From Newsgroup: sci.logic

On 1/13/26 1:43 PM, olcott wrote:

On 1/13/2026 6:10 AM, Richard Damon wrote:

On 1/12/26 11:46 PM, olcott wrote:

On 1/12/2026 9:16 PM, Richard Damon wrote:

On 1/12/26 4:41 PM, olcott wrote:

How The Well-Founded Semantics for General Logic Programs

of (Van Gelder, Ross & Schlipf, 1991)
Journal of the Association for Computing Machinery,
volume 38, number 3, pp. 620{650 (1991).
https://users.soe.ucsc.edu/%7Eavg/Papers/wf.pdf

handle the Liar Paradox when we construe
non-well-founded / undefined as not a truth-bearer?

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

WFS assigns undefined to self-referential paradoxes
without external support.

When we interpret undefined as lack of truth-bearer
status the Liar sentence fails to be about anything
that can bear truth values

The paradox dissolves - there's no contradiction
because there's no genuine proposition

This is actually similar to how some philosophers
(like the "gap theorists") handle the Liar: sentences
that fail to achieve determinate truth conditions
simply aren't truth-bearers. WFS's undefined value
provides a formal mechanism for identifying exactly
these cases.

A Subtle Point The occurs-check failure in Prolog is
slightly different from WFS's undefined assignment -
it's a structural constraint on term formation. But
both point to the same insight: circular, unsupported
self-reference doesn't create genuine semantic content.

I thought you said that no one in the past handled the liar paradox?

That is no one in the past handling the Liar Paradox.
That all happened today.

So, today is 1991?

The paper provides the basis for me to
handle the Liar Paradox today. The Paper
does not mention the Liar Paradox it
only shows how to implement Proof Theoretic
semantics in a logic programming system.

I guess you are just admitting you are just a liar.


Note, since Prolog's logic is not sufficient to handle PA,

I never said it was. A formal system anchored in
Proof Theoretic Semantics is powerful enough.

Nope. It can't handle PA.

It definitely can. I already showed you the details
of how.

Nope, you PRESUME that Godel is non-sense.

But, you can't show the step in his proof that he uses an incorrect
logic step.

All you are doing is proving that you are just a pathological liar that
can't cover his own lies.

And, your claim that it is just non-smese means that you claim of making
truth computable CAN'T be true.

A fundamental of Godel's proof is showing that a proof checker is a computatble operation. That is the essense of what all of Godel's
numbering and the relation he derives.

If you define that you can't even build a proof checker, how do you
expect to be able to determine if a statement is actually true?

your argument here doesn't affect the logic system that you are
trying to argue about, and you are just showing that you don't
understand that difference.

Many system can handle some self-references, which Prolog, and
yours, can't.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 1/14/2026 8:57 PM, Richard Damon wrote:

On 1/13/26 1:43 PM, olcott wrote:

On 1/13/2026 6:10 AM, Richard Damon wrote:

On 1/12/26 11:46 PM, olcott wrote:

On 1/12/2026 9:16 PM, Richard Damon wrote:

On 1/12/26 4:41 PM, olcott wrote:

How The Well-Founded Semantics for General Logic Programs

of (Van Gelder, Ross & Schlipf, 1991)
Journal of the Association for Computing Machinery,
volume 38, number 3, pp. 620{650 (1991).
https://users.soe.ucsc.edu/%7Eavg/Papers/wf.pdf

handle the Liar Paradox when we construe
non-well-founded / undefined as not a truth-bearer?

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

WFS assigns undefined to self-referential paradoxes
without external support.

When we interpret undefined as lack of truth-bearer
status the Liar sentence fails to be about anything
that can bear truth values

The paradox dissolves - there's no contradiction
because there's no genuine proposition

This is actually similar to how some philosophers
(like the "gap theorists") handle the Liar: sentences
that fail to achieve determinate truth conditions
simply aren't truth-bearers. WFS's undefined value
provides a formal mechanism for identifying exactly
these cases.

A Subtle Point The occurs-check failure in Prolog is
slightly different from WFS's undefined assignment -
it's a structural constraint on term formation. But
both point to the same insight: circular, unsupported
self-reference doesn't create genuine semantic content.

