Re: William T. Parry gets rid of Disjunction introduction

On 7/5/2026 3:40 PM, André G. Isaak wrote:
> On 2026-07-04 22:05, olcott wrote:
>> On 7/4/2026 10:52 PM, André G. Isaak wrote:
>>> On 2026-07-04 21:17, olcott wrote:
>>>> On 7/4/2026 8:28 PM, André G. Isaak wrote:
>>>>> Q is a necessary consequence of P
>>>>
>>>> seems best handled by
>>>> https://en.wikipedia.org/wiki/Relevance_logic
>>>> or Parry's Entailment Logic
>>>>
>>>> P □ Q
>>>> 0 0 0
>>>> 0 0 0
>>>> 1 0 0
>>>> 1 1 1
>>>>
>>>> Changes the notion of valid inference too much.
>>>
>>> It doesn't change anything. It's simply invalid since its not a well- 
>>> formed truth table.
>>>
>>>> I myself simply leap all the way to the end and
>>>> say that the full natural language semantic meaning
>>>> must be encoded for both P and Q such that P ⊢ Q
>>>> by semantic entailment specified syntactically.
>>>> This is accomplished in a language such as CycL.
>>>> https://en.wikipedia.org/wiki/CycL
>>>
>>> The above sheds no light on anything. In particular it doesn't 
>>> clarify what you think the difference between entailment and 
>>> necessary entailment is which is the question I have been trying to 
>>> get you to address.
>>>
>>>
>>
>> *This says the whole thing better*
>> P ⊢ Q means: syntactic derivation implements semantic entailment 
>> encoded in the language. The inference rules are syntactic rules that 
>> realize semantic entailment. These are the only allowed inference 
>> steps. The entailment rules depend on the represented domain.
>>
>> Dogs are cats ⊢ Monkeys have wings // rejected
> 
> The topic under discussion was Q, which contains neither dogs, cats, 
> monkeys, or wings.
> 

No it is: William T. Parry gets rid of Disjunction introduction

> Why don't you illustrate your claim with an actual example from 
> arithmetic. Say, for example 9 × 5 = 45. What exactly would be the 
> "semantic entailments encoded in the language" involved here?
> 
> André
> 

PTS takes the inference steps of PA as semantic
entailment in that case.

-- 
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).