Introducing the Trinary Curve: A Novel Heuristic for Artificial Intelligence Data Science Systems11/5/2018 Trinary Logic is not something new. It’s been around for decades, though it was more of a mathematical / highlevel framework. I should know, as I did my Masters thesis on this subject and how it applies to GIS. I even wrote code implementing the corresponding model I came up with, though in today’s programming world it seems like legacy code... Anyway, bottom line is that Trinary Logic is useful and could have a place in modern Information Systems, including data analytics projects. The question is, could it be applicable to A.I. too? The answer is, as usual, “it depends.” Trinary Logic on its own is quite limited and unless you are familiar with its 700+ gates, it may be like any novel idea: interesting but not exactly something worth delving into. After all, just like any system of reasoning, Trinary Logic is meaningless without an indepth understanding of its key contribution to the thorny issue we always tackle through reasoning: handling uncertainty effectively. Uncertainty, oftentimes modeled as noise or randomness (depending on who you ask), is everywhere. Since we cannot eliminate it without damaging the signal too, we find ways to cope with it. Trinary Logic offers an interesting way of doing that through the 3rd value of its variables, namely the “indifferent” state. Something can be True, False, or Indifferent, the latter being something inbetween. These are the states of those intermediate values in the membership functions of fuzzy variables, in Fuzzy Logic. The latter is a wellknown and quite established A.I. framework with lots of applications in data science. Do you see where I’m going with this? So Trinary Logic is a framework for reasoning, much like Fuzzy Logic, but the latter is an A.I. framework too, so Trinary Logic is A.I. also, right? Well, no. Trinary Logic is a mathematical construct, so unless it is applied to A.I. programmatically, and as a welldefined process, it is yet another concept that can’t even fetch an academic publication! But if it were to manifest as a heuristic of sorts and add value to a process in the A.I. sphere, things would be different. Enter the Trinary Curve, a heuristic (or metaheuristic, depending on how you use it) that encapsulates Trinary Logic in a simple yet not simplistic way, turning an input signal into something that an A.I. agent can understand and work with. Namely, it can engineer a new variable in the [1, 1] interval (notice the closed brackets in this case), that enables the corresponding module to have the inbetween state of uncertainty more evident. As a result, the A.I. agent is allowed to be unsure about something and examine it more closely, given the right architecture, instead of working with what it has and hope for the best. Note that the Trinary Curve can be customized, while its output can be normalized to a different interval (always closed) if needed. The Trinary Curve is differentiatable throughout the space it is defined, while it’s easy to use programmatically (at least in Julia). Perhaps the Trinary Curve is a novelty and an A.I. system can evolve adequately without it. However, it is something worth considering, instead of just experimenting with the countable parameters of existing A.I. systems solely. After all, Trinary Logic is compatible with existing A.I. frameworks so if it’s not utilized, it’s primarily because of some people’s unwillingness to think outside the box, and that’s something that doesn’t have any uncertainty about it...
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Zacharias Voulgaris, PhD
Passionate data scientist with a foxy approach to technology, particularly related to A.I. Archives
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