Correcting the AI hallucination of LLM systems

On 9/6/2024 6:41 PM, Richard Damon wrote:

On 9/6/24 8:24 AM, olcott wrote:

On 9/6/2024 6:43 AM, Mikko wrote:

On 2024-09-03 12:49:11 +0000, olcott said:
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On 9/3/2024 5:44 AM, Mikko wrote:

On 2024-09-02 12:24:38 +0000, olcott said:
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On 9/2/2024 3:29 AM, Mikko wrote:

On 2024-09-01 12:56:16 +0000, olcott said:
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On 8/31/2024 10:04 PM, olcott wrote:

*I just fixed the loophole of the Gettier cases*
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knowledge is a justified true belief such that the
justification is sufficient reason to accept the
truth of the belief.
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https://en.wikipedia.org/wiki/Gettier_problem
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With a Justified true belief, in the Gettier cases
the observer does not know enough to know its true
yet it remains stipulated to be true.
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My original correction to this was a JTB such that the
justification necessitates the truth of the belief.
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With a [Sufficiently Justified belief], it is stipulated
that the observer does have a sufficient reason to accept
the truth of the belief.

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What could be a sufficient reason? Every justification of every
belief involves other belifs that could be false.

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For the justification to be sufficient the consequence of
the belief must be semantically entailed by its justification.

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If the belief is about something real then its justification
involves claims about something real. Nothing real is certain.
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I don't think that is correct.
My left hand exists right now even if it is
a mere figment of my own imagination and five
minutes ago never existed.

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As I don't know and can't (at least now) verify whether your left
hand exists or ever existed I can't regard that as a counter-
example.
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If the belief is not about something real then it is not clear
whether it is correct to call it "belief".

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*An axiomatic chain of inference based on this*
By the theory of simple types I mean the doctrine which says
that the objects of thought (or, in another interpretation,
the symbolic expressions) are divided into types, namely:
individuals, properties of individuals, relations between
individuals, properties of such relations, etc.
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...sentences of the form: " a has the property φ ", " b bears
the relation R to c ", etc. are meaningless, if a, b, c, R, φ
are not of types fitting together.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944

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The concepts of knowledge and truth are applicable to the knowledge
whether that is what certain peple meant when using those words.
Whether or to what extent that theory can be said to be true is
another problem.
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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.

 But Prolog can't even handle full first order logic, only basic propositions. The way you keep falling back to it shows that your understanding of Logic is very limited.

The architecture Prolog implementations can be extended to
an arbitrary number of simultaneous orders of logic, like
type theory or a knowledge ontology inheritance hierarchy.
The only thing that were are taking from Prolog is the notion of
Facts and Rules and true means expression X is only true on L when
X is derived from Facts in L by applying Rules.
Facts apply to formal language and natural language and are
stipulated to be true. Here is what Haskell Curry calls them:
"an elementary theorem is an elementary statement which is true."
https://www.liarparadox.org/Haskell_Curry_45.pdf
Rules apply to natural language and are a sequence of truth
preserving operations.

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That is the way that all expressions X of language L are determined
to be true in L on the basis of the connection from X in L by truth preserving operations to the semantic meaning of X in L.

 Right, but the connection might be infinite in length.
 

That would not be true in L.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false. // indicates infinite evaluation sequence

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{Linguistic truth} is the philosophical foundation of truth
in math and logic, AKA relations between finite strings.
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 Which you can't seem to explain how it differs from the classical semantic truth created by the (possibly infinite) chain of logical steps from the fundamental truth-makers of the system.

The key difference is that all expressions that were
previously undecidable become rejected as not truth-bearers
in L. The key benefit of this is that Tarski Undefinability
is refuted enabling LLM systems to be able to detect their
own falsehoods thus getting rid of AI hallucination.
We certainly can never have reliable artificial general
intelligence (AGI) when an AI system has no way to tell a
lie from the truth.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer