Once we grasp the utility of minimal negation operators for partitioning a universe of discourse into several regions and any region into further parts, there are quite a few directions we might explore as far as our next steps go.
One thing I always did when I reached a new level of understanding about any logical issue was to see if I could actualize the insight in whatever programming projects I was working on at the time. Conversely and recursively the trials of doing that would often force me to modify my initial understanding in the direction of what works in brass tacks practice.
The use of cactus graphs to implement minimal negation operators made its way into the Theme One Program I worked on all through the 1980s and the applications I made of it went into the work I did for a master’s in psych. At any rate, I can finally answer the “what next” question by pointing to one of the exercises I set for the logical reasoning module of that program, as described in the following excerpt from its User Guide.
- Theme One Guide • Molly’s World (pdf)
The writing there is a little rough by my current standards, so I’ll work on revising it over the next few days.