I thought you said that no one in the past handled the liar paradox? >>>>>

That is no one in the past handling the Liar Paradox.
That all happened today.

So, today is 1991?

The paper provides the basis for me to
handle the Liar Paradox today. The Paper
does not mention the Liar Paradox it
only shows how to implement Proof Theoretic
semantics in a logic programming system.

I guess you are just admitting you are just a liar.


Note, since Prolog's logic is not sufficient to handle PA,

I never said it was. A formal system anchored in
Proof Theoretic Semantics is powerful enough.

Nope. It can't handle PA.

It definitely can. I already showed you the details
of how.

Nope,-a you PRESUME that Godel is non-sense.

rCLWhen PA is interpreted within proofrCatheoretic semantics, only wellrCafounded inferential structures are admissible as meaningful
statements. G||delrCOs diagonal construction produces an ungrounded, selfrCareferential formula whose proofrCadependency graph contains a cycle. Since such expressions are not truthbearers in this framework, the
classical incompleteness phenomenon does not arise. PA itself remains
sound and complete with respect to its grounded proof rules.rCY

But, you can't show the step in his proof that he uses an incorrect
logic step.

All you are doing is proving that you are just a pathological liar that can't cover his own lies.

And, your claim that it is just non-smese means that you claim of making truth computable CAN'T be true.

A fundamental of Godel's proof is showing that a proof checker is a computatble operation. That is the essense of what all of Godel's
numbering and the relation he derives.

If you define that you can't even build a proof checker, how do you
expect to be able to determine if a statement is actually true?

your argument here doesn't affect the logic system that you are
trying to argue about, and you are just showing that you don't
understand that difference.

Many system can handle some self-references, which Prolog, and
yours, can't.

--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 1/15/26 12:24 AM, olcott wrote:

On 1/14/2026 8:57 PM, Richard Damon wrote:

On 1/13/26 1:43 PM, olcott wrote:

On 1/13/2026 6:10 AM, Richard Damon wrote:

On 1/12/26 11:46 PM, olcott wrote:

On 1/12/2026 9:16 PM, Richard Damon wrote:

On 1/12/26 4:41 PM, olcott wrote:

How The Well-Founded Semantics for General Logic Programs

of (Van Gelder, Ross & Schlipf, 1991)
Journal of the Association for Computing Machinery,
volume 38, number 3, pp. 620{650 (1991).
https://users.soe.ucsc.edu/%7Eavg/Papers/wf.pdf

handle the Liar Paradox when we construe
non-well-founded / undefined as not a truth-bearer?

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

WFS assigns undefined to self-referential paradoxes
without external support.

When we interpret undefined as lack of truth-bearer
status the Liar sentence fails to be about anything
that can bear truth values

The paradox dissolves - there's no contradiction
because there's no genuine proposition

This is actually similar to how some philosophers
(like the "gap theorists") handle the Liar: sentences
that fail to achieve determinate truth conditions
simply aren't truth-bearers. WFS's undefined value
provides a formal mechanism for identifying exactly
these cases.

A Subtle Point The occurs-check failure in Prolog is
slightly different from WFS's undefined assignment -
it's a structural constraint on term formation. But
both point to the same insight: circular, unsupported
self-reference doesn't create genuine semantic content.

I thought you said that no one in the past handled the liar paradox? >>>>>>

That is no one in the past handling the Liar Paradox.
That all happened today.

So, today is 1991?

The paper provides the basis for me to
handle the Liar Paradox today. The Paper
does not mention the Liar Paradox it
only shows how to implement Proof Theoretic
semantics in a logic programming system.

I guess you are just admitting you are just a liar.


Note, since Prolog's logic is not sufficient to handle PA,

I never said it was. A formal system anchored in
Proof Theoretic Semantics is powerful enough.

Nope. It can't handle PA.

It definitely can. I already showed you the details
of how.

Nope,-a you PRESUME that Godel is non-sense.

rCLWhen PA is interpreted within proofrCatheoretic semantics, only wellrCafounded inferential structures are admissible as meaningful statements. G||delrCOs diagonal construction produces an ungrounded, selfrCareferential formula whose proofrCadependency graph contains a cycle. Since such expressions are not truthbearers in this framework, the
classical incompleteness phenomenon does not arise. PA itself remains
sound and complete with respect to its grounded proof rules.rCY

In other words, you are just admitting to be an idiot that deosn't care
what your words actually mean.

