Where can I find the proof of the completeness of
Lukasiewicz-Slupeki’s three-value logic?
Thanks in advance.
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19
Apr
A question about three-value logic
liur…@my-deja.com wrote:
> Where can I find the proof of the completeness of
> Lukasiewicz-Slupeki’s three-value logic?
> Thanks in advance.
> Sent via Deja.com
> http://www.deja.com/
What is Lukasiewicz-Slupeki three-valued logic? Lukasiewicz said in a
three-valued logic that one value would be indeterminate, with the other
two the traditional true and false, I think he called it U.
One way to consider the indeterminate value in that logic is to assign
to it the ~(T or F). This follows making it simple to construct
near-infinite base sets.
Ross
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> What I mean was Lukasiewicz-Slupeki’s caculus of three-value logic.
I want the proof of its completeness.
Thank you for your message.
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liur…@my-deja.com wrote:
> > What I mean was Lukasiewicz-Slupeki’s caculus of three-value logic.
> I want the proof of its completeness.
> Thank you for your message.
> Sent via Deja.com
> http://www.deja.com/
Hello,
To get proof of its "completeness", that would involve disproving any
"incompleteness". There are various interpretations of "completeness"
and "calculus", so, to prove "completeness" requires more definition of
that in this context.
I searched the Internet using regular tools for the name "Slupeki" and
did not find any links related to logic.
In terms of proving completeness of Lukasiewicz three-valued logic,
generally the term completeness has to do with Goedel sentence. Imagine
a set of all axioms, inconsistent and consistent. I would say that the
set of all axioms A misses no Goedel sentence, because any axiom or
sentence is in A. Perhaps the Goedel sentence is like the set of all
sets not containing themselves, which would contain a lot of well-founded
sets, except for one impossible set element: the set not containing
itself not containing itself, etc, the run-on sentence.
Ross
–
Ross Andrew Finlayson
Finlayson Consulting
Ross at Tiki-Lounge: http://www.tiki-lounge.com/~raf/
"The best mathematician in the world is Maplev in Ontario." - Pertti L.
Hi, Ross:
I made a mistake.It’s "Slupecki", not "Slupeki".I am sorry.
what I mean is the axiom system of three-valued logic constructed by
Lukasiewicz and revised by Slupecki.I donnot know how to prove its
completeness. That is, every well-formed-formula which can be proved in
this system is valid according to the semantic definiation.
I have seen your personal web page.We are friend.
liu
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Hi, Ross:
I made a mistake.It’s "Slupecki", not "Slupeki".I am sorry.
what I mean is the axiom system of three-valued logic constructed by
Lukasiewicz and revised by Slupecki.I donnot know how to prove its
completeness. That is, every well-formed-formula which can be proved in
this system is valid according to the semantic definiation.
Thanks for your patient.
liu
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liur…@my-deja.com wrote:
> Hi, Ross:
> I made a mistake.It’s "Slupecki", not "Slupeki".I am sorry.
> what I mean is the axiom system of three-valued logic constructed by
> Lukasiewicz and revised by Slupecki.I donnot know how to prove its
> completeness. That is, every well-formed-formula which can be proved in
> this system is valid according to the semantic definiation.
> I have seen your personal web page.We are friend.
> liu
> Sent via Deja.com
> http://www.deja.com/
Ah ha, thank you. It appears to be Jerzy Slupecki, 1904-1987. The
Internet tells me he worked with Lukasiewicz. A page in French describes a
non-classic multivalued logic, with Slupecki among the names Lukasiewicz,
Post, Kleene, and Bochvar.
We have had discussion of completeness in classical logic here. Can you
say if you are proving completeness of multi-valued logic?
Ross
—
Ross Andrew Finlayson
Finlayson Consulting
Ross at Tiki-Lounge: http://www.tiki-lounge.com/~raf/
"The best mathematician in the world is Maplev in Ontario." - Pertti L.
Hi,Ross:
Yes,what I what is really the proof of the completeness of three-
value logic.
liu
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liur…@my-deja.com wrote:
> Where can I find the proof of the completeness of
> Lukasiewicz-Slupeki’s three-value logic?
> Thanks in advance.
> Sent via Deja.com
> http://www.deja.com/
Perhaps, J B Rosser & A R Turquette _Axiom schemes for m-valued
propositional calculi_ JSL 10 (1945) pp 61-82 and ibid 14 (1949) pp
219-24. In Tarski’s _Logic, Semantics, Metamathematics_ Ch IV, you will
find references to Polish papers. The paper in LSM is also in
Lukasiewicz’s collected papers. Rosser and Turquette wrote a (N-H?)
book. More recent is Malinowski _Many valued logics_, OUP, BUT I DON’T
KNOW what’s in it.
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