From Newsgroup: comp.ai.philosophy

On 7/8/2026 2:24 AM, Mikko wrote:

On 06/07/2026 18:15, olcott wrote:

P ⊢ Q where the rules of inference are only
semantic entailment specified syntactically.

Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/

Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that the conclusion is semantically
entailed by its premises.

We do not use model theory to do this we use proof
theoretic semantics.

What does "semantic entailment" mean when model theory
is not used?

P ⊢ Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
This is the only inference steps allowed.

"I drove my car to Walmart"
entails that my motor vehicle consumed energy.

It turns out that all HOL and type theory can be
encoded in Prolog even though it cannot be processed
in Prolog.

It took me all day to come up with that.
--
Copyright 2026 Olcott

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

On 08/07/2026 23:26, olcott wrote:

On 7/8/2026 2:24 AM, Mikko wrote:

On 06/07/2026 18:15, olcott wrote:

P ⊢ Q where the rules of inference are only
semantic entailment specified syntactically.

Validity and Soundness
A deductive argument is said to be valid if and only
if it takes a form that makes it impossible for the
premises to be true and the conclusion nevertheless
to be false. https://iep.utm.edu/val-snd/

Is corrected to mean
A deductive argument is said to be valid if and only
if it takes a form that the conclusion is semantically
entailed by its premises.

We do not use model theory to do this we use proof
theoretic semantics.

What does "semantic entailment" mean when model theory
is not used?

P ⊢ Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
This is the only inference steps allowed.

That does not answer the question. It does not specify
what "semantic entailment" means nor what inference
steps are allowed.

"I drove my car to Walmart"
entails that my motor vehicle consumed energy.

Not without additional premises that relate driving and car
to consumption and energy.

It turns out that all HOL and type theory can be
encoded in Prolog even though it cannot be processed
in Prolog.

Or C or any language that supports long character strings.
--
Mikko
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