XPost: comp.theory, sci.logic, sci.math
On 4/29/2022 8:29 PM, Jeff Barnett wrote:
On 4/29/2022 5:10 PM, Richard Damon wrote:
On 4/29/22 6:30 PM, olcott wrote:
<SNIP>
When this is encoded in Prolog it is rejected as an infinite term as
my paper clearly shows.
As it should, since G uses Higher Order Logic which can NOT be
properly expressed in the first order logic of Prolog.
Unless Prolog has changed wildly in the last several years, it isn't
even close to FOL. I remember it as a toy that could only represent and reason with Horn clauses. Can Prolog now deal with quantifiers and
negation on both sides of an implication? That would be very impressive.
As a side note, I think it was this paucity of power that caused many
folks to not understand that "A -> B" could be true when "B" was false.
It resolves the Liar Paradox to semantically malformed:
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
(SWI-Prolog (threaded, 64 bits, version 7.6.4)
https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer
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