You CAN NOT consistantly interpreted PA withiing proof-theoretic semantics.

Godels statement *WAS* built bu well-founded inferential methods.

His statement *IS* a truth bearer by the rules of the logic.

You can't just say otherwise.

Your problem is you just can't "redefine" what a word, like truth means,
in a system.

You don't seem to understand that the paper you are reading admits that
it isn't handling thw whole of the space, but only giving PARTIAL answers.

But, you can't show the step in his proof that he uses an incorrect
logic step.

All you are doing is proving that you are just a pathological liar
that can't cover his own lies.

And, your claim that it is just non-smese means that you claim of
making truth computable CAN'T be true.

A fundamental of Godel's proof is showing that a proof checker is a
computatble operation. That is the essense of what all of Godel's
numbering and the relation he derives.

If you define that you can't even build a proof checker, how do you
expect to be able to determine if a statement is actually true?

your argument here doesn't affect the logic system that you are
trying to argue about, and you are just showing that you don't
understand that difference.

Many system can handle some self-references, which Prolog, and
yours, can't.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 15/01/2026 02:57, Richard Damon wrote:

A fundamental of Godel's proof is showing that a proof checker is a computatble operation. That is the essense of what all of Godel's
numbering and the relation he derives.

A proof checker rejects the proof in G||del's 1931 paper because you need
an ATP to fill in the proof of proposition V which he doesn't prove in
his 1931 paper.
--
Tristan Wibberley

The message body is Copyright (C) 2026 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 15/01/2026 02:57, Richard Damon wrote:

A fundamental of Godel's proof is showing that a proof checker is a computatble operation. That is the essense of what all of Godel's
numbering and the relation he derives.

A proof checker rejects the proof in G||del's 1931 paper because you need
an ATP to fill in the proof of proposition V which he doesn't prove in
his 1931 paper.
--
Tristan Wibberley

The message body is Copyright (C) 2026 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 15/01/2026 11:50, Richard Damon wrote:

Godels statement *WAS* built bu well-founded inferential methods.

His statement *IS* a truth bearer by the rules of the logic.

You can't just say otherwise.

You can't just say /so/ either. The most you can say is that /you/
believe in it.
--
Tristan Wibberley

The message body is Copyright (C) 2026 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 1/15/2026 5:50 AM, Richard Damon wrote:

On 1/15/26 12:24 AM, olcott wrote:

On 1/14/2026 8:57 PM, Richard Damon wrote:

On 1/13/26 1:43 PM, olcott wrote:

On 1/13/2026 6:10 AM, Richard Damon wrote:

On 1/12/26 11:46 PM, olcott wrote:

On 1/12/2026 9:16 PM, Richard Damon wrote:

On 1/12/26 4:41 PM, olcott wrote:

How The Well-Founded Semantics for General Logic Programs

of (Van Gelder, Ross & Schlipf, 1991)
Journal of the Association for Computing Machinery,
volume 38, number 3, pp. 620{650 (1991).
https://users.soe.ucsc.edu/%7Eavg/Papers/wf.pdf

handle the Liar Paradox when we construe
non-well-founded / undefined as not a truth-bearer?

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

WFS assigns undefined to self-referential paradoxes
without external support.

When we interpret undefined as lack of truth-bearer
status the Liar sentence fails to be about anything
that can bear truth values

The paradox dissolves - there's no contradiction
because there's no genuine proposition

This is actually similar to how some philosophers
(like the "gap theorists") handle the Liar: sentences
that fail to achieve determinate truth conditions
simply aren't truth-bearers. WFS's undefined value
provides a formal mechanism for identifying exactly
these cases.

A Subtle Point The occurs-check failure in Prolog is
slightly different from WFS's undefined assignment -
it's a structural constraint on term formation. But
both point to the same insight: circular, unsupported
self-reference doesn't create genuine semantic content.

I thought you said that no one in the past handled the liar paradox? >>>>>>>

That is no one in the past handling the Liar Paradox.
That all happened today.

