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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: The key undecidable instance that I know about
Date: Mon, 10 Mar 2025 11:48:14 +0200
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On 2025-03-09 17:15:13 +0000, olcott said:

> Is the Liar Paradox True or False?
> 
> LP := ~True(LP)

In typical languages of formal logic that is not a syntactically valid
expression.

> ?- LP = not(true(LP)).
> LP = not(true(LP)).

Apparently you were using a Prolog implementation that does not check
whether a cyclic data structure is produced. Another Prolog implementation
could say false instead.

> ?- unify_with_occurs_check(LP, not(true(LP))).
> false.

For this quesry the only permitted answer is false.

> Its infinitely recursive structure makes it neither true nor false.

What is that "its" intended to refer to? According to Prolog rules
unify_with_occurs_check(LP, not(true(LP))) is false. Accordint to
the implementation you were using LP = not(true(LP)) is true but
another implementation might say it is false. If you mean LP itself,
that is neither true nor false just lke 42 is neither true nor false.

-- 
Mikko