Re: Olcott's big correction to symbolic logic

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).