So, today is 1991?

The paper provides the basis for me to
handle the Liar Paradox today. The Paper
does not mention the Liar Paradox it
only shows how to implement Proof Theoretic
semantics in a logic programming system.

I guess you are just admitting you are just a liar.


Note, since Prolog's logic is not sufficient to handle PA,

I never said it was. A formal system anchored in
Proof Theoretic Semantics is powerful enough.

Nope. It can't handle PA.

It definitely can. I already showed you the details
of how.

Nope,-a you PRESUME that Godel is non-sense.

rCLWhen PA is interpreted within proofrCatheoretic semantics, only
wellrCafounded inferential structures are admissible as meaningful
statements. G||delrCOs diagonal construction produces an ungrounded,
selfrCareferential formula whose proofrCadependency graph contains a
cycle. Since such expressions are not truthbearers in this framework,
the classical incompleteness phenomenon does not arise. PA itself
remains sound and complete with respect to its grounded proof rules.rCY

In other words, you are just admitting to be an idiot that deosn't care
what your words actually mean.

The term *proofrCatheoretic semantics* has always
proved my point long before I ever heard of it.
--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 1/15/26 6:40 PM, olcott wrote:

On 1/15/2026 5:50 AM, Richard Damon wrote:

On 1/15/26 12:24 AM, olcott wrote:

On 1/14/2026 8:57 PM, Richard Damon wrote:

On 1/13/26 1:43 PM, olcott wrote:

On 1/13/2026 6:10 AM, Richard Damon wrote:

On 1/12/26 11:46 PM, olcott wrote:

On 1/12/2026 9:16 PM, Richard Damon wrote:

On 1/12/26 4:41 PM, olcott wrote:

How The Well-Founded Semantics for General Logic Programs

of (Van Gelder, Ross & Schlipf, 1991)
Journal of the Association for Computing Machinery,
volume 38, number 3, pp. 620{650 (1991).
https://users.soe.ucsc.edu/%7Eavg/Papers/wf.pdf

handle the Liar Paradox when we construe
non-well-founded / undefined as not a truth-bearer?

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

WFS assigns undefined to self-referential paradoxes
without external support.

When we interpret undefined as lack of truth-bearer
status the Liar sentence fails to be about anything
that can bear truth values

The paradox dissolves - there's no contradiction
because there's no genuine proposition

This is actually similar to how some philosophers
(like the "gap theorists") handle the Liar: sentences
that fail to achieve determinate truth conditions
simply aren't truth-bearers. WFS's undefined value
provides a formal mechanism for identifying exactly
these cases.

A Subtle Point The occurs-check failure in Prolog is
slightly different from WFS's undefined assignment -
it's a structural constraint on term formation. But
both point to the same insight: circular, unsupported
self-reference doesn't create genuine semantic content.

I thought you said that no one in the past handled the liar
paradox?

That is no one in the past handling the Liar Paradox.
That all happened today.

So, today is 1991?

The paper provides the basis for me to
handle the Liar Paradox today. The Paper
does not mention the Liar Paradox it
only shows how to implement Proof Theoretic
semantics in a logic programming system.

I guess you are just admitting you are just a liar.


Note, since Prolog's logic is not sufficient to handle PA,

I never said it was. A formal system anchored in
Proof Theoretic Semantics is powerful enough.

Nope. It can't handle PA.

It definitely can. I already showed you the details
of how.

Nope,-a you PRESUME that Godel is non-sense.

rCLWhen PA is interpreted within proofrCatheoretic semantics, only
wellrCafounded inferential structures are admissible as meaningful
statements. G||delrCOs diagonal construction produces an ungrounded,
selfrCareferential formula whose proofrCadependency graph contains a
cycle. Since such expressions are not truthbearers in this framework,
the classical incompleteness phenomenon does not arise. PA itself
remains sound and complete with respect to its grounded proof rules.rCY

In other words, you are just admitting to be an idiot that deosn't
care what your words actually mean.

The term *proofrCatheoretic semantics* has always
proved my point long before I ever heard of it.

Nope, just sbows you don't understand what you are talking about.

The problem is you can't just "bolt on" a new interpretation to a
system, and thus it can't help you try to refute any of the things you
don't like.

