Hello insyder-ga,
Thanks for asking such an interesting question...and for giving me the
opportunity to answer it. Since advanced logic isn't necessarily my
forte, I am going to answer your question mostly by quoting from a key
paper on the topic of "ternary logic" -- one that directly addresses
the 27 relationships you asked about.
First, the paper itself is: "A Brief Introduction to Ternary Logic"
by Jorge Pedraza Arpasi. You can find it on the web at:
http://www.aymara.org/ternary/ternary.pdf
The paper begins by distinguishing binary logic (true/false) from
ternary logic (true/false/"perhaps true perhaps false"). As the paper
puts it:
--In this note, for the binary case, we will use the values {0, 1}
which means true=1 and false=0. Whereas that for ternary case we will
use the values {0, 1, 2} which means true=1,
false=2, and "perhaps true perhaps false" =0.
-----
In the binary system, and given a set of basic assumptions, there are
are 16 basic operations that emerge:
--Over L are defined the following basic
operations...negation...disjunction...conjunction...From these three
operations we can derive 16 binary operations, among them the
implication...and the equivalence...
-----
For ternary logic, and under appropriate conditions, there are 27 such operations:
--When n = 1 we have one-variable functions f(x), and there are [3 e
3] = 27 of these functions, among them are, the Identity or
Affirmation id(x), the negation N(x), the Tautology...and the
contradiction... All these 27 functions are also called modal
functions of x and they are shown in the Table 8 [NOTE from
pafalafa-ga -- see Table 8 in the paper for a fuller description].
-----
The 27 relationships emerge from simple assumptions about one-variable
functions...under a more complex scenario of two variables, thousands
of relationships can emerge.
==========
I did not come across any site that actually assigned English names to
all 27 of the relationships you asked about, and I'm not sure that
such names exist (as I mentioned earlier, more complex systems can
have sets of thousands or even millions of such relationships).
For an additional discussion of ternary logic, you might want to have
a look at "The Logic of More" at:
http://ternarylogic.home.att.net/
==========
I hope this information fully meets your needs. If you find you need
additional information about anything I have posted here, please don't
hesitate to post a Request for Clarification to let me know how I can
help you further.
You are also, certainly, invited to post additional questions here at
Google Answers if you want to explore other aspects of ternary logic
with the researchers here.
All the best.
pafalafa-ga
search strategy: Google searches on:
(27 OR "twenty seven") (logic OR logical) (relations OR relationships)
(27 OR "twenty seven") tautology affirmation contradiction negation |