26 17:24 +0200
    Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-26 10:51 -0500
      Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-04-26 17:48 +0000
        Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-26 17:10 -0500
        Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-26 17:22 -0500
          Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-04-27 01:13 +0000
            Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 11:23 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-04-27 18:26 +0000
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Paul Rubin <no.email@nospam.invalid> - 2019-04-27 14:44 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-04-28 03:40 +0000
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 16:48 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Paul Rubin <no.email@nospam.invalid> - 2019-04-27 14:52 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 17:44 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Jeff Barnett <jbb@notatt.com> - 2019-04-27 17:12 -0600
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 18:41 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 18:59 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Paul Rubin <no.email@nospam.invalid> - 2019-04-27 17:10 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 19:44 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Jeff Barnett <jbb@notatt.com> - 2019-04-27 19:26 -0600
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Paul Rubin <no.email@nospam.invalid> - 2019-04-27 18:52 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 21:38 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-29 21:53 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) "Pascal J. Bourguignon" <pjb@informatimago.com> - 2019-04-30 07:08 +0200
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-30 00:41 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) taruss@google.com - 2019-04-30 09:23 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) "Pascal J. Bourguignon" <pjb@informatimago.com> - 2019-04-30 18:47 +0200
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-30 12:02 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 07:50 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) "Pascal J. Bourguignon" <pjb@informatimago.com> - 2019-05-01 14:53 +0200
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 09:29 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) "Pascal J. Bourguignon" <pjb@informatimago.com> - 2019-05-01 18:37 +0200
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 13:53 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 13:56 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Keith Thompson <kst-u@mib.org> - 2019-05-01 10:48 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Bonita Montero <Bonita.Montero@gmail.com> - 2019-05-01 20:25 +0200
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (HP Proof refutation) peteolcott <Here@Home> - 2019-05-01 15:01 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 14:01 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) David Brown <david.brown@hesbynett.no> - 2019-05-01 23:28 +0200
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 15:14 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-30 11:55 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 21:28 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 15:12 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 15:12 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Spiros Bousbouras <spibou@gmail.com> - 2019-04-28 00:16 +0000
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 19:48 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) paul wallich <pw@panix.com> - 2019-04-29 17:53 -0400
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-29 18:43 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) luserdroog <mijoryx@yahoo.com> - 2019-04-29 17:22 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-29 22:06 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-04-30 00:18 +0000
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Paul Rubin <no.email@nospam.invalid> - 2019-04-29 18:11 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-29 21:58 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Stefan Monnier <monnier@iro.umontreal.ca> - 2019-05-02 15:11 -0400
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Jeff Barnett <jbb@notatt.com> - 2019-05-02 16:46 -0600
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-05-02 23:21 +0000
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-02 22:04 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Jeff Barnett <jbb@notatt.com> - 2019-05-02 21:13 -0600
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-02 22:42 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Halting Problem) peteolcott <Here@Home> - 2019-05-02 22:46 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 16:58 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 17:13 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 17:28 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 17:49 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 15:10 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Richard Damon <Richard@Damon-Family.org> - 2019-05-04 15:05 -0400
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-04 15:07 -0500
  Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Keith Thompson <kst-u@mib.org> - 2019-04-26 19:43 -0700
  Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Bonita Montero <Bonita.Montero@gmail.com> - 2019-05-01 17:56 +0200
  Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Rabican <gavinschuette@gmail.com> - 2019-05-06 05:51 -0700

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