[Fis] The ternary logic. Neutrosophic logic

[Louis Kauffman]

Dear Folks,
There is a very nice way (not the only way!) to start in multiple valued logics by extending from 0 and 1 to all the values between 0 and 1 in the real numbers.
This actually was done by Boole. In a modern version I will let ~x = 1-x where x is in [0,1] = {x| 0<= x<= 1}. We can let x AND y = x ^ y = xy the usual product of numbers.
Thus 0^0 = 0, 0^1=0, 1^1=1. Then define x v y = ~(~x ^ ~y) to preserve the DeMorgan rule.
Then x v y = ~(~x ^ ~y) = 1 - (1-x)(1-y) = 1-(1-x-y+xy) = x+y - xy. (Note that 1 v 1 = 1 + 1 - 1x1 = 1 as desired for Boolean algebra.) Then we have Boolean algebra for 0 and 1 and an extension that can be thought of as probabilistic for values between
0 and 1. Note that ~(1/2) = (1/2) so there is a Third Value that sits on the fence. Since this works for 0 and 1, you can write a computer program with these formulas and then compute in Boolean by taking 0 and 1 values.
Best,
Lou


> On May 1, 2024, at 1:40 AM, joe.brenner at bluewin.ch wrote:
> 
> Dear Krassimir,
> 
> You and others interested in this form of epistemic logic should by all means look at the 3VL neutrosophic logic of the Romanian-American Florentin Smarandache at the U. of New Mexico. It is a highly sophisticated fuzzy intuitionist logic that offers more operators than simple ternary logic.
> 
> As I discussed with Florentin some ten years ago, there is no relation between neutrosophic logics and an ontological logic of processes. They can be applied without reference to it.
> 
> Best wishes,
> Joseph
> ----Message d'origine----
> De : itheaiss at gmail.com
> Date : 30/04/2024 - 22:09 (E)
> À : fis at listas.unizar.es
> Objet : [Fis] The ternary logic
> 
> Dear Kate,
> 
> I want to point out that my note was just one variation of the well-known ternary logic.
> 
> The ternary logic, or three-valued logic (3VL), is a logic system with three truth values: TRUE, FALSE, and UNKNOWN. It is superior to binary logic, but because of the significantly larger set of 27 unary operators, the engineer who created the first electronic computer (do you know who he was?) preferred the simpler binary (Boolean) logic.
> 
> Boolean logic allows 22 = 4 unary operators; the addition of a third value in ternary logic leads to a total of 33 = 27 distinct operators on a single input value.
> 
> At the same time, if we want to achieve development in the field of artificial intelligence and its applications, it is better to use ternary logic. It can be implemented programmatically without much effort, so it is not a question of implementation, but rather of using it expediently.
> 
> For instance the database structural query language SQL implements ternary logic as a means of handling comparisons with NULL field content. NULL was originally intended to be used as a sentinel value in SQL to represent missing data in a database, i.e. the assumption that an actual value exists, but that the value is not currently recorded in the database. In SQL, the intermediate value is intended to be interpreted as UNKNOWN.
> 
> In the 3VL logic based on -1,0,1 the intermediate value is 0.
> 
> Thank you Kate for the very interesting interpretation of intermediate value for the case of emotions!
> 
>  
> Dear Stu,
> 
> I would like to touch briefly on the "Hindu Jain concept of Unmanifest, True, Unmanifest, False" you noted.
> 
> This is not analogous to "I don't know," because "I don't know" means "I have no way of knowing." This is a ternary logic - "Yes", "No" and "Unknown".
> 
> In my opinion, "Unmanifest, True, Unmanifest, False", is based on the recommendation to perceive reality as "it is" and at the same time as "it is not", qualified with "perhaps", to understand Absolute Reality. This is a variant of binary logic, in probably one of its oldest versions.
> 
> I will recall that any change in a given entity, as a result of interaction with another (= reflection = data = ontological information), only after being recognized by the Infos (= human = agent = subject) becomes a mental model (= information = data with meaning = knowledge = epistemological information).
> 
> This is what leads to the confusion of what "information" is, because in everyday life we use the term “information” for both data and knowledge. And in fact, information appears during the transition from data to knowledge, which takes place in the temporary (working) memory of the brain. Data enters it, is recognized, and is perceived as information (the data acquires meaning), after which it is stored in long-term memory. Thus, the temporary memory can be considered as a converter of the data coming at the input into information that is stored in the permanent memory and we usually call "knowledge".  The opposite transition from knowledge to data is possible.
> 
> But the reflection (the data, the ontological information) may not be recognized by the Infos (= human = agent = subject) and, under certain conditions, continue to exist in long-term memory as a reflection without meaning. This is exactly the case with "I don't know". Thus we enter the ternary aspect of consciousness, which is actually the engine of knowledge because it leads to the generation of new mental models.
> 
> If we make an analogy with Schrödinger's Cat, then in ternary logic the observation can give one of three answers: "The cat is alive", "The cat is dead", "That in the box is not a cat and one cannot recognize what it is"!
> 
> This suggests that our brain is not quantum, but a vastly more complex system.
> 
> If we want the Jain concept to become a ternary, then we should have three concepts - "Unmanifest, True", "Unmanifest, False", and "Unmanifest, Unknown ".
> 
> With respect,
> 
> Krassimir
> 
> PS: In the future, possibly it will be interesting to discuss information trialectics philosophy.
> 
>  
> 
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