After having built my first 8 two-input logic gates, I needed to figure out what to name them. The first four, Min, Max, Antimin, and Antimax came from Dr. Jones' work here. The next four were nameless, but very similar to the first four. I realized I didn't really have a full grasp of the relationship between binary and ternary and needed to learn a bit more about "-arity" as an abstract. This took me into symbolic logic.

In symbolic logic a binary system has 16 different "connectives". These are what we know as the logic gates. Mathematicians call them connectives because they connect statements. For example: Joe ate apples AND oranges. The logic gate is the connective. In a ternary system, nobody could ever hope to name all 19,683 connectives, but each of the binary connectives does have an analog in the set of ternary gates; a ternary gate "most like" the binary connective. This was mildly interesting and since looking over the subject had revealed the very useful datum that I had a functionally complete set of gates, I decided to look deeper and find the ternary gate that corresponded to each of the 16 binary connectives.

For two inputs, P and Q, these are the 16 connectives.

In a ternary system the first 6, Tautology - Negation Q, are trivial and consist of connections to signal reference voltages, the buffer(P), and the simple inverter(5). The next 8 are combinations of the buffer and simple inverter. The final two, Exclusive Disjunction and Biconditional are a bit more complicated and I have not built them yet.

With the possible exception of XOR and XNOR, I can build all of the ternary equivalents to the binary system with nothing but combinations of the buffer and the simple inverter. I already know that The Min gate, Max gate, and the monadics "Is False", "Is Unknown", and "Is True" form a functionally complete set, but Min and Max are combinations of the buffer and the simple inverter. So really, just those five monadic gates are a functionally complete set. I'm highly suspicious that I'll be able to make the ternary equivalents of XOR and XNOR with just the 5 and P as well.