Thursday, May 19, 2005

Three valued logic beginnings

I've recently begun following some logic blogs in an attempt to find an outlet for my work in three-valued logic. I've been told that my results are probably not publishable, but I want to discuss them. I mentioned earlier that I don't clearly recall when I became interested in logic, but I can describe some of how I developed this topic.
Between 1981 and 1984, I spent many hours in the mathematics section of the BYU library, and in the process kept my knowledge of logic from dissolving into rust, as well as picked up a smattering of predicate logic. For various reasons, related to the early-20th century "Crisis" in mathematical foundations, I encountered reason to suspect that classical two-valued logic was good for mathematics, but there were doubts that it was sufficient, especially when it dealt with infinite sets. Mathematicians became concerned about the difference between "True" and "provable". I read about various paradoxes in set theory, and did a little bit of playing with them. Russell's paradox attracted my special attention, as did the discussion that even going to a three-valued logic wouldn't necessarily resolve it. I also encountered an article which attempted to analyze Anselm's proof of the existence of God using modal logic, which attracted my attention to that subject.
As I recall now, it was about this time that I started tinkering with what I called a "logic of indecision", using three values. Among my early attempts were truth tables for negation, disjunction (using the OR), and conjuncion (AND), and I used symbols. T, U (or I), and F for the truth values.

1 comment:

mike bauer said...

Hi, my name is Mike Bauer. I came across your blogg while searching information on Jan Lukasiewicz and 3 valued logic. I am working on a compiler/interpreter of
Z notation. I would be interested in what you are working on.