Oops! I forgot to mention one of the most key datums that make this whole project possible. Since I'm using comparators... what am I comparing the incoming signal to? Well, in any logic system you need to define what range of voltages define the various states. This is called the logic family.
In the ternary logic family I've developed for testing there are five different voltages that are used to delineate the three states. The power supply provides a -5V rail, a 0V ground, and a +5V rail. From the -5V rail I use two resistors to create an approximately -1V rail and on the +5 side I do the same to create an approximately 1V rail.
The - state is -5V to -1V
The 0 state is -1V to 1V
The + state is 1V to 5V
Example: If I want to implement the monadic operation "R" (00+), I hook up a comparator from the LM319 with ground connected to 0V to set the low signal to 0 and then attach the output to 5V to set the high signal. Then I attach the negative input of the comparator to 1V. If the incoming signal to the positive input of the comparator is greater than 1V (i.e. it's 5V) then the output is + (5V). If the incoming signal is less than 1V (i.e. it's -5V or 0V), then the output is 0 (0V).
This was all in the diagrams linked to in the post "Monadic Gates, Take 1", but with no explanation.