|Text and/or other creative content from Multi-valued logic was copied or moved into Many-valued logic with this edit on 14:12, 21 January 2011. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted so long as the latter page exists. The former page's talk page can be accessed at Talk:Multi-valued logic.|
|WikiProject Philosophy||(Rated Start-class)|
The fact that Aristotle didn't fully accept the law of the excluded middle doesn't seem to be mentioned in the Laws of thought article nor in the article on Lotfi Askar Zadeh. The difference between this article and those two are slightly confusing. The best I can gather is that Aristotle put forth the law of noncontradiction and the law of the excluded middle, but expressed in De Interpretatione that the law of the excluded middle could produce some problems. Perhaps somebody that knows this subject could tweak the wording in these articles to clarify things a tad. -Chira 21:39, 11 August 2005 (UTC)
I've tried to answer Chira's question (again.) Moved from article: (the law may originate from one of them, Chrysippus). Meaning what? He lived after Aristotle, and Aristotle's laws imply the law in question. Dan 23:05, 6 April 2006 (UTC)
Could someone write an example who understands this? Or maybe a link to a tutorial? Thank you --Gaborgulya 23:06, 15 May 2007 (UTC)
"Many-valued logic" is somewhat more common, according to Google Scholar than "multi-valued" logic, by a margin of about 50%. Additionally, "multi-" seems to be mostly used in the specific subfield of the design of ALUs in digital circuits - relevant, but not the core of the topic.
Is it worth changing the name? I lean to saying it is. — Charles Stewart (talk) 08:21, 29 April 2009 (UTC)
- I lean to agreeing with you. At least, insofar as my experience points to the greater frequency of many v. multi in this particular arrangement.—αrgumziω ϝ 19:52, 21 August 2009 (UTC)
Merging with Multi-valued logic
- Boolean algebra is an algebraic structure, not a logic. The corresponding logic is classical propositional logic, and it is not included in any of the logics listed (P3 has the same tautologies as classical logic, but does not satisfy the rule of modus ponens). That should not come as a surprise, as classical logic has no proper consistent extension.—Emil J. 10:56, 3 May 2013 (UTC)
- What I meant is: since there is a truth table for each logic given on this page (i.e. Priest's P3, Bochvar's B3, and Belnap's B4), it can also be viewed as an algebra (like G.Boole did for the usual 2-valued logic). It may then be asked whether e.g. "∧" is commutative, associative, and so on. Birkhoff  gave 9 laws (about "¬", "∧", "∨", but not involving "→" and "↔") to be satisfied in order to be called a Boolean algebra.
- Meanwhile I achieved to write a little C program to check these laws on the truth tables given on this page. None of them satisfies (x ∧ ¬x) = F or (x ∨ ¬x) = T (btw: this tautology is satisfied by classical logic; so P3 seems to me not to have "the same tautologies as classical logic" - ?). Bochvar's B3 in addition violates the absorption laws, viz. (x ∧ (x ∨ y)) = x and its dual. All other laws are satisfied. In particular, each logic on this page leads to a distributive lattice. If inB4 the truth table for negation is modified such that (¬ N) = B and (¬ B) = N, then it leads even to a Boolean algebra, according to my C program. Jochen Burghardt (talk) 11:39, 4 May 2013 (UTC)
- Lattice Theory, Am. Math. Soc., Providence, 1967
- In P3, I is also a "designated truth value". So x ∨ ¬x would be a tautology. —Ruud 13:29, 4 May 2013 (UTC)
Laws of Form
wow, amazing this document didn't mention spencer G Brown and Laws of form (there is a 1979 edition), where an indication is made that an imaginary logic value is needed to help to resolve Goedels incompleteness theorem type paradoxes. In this case, a third logic value would actually be an oscillation between true and false as i appears to be an oscillation between 1 and -1. The famous sentence "This sentence is false" resolves with an oscillating logic value. (Contributed by Matthew Scott)