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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception --- Tarski
Date: Tue, 25 Feb 2025 17:27:13 +0200
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On 2025-02-24 21:31:26 +0000, olcott said:

> On 2/24/2025 2:51 AM, Mikko wrote:
>> 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.
> 
> Go freaking read the Clocksin and Mellish.
> an "infinite term" means NOT SEMANTICALLY VALID.

Prolog does not define any semantics other than the execution semantics
of a prolog program. Therefore no data structure has any own semantics.

The result of the exectution of an instruction like LP == not(true(LP))
is not fully defined by the standard so we may say that that instruction
is semantically invalid.

-- 
Mikko