Questions tagged [multivalued-logic]

Multivalued logic is a propositional calculus in which there are more than two truth values.

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-valued (infinitely-many-valued), such as fuzzy logic and probability logic.The first known classical logician who did not fully accept the law of excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of logic")

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Why mathematical reasoning is built on two-valued logic?

I have a very basic question. How would you answer to somebody that is asking you why in mathematics we use two-valued logic as the very ground of math reasoning instead of some multi-valued logic? Is the reason purely practical, but – at the same…
Kolmin
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Proving chain order from Peirce's Law

I am trying to prove any one of the following statements $((p \to r) \lor (q \to s)) \to ((p \to s) \lor (q \to r))$ $(p \to q) \lor (q \to r)$ $((p \to q) \to q) \to (p \lor q)$ $(p \to q) \lor (q \to p)$ in the logical system 4CL. All of (1),…
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Can Naive Set Comprehension survive in multi-valued logic?

If $\phi$ is a formula in which $x$ is not free, then: $(\exists x \ \forall y \ (y \in x \leftrightarrow\ \phi)) $ is an axiom. This is the inconsistent Naive comprehension axiom. Is this a paradox limited to classical [binary valued] first order…
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Sources for Gödel and Łukasiewicz logics

Gödel defined the min-max rule for the conjunction and disjunction in his multi-valued logic as $$ u\land v=\min\{u,v\} \quad \operatorname{and} \quad u\lor v=\max\{u,v\} $$ Łukasiewicz defined rules for the negation and implication in his…
Eugene Zhang
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Textbook (or similar) for finite multivalued logic

There are a few sources mentioned on some questions on this site regarding multivalued logics, but usually they are to original papers, or to texts on fuzzy logic. I have access to some fuzzy logic texts, but even these aren't really "textbooks" in…
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Affine existence in three-valued logic

Background on three-valued logic Consider logic over three values $$ f
Jim
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