From Newsgroup: comp.theory

https://github.com/plolcott/x86utm/blob/master/README.md

Axiom 1 --- Paraphrase of Emil Post definition of computation
All computations are equivalent to the application of finite string transformation rules to finite string inputs to derive any and all
outputs.

Axiom 2
Computation inherently requires relevant rather than arbitrary finite
string transformations. To determine the sum of 2 + 3 relevant steps
must be performed.

The term-of-the-art definition of a decider ignores this and includes computations that ignore their input and simply halt. We are augmenting
this: A decider must apply finite string transformations to its finite
string input that are relevant to the decision criteria.

A decider that accepts a finite string of integer values as within the
ASCII uppercase alphabetic range of 65 to 90 must actually examine its
input for these values.

A halt decider must apply finite string transformations to its finite
string input that are semantically relevant to determining the halting
property specified by this finite string input.

Halt decider H must apply finite string transformations to finite string
input D strictly according to the operational semantics of the source
language of the computation. This applies universally to all models of computation, including the source code of Turing Machines.
--
Copyright 2026 Olcott

*Succinct refutation of the Halting Theorem* https://github.com/plolcott/x86utm/blob/master/README.md

The essence of computation is applying finite
string transformations to finite string inputs
to derive outputs. // paraphrase of Emil Post

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).

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From Newsgroup: comp.theory

On 20/10/2026 07:50, olcott wrote:

https://github.com/plolcott/x86utm/blob/master/README.md

Axiom 1 --- Paraphrase of Emil Post definition of computation
All computations are equivalent to the application of finite string transformation rules to finite string inputs to derive any and all
outputs.

Axiom 2
Computation inherently requires relevant rather than arbitrary finite
string transformations. To determine the sum of 2 + 3 relevant steps
must be performed.

THe meaning of the axiom is not clear. By the usual meaning of the word
a computation may imvolve irrelevant transromations. Even the entire computation can be irrelevant. In any case, nothing is inherently
relevant. What is relevant to something is irrelevant to something else.

For the special case of 2 + 3 possible relevant steps are to note that
both 2 and 3 are less than 10 and pick the number at the position (2, 3)
in the addition table; larger numgers would require different steps. It
would be irrelevant to check whether the numbers are even or odd. But
another possible way is to start with the observation that 2 is even
and 3 is odd so the last bit of the result is 1 and then to continue
with 1 and 1. So the determination of whether a number is even or odd
is not necessary but is relevant to purpose of the computation.
--
Mikko

--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 10/20/2026 2:39 AM, Mikko wrote:

On 20/10/2026 07:50, olcott wrote:

https://github.com/plolcott/x86utm/blob/master/README.md

Axiom 1 --- Paraphrase of Emil Post definition of computation
All computations are equivalent to the application of finite string
transformation rules to finite string inputs to derive any and all
outputs.

Axiom 2
Computation inherently requires relevant rather than arbitrary finite
string transformations. To determine the sum of 2 + 3 relevant steps
must be performed.

THe meaning of the axiom is not clear. By the usual meaning of the word
a computation

Is stupidly incorrect. Likewise for a decider that ignores its input.

may imvolve irrelevant transromations. Even the entire
computation can be irrelevant. In any case, nothing is inherently
relevant. What is relevant to something is irrelevant to something else.

For the special case of 2 + 3 possible relevant steps are to note that
both 2 and 3 are less than 10 and pick the number at the position (2, 3)
in the addition table;

Sure my updated requirement now clearly includes that. In fact
for single digits even humans use a lookup table.

larger numgers would require different steps. It
would be irrelevant to check whether the numbers are even or odd. But
another possible way is to start with the observation that 2 is even
and 3 is odd so the last bit of the result is 1 and then to continue
with 1 and 1. So the determination of whether a number is even or odd
is not necessary but is relevant to purpose of the computation.

In theory irrelevant steps could be included along with
relevant steps. Since my end goal is an optimal system
that computes every element on the body of general
knowledge irrelevant steps are not allowed. This is
somewhat similar to proof theoretic semantics eliminating
detours to derive canonical proofs.
--
Copyright 2026 Olcott

*Succinct refutation of the Halting Theorem* https://github.com/plolcott/x86utm/blob/master/README.md


The essence of computation is applying finite
string transformations to finite string inputs
to derive outputs. // paraphrase of Emil Post

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).
--- Synchronet 3.22a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 20/10/2026 17:47, olcott wrote:

On 10/20/2026 2:39 AM, Mikko wrote:

On 20/10/2026 07:50, olcott wrote:

https://github.com/plolcott/x86utm/blob/master/README.md

Axiom 1 --- Paraphrase of Emil Post definition of computation
All computations are equivalent to the application of finite string
transformation rules to finite string inputs to derive any and all
outputs.

Axiom 2
Computation inherently requires relevant rather than arbitrary finite
string transformations. To determine the sum of 2 + 3 relevant steps
must be performed.

THe meaning of the axiom is not clear. By the usual meaning of the word
a computation

Is stupidly incorrect. Likewise for a decider that ignores its input.

No, the meaning 'stupidly incorrect' of the word "computation" is not
usual.
--
Mikko
--- Synchronet 3.22a-Linux NewsLink 1.2