You could try to learn how they actually work and then see if you can
make new versions of those system that work under those rules and see if
they do ANYTHING actually useful.

My guess is not, at least not on the scale you would need, as
"mathematics" just doesn't fit that model.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 1/15/26 9:30 AM, Tristan Wibberley wrote:

On 15/01/2026 02:57, Richard Damon wrote:

A fundamental of Godel's proof is showing that a proof checker is a
computatble operation. That is the essense of what all of Godel's
numbering and the relation he derives.

A proof checker rejects the proof in G||del's 1931 paper because you need
an ATP to fill in the proof of proposition V which he doesn't prove in
his 1931 paper.

Why don't you write up your analysis and publish it?

Note, the proof checker isn't checking his proof, it is checking the
proof of his statement.

I guess you don't understand what he was talking about.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 16/01/2026 01:40, olcott wrote:

On 1/15/2026 5:50 AM, Richard Damon wrote:

On 1/15/26 12:24 AM, olcott wrote:

On 1/14/2026 8:57 PM, Richard Damon wrote:

On 1/13/26 1:43 PM, olcott wrote:

On 1/13/2026 6:10 AM, Richard Damon wrote:

On 1/12/26 11:46 PM, olcott wrote:

On 1/12/2026 9:16 PM, Richard Damon wrote:

On 1/12/26 4:41 PM, olcott wrote:

How The Well-Founded Semantics for General Logic Programs

of (Van Gelder, Ross & Schlipf, 1991)
Journal of the Association for Computing Machinery,
volume 38, number 3, pp. 620{650 (1991).
https://users.soe.ucsc.edu/%7Eavg/Papers/wf.pdf

handle the Liar Paradox when we construe
non-well-founded / undefined as not a truth-bearer?

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

WFS assigns undefined to self-referential paradoxes
without external support.

When we interpret undefined as lack of truth-bearer
status the Liar sentence fails to be about anything
that can bear truth values

The paradox dissolves - there's no contradiction
because there's no genuine proposition

This is actually similar to how some philosophers
(like the "gap theorists") handle the Liar: sentences
that fail to achieve determinate truth conditions
simply aren't truth-bearers. WFS's undefined value
provides a formal mechanism for identifying exactly
these cases.

A Subtle Point The occurs-check failure in Prolog is
slightly different from WFS's undefined assignment -
it's a structural constraint on term formation. But
both point to the same insight: circular, unsupported
self-reference doesn't create genuine semantic content.

I thought you said that no one in the past handled the liar
paradox?

That is no one in the past handling the Liar Paradox.
That all happened today.

So, today is 1991?

The paper provides the basis for me to
handle the Liar Paradox today. The Paper
does not mention the Liar Paradox it
only shows how to implement Proof Theoretic
semantics in a logic programming system.

I guess you are just admitting you are just a liar.


Note, since Prolog's logic is not sufficient to handle PA,

I never said it was. A formal system anchored in
Proof Theoretic Semantics is powerful enough.

Nope. It can't handle PA.

It definitely can. I already showed you the details
of how.

Nope,-a you PRESUME that Godel is non-sense.

rCLWhen PA is interpreted within proofrCatheoretic semantics, only
wellrCafounded inferential structures are admissible as meaningful
statements. G||delrCOs diagonal construction produces an ungrounded,
selfrCareferential formula whose proofrCadependency graph contains a
cycle. Since such expressions are not truthbearers in this framework,
the classical incompleteness phenomenon does not arise. PA itself
remains sound and complete with respect to its grounded proof rules.rCY

In other words, you are just admitting to be an idiot that deosn't
care what your words actually mean.

The term *proofrCatheoretic semantics* has always
proved my point long before I ever heard of it.

