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Halting Problem and Proof Theoretic Semantics --- VALIDATED

From olcott <polcott333@gmail.com>
Newsgroups comp.theory, sci.logic, sci.math, comp.theory, comp.lang.prolog, comp.software-eng
Subject Halting Problem and Proof Theoretic Semantics --- VALIDATED
Date 2026-02-01 21:32 -0600
Organization A noiseless patient Spider
Message-ID <10lp5t3$angq$2@dont-email.me> (permalink)

Cross-posted to 6 groups.

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int DD()
{
  int Halt_Status = HHH(DD);
  if (Halt_Status)
  HERE: goto HERE;
  return Halt_Status;
}

HHH simulates DD step-by-step according to the
semantics of the C programming language.

HHH correctly determines that DD does not have
a well-founded justification tree within Proof
theoretic semantics.

When HHH is construed as a proof theoretic halting
prover HHH detects the pathological self-reference
of its input and rejects DD as non-well-founded on
this basis.

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

The Liar Paradox is formally rejected by Prolog
occurs_check for this same reason.

occurs_check correctly determines that LP does not
have a well-founded justification tree within Proof
theoretic semantics




All five LLM systems agree with the above
this one is the most succinct agreement:

*Halting Problem and Proof Theoretic Semantics*
https://philpapers.org/archive/OLCHPA.pdf

https://philpapers.org/rec/OLCHPA

https://www.researchgate.net/publication/400341134_Halting_Problem_and_Proof_Theoretic_Semantics

-- 
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable for the entire body of knowledge.<br><br>

This required establishing a new foundation<br>

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Halting Problem and Proof Theoretic Semantics --- VALIDATED olcott <polcott333@gmail.com> - 2026-02-01 21:32 -0600
  Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED Richard Damon <Richard@Damon-Family.org> - 2026-02-02 06:48 -0500
    Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED olcott <polcott333@gmail.com> - 2026-02-02 07:49 -0600
      Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED Richard Damon <Richard@Damon-Family.org> - 2026-02-02 18:46 -0500
        Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED olcott <polcott333@gmail.com> - 2026-02-02 17:55 -0600
          Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED Richard Damon <Richard@Damon-Family.org> - 2026-02-02 23:11 -0500
            Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED olcott <polcott333@gmail.com> - 2026-02-02 22:30 -0600
              Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED Richard Damon <Richard@Damon-Family.org> - 2026-02-03 07:18 -0500
                Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED olcott <polcott333@gmail.com> - 2026-02-03 09:26 -0600
                Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED Richard Damon <Richard@Damon-Family.org> - 2026-02-03 21:33 -0500
                Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED olcott <polcott333@gmail.com> - 2026-02-03 20:48 -0600
                Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED Richard Damon <Richard@Damon-Family.org> - 2026-02-03 22:45 -0500
                Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED olcott <polcott333@gmail.com> - 2026-02-03 22:51 -0600
                Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED Richard Damon <Richard@Damon-Family.org> - 2026-02-04 07:29 -0500
                Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED olcott <polcott333@gmail.com> - 2026-02-04 08:40 -0600
                Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED Richard Damon <Richard@Damon-Family.org> - 2026-02-04 21:29 -0500
  Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED olcott <polcott333@gmail.com> - 2026-02-02 23:41 -0600
    Re: Halting Problem and Proof Theoretic Semantics --- VALIDATED Richard Damon <Richard@Damon-Family.org> - 2026-02-03 07:18 -0500

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