From Newsgroup: comp.ai.philosophy

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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