A Universal Set Theory with Ternary Logic

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BrianT
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A Universal Set Theory with Ternary Logic

Post by BrianT » Mon Oct 03, 2005 10:30 am

Is anyone here familiar with models and the axioms of set theory and nonclassical logic and would also like to help me find faults with my paper? If so, I can post a link to it or pm you if no one else cares. Any feedback would be appreciated.
--Brian

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DHodges
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A Universal Set Theory with Ternary Logic

Post by DHodges » Tue Oct 04, 2005 10:26 pm

It's not quite my field, but I'll take a look at it if you like. You can email me if you'd rather discuss it non-publicly.

BrianT
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Post by BrianT » Sat Oct 08, 2005 4:53 am

I'm going to post a reply to your email here just because the quoting feature on this forum is better. It will be clearer to us who is writing what and what is a quote.

If you are someone else and want to read the paper then get it here: http://home.comcast.net/~morlai/universal.pdf .

Thanks again David!
--Brian

BrianT
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Joined: Tue Aug 23, 2005 5:29 am

Post by BrianT » Sat Oct 08, 2005 5:19 am

A few comments on section 1; mostly typos, a few bits that could use some clarifying.

In the first table (in section 1.1), the last three entries in the last column are reversed. They should be T instead of F.

You define four functions on page 2. The last two functions have an "a" which should be a phi.
Done. Thanks.
At the bottom of page 2, you say: "I observe that in ternary logic, phi -> psi is a different statement than if phi then psi." However, above that you had shown the truth table for "phi(1) -> phi(2)", which you defined to be the same as "-phi(1) or phi(2)" (both having the same truth table).
I'm not exactly sure what you're getting at. Well, check out the edit and see if that makes it ok.
At the bottom of page 2, you write: "In mathematical English, I use binary logic." I take that to mean that when you write "phi -> psi" you mean you are referring to ternary, and when you write out "if phi then psi", then you are referring to binary logic.
Yes that is what I meant to convey. It's mainly for models to model a formula I want either true or false even is the formula has the third truth value. phi <--> psi is different from "phi iff psi" as you know but I do want to be able to use English on ternary formulas in the way discussed in "the convention," defined by induction of formulas with V+.

You might also consider a section at the top discussing what a third truth value means. I thought about it a bit, coming up with a few different interpretations: the truth value is unknown; the statement is not well-formed; the statement is partially true. The truth tables seem to be independant of the particular interpretation, which is good, and maybe worth noting.
Done. See remarks in the beginning of version 1.1 which is in your inbox (a link, at least).
--Brian

gaspar
Posts: 1
Joined: Mon Feb 20, 2006 3:24 pm

aymara logic

Post by gaspar » Mon Feb 20, 2006 4:00 pm

as i understand it, the aymara language has fascinated linguists
because of its so called ternary
logic structure.

google "aymara" and "ternary logic" in
order to get an idea of what's out
in cyberspace.

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