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00:48:46 <esolangs> [[User:Hotcrystal0/Sandbox]] https://esolangs.org/w/index.php?diff=161356&oldid=161353 * Hotcrystal0 * (+308)
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02:30:08 <esolangs> [[Nested one input functions]] https://esolangs.org/w/index.php?diff=161357&oldid=160016 * BestCoder * (+54) /* One more thing */
03:54:50 <zzo38> I read in a book about a kind of logic that the value can be a set of booleans; NOT X is true iff X is false and false iff X is true; X AND Y is true if both are and false if at least one is; X OR Y is true if at least one is and false if both are. (So, I think law of excluded middle will not be valid with a kind of logic that is possible to assign values in this way.)
03:55:10 <zzo38> Other variants are possible, e.g. using a multiset instead of a set
03:55:19 <zzo38> (although, they did not mention this other variant in that book)
03:57:15 <korvo> Yes. Such sets are called "Boolean algebras", which is a painful name. I think of them as "CABAs", complete atomic Boolean algebras. For a set of labels S, its CABA is the function type S → 2 which sends each s in S to a Boolean value.
04:00:22 <korvo> It turns out that sets and CABAs are only equivalent with excluded middle. Otherwise there are CABAs which aren't dual to any particular set.
04:00:57 <zzo38> (If you are using multisets, then the value of X AND Y will be whichever is less true and more false, I think.)
04:01:06 <korvo> (Or, more technically, it turns out that power sets P(S) and CABAs S → 2 are *not* the same sort of thing without excluded middle.)
04:02:05 <korvo> Yeah. Multisets give free vector spaces over the integers Z, I think? Or something like Z-modules.
04:02:31 <korvo> And logic over vector spaces -- or spaces in general -- doesn't have to be Boolean.
04:04:26 <zzo38> With the original one from the book that I mentioned, you could perhaps add a set complement operator and then make up a variant of law of excluded middle which will use that, which will be true regardless of what values you assign to the symbols (in some cases it is false and true, but always it will be true whether or not it is also false).
04:05:32 <korvo> Yes. And any decent logic will have double-negation (X implies ~~X) and non-contradiction (it's not true that X & ~X) as theorems or axioms.
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05:09:33 <esolangs> [[Special:Log/newusers]] create * User167809 * New user account
05:14:07 <esolangs> [[Esolang:Introduce yourself]] https://esolangs.org/w/index.php?diff=161358&oldid=161323 * User167809 * (+267) Just my lil ol introduction
05:18:27 <esolangs> [[Brainfuck implementations]] M https://esolangs.org/w/index.php?diff=161359&oldid=158830 * User167809 * (+176) Add YABAFOC (by me)
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09:41:35 <esolangs> [[Chainlang]] M https://esolangs.org/w/index.php?diff=161360&oldid=161344 * PkmnQ * (-1) /* Symbol and Variable Handling */
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10:45:11 <esolangs> [[Chainlang]] https://esolangs.org/w/index.php?diff=161361&oldid=161360 * PkmnQ * (+48) /* Stack Manipulation */
10:45:45 <esolangs> [[Chainlang]] M https://esolangs.org/w/index.php?diff=161362&oldid=161361 * PkmnQ * (-7) /* Stack Manipulation */
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14:53:32 <esolangs> [[User talk:/w/wiki/index.php/Talk:index.php/Main page]] https://esolangs.org/w/index.php?diff=161363&oldid=161354 * Pifrited * (+1227) /* Commands */
14:56:03 <esolangs> [[User talk:/w/wiki/index.php/Talk:index.php/Main page]] M https://esolangs.org/w/index.php?diff=161364&oldid=161363 * Pifrited * (+3) Typo
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18:18:01 <b_jonas> uh… there might be an olist, but https://www.giantitp.com/comics/oots.html lists the latest strips in a weird order, as in 1329, 1330, 1328, 1327, ... so I can't quite confirm yet
18:21:01 <HackEso> olist <https://www.giantitp.com/comics/oots1330.html>: shachaf oerjan Sgeo boily nortti b_jonas Noisytoot
18:21:03 <b_jonas> I dont' know why the order is so weird
18:23:39 <Sgeo> b_jonas, I just posted about it in the forum
18:24:52 <Sgeo> Oh, other people mentioned it on Bluesky too
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19:16:18 <esolangs> [[User talk:/w/wiki/index.php/Talk:index.php/Main page]] https://esolangs.org/w/index.php?diff=161365&oldid=161364 * Hotcrystal0 * (+85)
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