Question

What do you call a logic that is a gradient betweena gradient between two extremesand a single point. So, for simplicity, let’s say an upside-down triangle (▼)… In my case, specifically, the top corners of that triangle are "False" and "True", and the bottom corner is "Don’t know".So the vertical axis is how sure we are, and the horizontal axis is normal one-dimensional fuzzy logic. The best I could come up with it "fuzzy ternary logic". But that’s no good, since the two dimensions are separate things. While "dual fuzzy logic" implies a cube with two corners at the bottom too. So I thought there’s probably a professor out there who spend years on deep-diving into this and it is probably a whole sub-field of logic. :) The reason I’m asking, is because this seems to represent the logic of scientific research best, yet I haven’t ever seen a name for it. (Mostly because most of the time, vertical axis is unfortunately ignored in science communication.) (As you can probably tell, I’m not a professional philosopher by any stretch. So be kind. :) the vertical axis is how sure we are, and the horizontal axis is

normal one-dimensional fuzzy logic. This would be called probabilistic fuzzy logic. (The three-valued logic of Łukasiewicz represents the corners of your triangle. He began with a three-valued modal logic; it was later generalized to n-valued as well as infinitely-many-valued variants, both propositional and first order. Łukasiewicz logic was motivated by Aristotle's suggestion that
bivalent logic was not applicable to future contingents, e.g. the
statement There will be a sea battle tomorrow. In other words,
statements about the future were neither true nor false, but an
intermediate value could be assigned to them, to represent their
possibility of becoming true in the future.-from the Wikipedia
articleŁukasiewicz logic The third or middle truth value can be interpreted as Unknown, but alternate interpretations such as Possibly and possibly not, Neither proven nor disproven and Contingent: Neither necessary nor impossible are also possible. Fuzzy logic was developed independently and assigns real numbers between 0 and 1 to the truth values.
Łukasiewicz logic, (or at least a modest extension of it which defines a strict Łukasiewicz conditional) and fuzzy logic are both examples of a deMorgan algebra (a generalization of Boolean algebra). As far as I know, the connections between Łukasiewicz logic, especially the infinite valued version, and fuzzy logic have not been fully explored.

Answer 1

The logic you are describing is called probabilistic fuzzy logic, which combines fuzzy logic with probability theory. The three-valued logic of Łukasiewicz, representing the corners of the triangle, is related to this concept.

Step-by-step explanation:

The logic you are describing, with a range between two extremes (False and True) and a single point (Don't know), can be called probabilistic fuzzy logic. This type of logic combines fuzzy logic, which assigns real numbers between 0 and 1 to truth values, with probability theory.

The three-valued logic of Łukasiewicz represents the corners of your triangle and is a related concept. It was developed to represent statements about future contingents and allows for a third truth value beyond True and False.