A term does not prove anything. Only a proof proves.
--
Mikko
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: sci.logic

On 1/18/2026 5:54 AM, Mikko wrote:

On 16/01/2026 01:40, olcott wrote:

On 1/15/2026 5:50 AM, Richard Damon wrote:

On 1/15/26 12:24 AM, olcott wrote:

On 1/14/2026 8:57 PM, Richard Damon wrote:

On 1/13/26 1:43 PM, olcott wrote:

On 1/13/2026 6:10 AM, Richard Damon wrote:

On 1/12/26 11:46 PM, olcott wrote:

On 1/12/2026 9:16 PM, Richard Damon wrote:

On 1/12/26 4:41 PM, olcott wrote:

How The Well-Founded Semantics for General Logic Programs

of (Van Gelder, Ross & Schlipf, 1991)
Journal of the Association for Computing Machinery,
volume 38, number 3, pp. 620{650 (1991).
https://users.soe.ucsc.edu/%7Eavg/Papers/wf.pdf

handle the Liar Paradox when we construe
non-well-founded / undefined as not a truth-bearer?

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

WFS assigns undefined to self-referential paradoxes
without external support.

When we interpret undefined as lack of truth-bearer
status the Liar sentence fails to be about anything
that can bear truth values

The paradox dissolves - there's no contradiction
because there's no genuine proposition

This is actually similar to how some philosophers
(like the "gap theorists") handle the Liar: sentences
that fail to achieve determinate truth conditions
simply aren't truth-bearers. WFS's undefined value
provides a formal mechanism for identifying exactly
these cases.

A Subtle Point The occurs-check failure in Prolog is
slightly different from WFS's undefined assignment -
it's a structural constraint on term formation. But
both point to the same insight: circular, unsupported
self-reference doesn't create genuine semantic content.

I thought you said that no one in the past handled the liar >>>>>>>>> paradox?

That is no one in the past handling the Liar Paradox.
That all happened today.

So, today is 1991?

The paper provides the basis for me to
handle the Liar Paradox today. The Paper
does not mention the Liar Paradox it
only shows how to implement Proof Theoretic
semantics in a logic programming system.

I guess you are just admitting you are just a liar.


Note, since Prolog's logic is not sufficient to handle PA,

I never said it was. A formal system anchored in
Proof Theoretic Semantics is powerful enough.

Nope. It can't handle PA.

It definitely can. I already showed you the details
of how.

Nope,-a you PRESUME that Godel is non-sense.

rCLWhen PA is interpreted within proofrCatheoretic semantics, only
wellrCafounded inferential structures are admissible as meaningful
statements. G||delrCOs diagonal construction produces an ungrounded,
selfrCareferential formula whose proofrCadependency graph contains a
cycle. Since such expressions are not truthbearers in this
framework, the classical incompleteness phenomenon does not arise.
PA itself remains sound and complete with respect to its grounded
proof rules.rCY

In other words, you are just admitting to be an idiot that deosn't
care what your words actually mean.

The term *proofrCatheoretic semantics* has always
proved my point long before I ever heard of it.

A term does not prove anything. Only a proof proves.

Proof Theoretic Semantics with the notion of
non-well-founded expressions is the same thing
that I have been saying for years.

True and False in PA have always been x or ~x is
provable from the actual axioms of PA, otherwise
x is simply not a truth bearer in PA. The only
clarification that I make now explicitly adding a
truth predicate to PA.

reCx ree PA ((True(PA, x) rei (PA reo x))
reCx ree PA ((False(PA, x) rei (PA reo ~x))
reCx ree PA ((~True(PA, x) reo (~False(PA, x) rei ~TruthBearer(PA, x))
--
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
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From Newsgroup: sci.logic

On 1/18/26 8:45 AM, olcott wrote:

On 1/18/2026 5:54 AM, Mikko wrote:

On 16/01/2026 01:40, olcott wrote:

On 1/15/2026 5:50 AM, Richard Damon wrote:

On 1/15/26 12:24 AM, olcott wrote:

On 1/14/2026 8:57 PM, Richard Damon wrote:

On 1/13/26 1:43 PM, olcott wrote:

On 1/13/2026 6:10 AM, Richard Damon wrote:

On 1/12/26 11:46 PM, olcott wrote:

On 1/12/2026 9:16 PM, Richard Damon wrote:

On 1/12/26 4:41 PM, olcott wrote:

How The Well-Founded Semantics for General Logic Programs >>>>>>>>>>>
of (Van Gelder, Ross & Schlipf, 1991)
Journal of the Association for Computing Machinery,
volume 38, number 3, pp. 620{650 (1991).
https://users.soe.ucsc.edu/%7Eavg/Papers/wf.pdf

handle the Liar Paradox when we construe
non-well-founded / undefined as not a truth-bearer?

% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

WFS assigns undefined to self-referential paradoxes
without external support.

When we interpret undefined as lack of truth-bearer
status the Liar sentence fails to be about anything
that can bear truth values

The paradox dissolves - there's no contradiction
because there's no genuine proposition

This is actually similar to how some philosophers
(like the "gap theorists") handle the Liar: sentences
that fail to achieve determinate truth conditions
simply aren't truth-bearers. WFS's undefined value
provides a formal mechanism for identifying exactly
these cases.

A Subtle Point The occurs-check failure in Prolog is
slightly different from WFS's undefined assignment -
it's a structural constraint on term formation. But
both point to the same insight: circular, unsupported
self-reference doesn't create genuine semantic content.

I thought you said that no one in the past handled the liar >>>>>>>>>> paradox?

That is no one in the past handling the Liar Paradox.
That all happened today.

So, today is 1991?

The paper provides the basis for me to
handle the Liar Paradox today. The Paper
does not mention the Liar Paradox it
only shows how to implement Proof Theoretic
semantics in a logic programming system.

I guess you are just admitting you are just a liar.


Note, since Prolog's logic is not sufficient to handle PA, >>>>>>>>>

I never said it was. A formal system anchored in
Proof Theoretic Semantics is powerful enough.

Nope. It can't handle PA.

It definitely can. I already showed you the details
of how.

Nope,-a you PRESUME that Godel is non-sense.

rCLWhen PA is interpreted within proofrCatheoretic semantics, only
wellrCafounded inferential structures are admissible as meaningful
statements. G||delrCOs diagonal construction produces an ungrounded, >>>>> selfrCareferential formula whose proofrCadependency graph contains a >>>>> cycle. Since such expressions are not truthbearers in this
framework, the classical incompleteness phenomenon does not arise.
PA itself remains sound and complete with respect to its grounded
proof rules.rCY

In other words, you are just admitting to be an idiot that deosn't
care what your words actually mean.

The term *proofrCatheoretic semantics* has always
proved my point long before I ever heard of it.

A term does not prove anything. Only a proof proves.

Proof Theoretic Semantics with the notion of
non-well-founded expressions is the same thing
that I have been saying for years.

True and False in PA have always been x or ~x is
provable from the actual axioms of PA, otherwise
x is simply not a truth bearer in PA. The only
clarification that I make now explicitly adding a
truth predicate to PA.

reCx ree PA ((True(PA, x)-a rei (PA reo x))
reCx ree PA ((False(PA, x) rei (PA reo ~x))
reCx ree PA ((~True(PA, x) reo (~False(PA, x) rei ~TruthBearer(PA, x))

No, because your embodyment uses a non-well-founded criteria.

The problem is you can't always prove "TruthBearer" or "~TruthBearer" so
your third line is just non-well-founded, and isn't a TruthBearing
statement for all x.

It seems you forget that is was proven that adding a truth predicate to
PA makes in inconsistent, and you haven't shown where Tarski was wrong.

At best you say that a result he gets must be wrong, but can't show the
actual error in his work.
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From Newsgroup: sci.logic

On 18/01/2026 15:45, olcott wrote:

On 1/18/2026 5:54 AM, Mikko wrote:

On 16/01/2026 01:40, olcott wrote:

The term *proofrCatheoretic semantics* has always
proved my point long before I ever heard of it.

A term does not prove anything. Only a proof proves.

Note that my comment is not conradicted nor denied below:

Proof Theoretic Semantics with the notion of
non-well-founded expressions is the same thing
that I have been saying for years.

True and False in PA have always been x or ~x is
provable from the actual axioms of PA, otherwise
x is simply not a truth bearer in PA. The only
clarification that I make now explicitly adding a
truth predicate to PA.

reCx ree PA ((True(PA, x)-a rei (PA reo x))
reCx ree PA ((False(PA, x) rei (PA reo ~x))
reCx ree PA ((~True(PA, x) reo (~False(PA, x) rei ~TruthBearer(PA, x))

--
Mikko
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