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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: This is how I overturn the Tarski Undefinability theorem
Date: Mon, 9 Sep 2024 08:12:13 -0500
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On 9/9/2024 4:05 AM, Mikko wrote:
> On 2024-09-08 14:38:51 +0000, olcott said:
> 
>> On 9/8/2024 9:31 AM, Mikko wrote:
>>> On 2024-09-08 12:44:56 +0000, olcott said:
>>>
>>>> On 9/8/2024 3:45 AM, Mikko wrote:
>>>>> On 2024-09-07 13:06:52 +0000, olcott said:
>>>>>
>>>>>> On 9/7/2024 3:35 AM, Mikko wrote:
>>>>>>> On 2024-09-06 12:22:04 +0000, olcott said:
>>>>>>>>
>>>>>>>> The fundamental architectural overview of all Prolog 
>>>>>>>> implementations
>>>>>>>> is the same True(x) means X is derived by applying Rules (AKA 
>>>>>>>> truth preserving operations) to Facts.
>>>>>>>
>>>>>>> The details are permitted to differ.
>>>>>>>
>>>>>>
>>>>>> Instead of using any single order of logic we simultaneously
>>>>>> represent an arbitrary number of orders of logic in a type
>>>>>> hierarchy knowledge ontology.
>>>>>
>>>>> The type system of Prolog is different.
>>>>>
>>>>
>>>> Yes I know that. The architecture of Prolog is used
>>>> the implementation details are scrapped.
>>>>
>>>> ?- LP = not(true(LP)).
>>>> LP = not(true(LP)).
>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>> false. // LP is rejected as cyclic
>>>>
>>>> Even with Prolog just the way it is it is not as stupid
>>>> as Tarski's system that doesn't know to reject the Liar
>>>> Paradox.
>>>>
>>>> https://liarparadox.org/Tarski_247_248.pdf
>>>
>>> Most Prolog implementations don't reject L = not(ture(LP)).
>>>
>>
>> ?- unify_with_occurs_check(LP, not(true(LP))).
>> Prolog just gets stuck in an infinite loop
>> when a cyclic term is unified.
> 
> You can ask "unify_with_occurs_check(LP, not(true(LP)))" but you
> needn't. If you don't ask it doen't reject. 

It gets stuck in an infinite loop.

> You can say that
> "LP = not(true(LP))" and most Prolog implementations simply
> assign not(true(LP) to LP. Whether your program gets stuck in
> an infinite loop depends on what you try to do with LP.
> 

?- LP. % Gets stuck in an infinite loop

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer