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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception --- Tarski
Date: Mon, 24 Feb 2025 10:51:29 +0200
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On 2025-02-22 17:24:59 +0000, olcott said:

> On 2/22/2025 3:12 AM, Mikko wrote:
>> On 2025-02-21 23:22:23 +0000, olcott said:
>> 
>>> On 2/20/2025 3:01 AM, Mikko wrote:
>>>> On 2025-02-18 13:50:22 +0000, olcott said:
>>>> 
>>>>> There is nothing like that in the following concrete example:
>>>>> LP := ~True(LP)
>>>>> 
>>>>> In other words you are saying the Prolog is incorrect
>>>>> to reject the Liar Paradox.
>>>>> 
>>>>> Above translated to Prolog
>>>>> 
>>>>> ?- LP = not(true(LP)).
>>>>> LP = not(true(LP)).
>>>> 
>>>> According to Prolog rules LP = not(true(LP)) is permitted to fail.
>>>> If it succeeds the operations using LP may misbehave. A memory
>>>> leak is also possible.
>>>> 
>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>>> false
>>>> 
>>>> This merely means that the result of unification would be that LP conains
>>>> itself. It could be a selmantically valid result but is not in the scope
>>>> of Prolog language.
>>>> 
>>> 
>>> It does not mean that. You are wrong.
>> 
>> It does in the context where it was presented. More generally,
>> unify_with_occurs_check also fails if the arguments are not
>> unfiable. But this possibility is already excluded by their
>> successfull unification.
>> 
> 
> IT CANNOT POSSIBLY BE SEMANTICALLY VALID

Of course it is. Its semantics is well defined by the Prolog standard.
Whether you like that semantics or not is irrelevant.

-- 
Mikko