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user400188

06:51

I recently answered a question and received a downvote for that answer, and I was wondering if anyone could suggest some possible reasons for it.
https://math.stackexchange.com/questions/3661264/generalization-of-boolean-domain-and-examples-of-boolean-variable/3666009#3666009

Martin Sleziak

If you don't mind, I include link in the following forms: Generalization of Boolean domain and examples of Boolean variable and

-1

A: Generalization of Boolean domain and examples of Boolean variable

A Boolean variable is a variable that is either true or false. For instance, denote the sentence "it is raining outside" as $R$. $R$ is either a true or a false statement, and therefore is a Boolean variable. \begin{equation}\tag{R} \text{It is raining outside} \end{equation} Another example i...

user400188

Thank you, I was unsure how to do that.

Martin Sleziak

In this way, other users see at least the title and some preview. It helps - users know whether or not it's a topic they know about without having to click on the link.

user400188

Thanks again, your making my day a lot better :)

Some more information: In the answer, I suggest that there is a mistake in the Wikipedia article that the OP linked to. I wanted to omit talking about it in the answer, but the OP asked for the section of the article containing the mistake to be explained, so I do not think I could have fully answered the question and avoided talking about the article.

Martin Sleziak

@user400188 I posted a bit more on formatting links in chat messages in another room. I did not want to digress in this room from the intended topic.

4 hours later…

Martin Sleziak

10:36

Let me preface this by saying that I know basically nothing about multivalued logic, I just googled a little.

@user400188 It seems that your answer depends on the law of excluded middle. And this seems to be problematic in multivalued logic.

I would be glad if I was able to find a better reference. Anyway, I found at least some answer on Mathematics and a Wikipedia article where this is briefly discussed.

A: Attempt to make a meaningful ternary logic

My conclusion from reviewing MVL, the Lewis systems, and intuitionist logic has been that is not possible to consistently retain: a) the law of the excluded middle in strict form, (not possible for $P ∧ \neg P$) b) The material conditional ($\neg P ∨ Q$), c) truth functional behavior, and d)...

Many-valued logic

In logic, a many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false") for any proposition. Classical two-valued logic may be extended to n-valued logic for n greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values "true", "false", and "unknown"), the finite-valued (finitely-many valued) with more than three values, and the infinite-value...

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