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07:01:30 <hppavilion[1]> The existential quantifier (upside down E) is basically the logical counterpart to big sigma, while the universal quantifier (upside down A) is the logical counterpart to big pi. "Big conjunction" and "big disjunction."
07:19:40 <hppavilion[1]> You could do a "big xor"-type quantifier but only over a finite number of values. True when an odd number of cases is true. Material implication is non-associative so it wouldn't be much use.
07:25:26 <hppavilion[1]> Lives a secret double life as "Mirrored over the y axis E"
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08:26:28 <FireFly> would "exactly one of" be a more useful generalisation?
08:26:53 <FireFly> wouldn't be just folding with xor though I suppose
08:56:00 <shachaf> I'd expect it to behave like an xor clause in SAT solvers.
08:56:08 <shachaf> Though I guess really there's just one solver with xor clauses.
08:56:46 <shachaf> "exactly one" is a standard thing, anyway, it's just called "exists unique".
09:07:07 <hppavilion[1]> I think to have an operation which folds to uniqueness quantification you'd need to take a visit to 3-level logic.
09:08:20 <shachaf> 3-level? You mean 3 nested quantifiers?
09:08:43 <hppavilion[1]> I mean logic with 3 truth values rather than 2. I'm sure there are other ways to do it but this is the most straightforward way I can think of.
09:10:30 <hppavilion[1]> truth values {f, t, T}, but with inputs strictly over {f, t}. f$f = f, f$t = T, t$t = f, T$f = T, T$t = f, with $ commutative. If you fold $ over arbitrarily many inputs then collapse {t, T}, you get uniqueness quantification.
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09:28:06 <hppavilion[1]> Slightly more elegant version. data Counter = None | One | Many; and count :: Counter -> Bool -> Counter. count x false = x; count None true = One; count One true = Many; count Many true = Many. `foldl count None` takes your list and outputs Counter.
09:28:55 <hppavilion[1]> So if I've done it right (==One) . (foldl count None) is a uniqueness quantifier.
09:29:30 <b_jonas> at least write it lazy like count Many _ = Many as the first definition, so you don't have to continue on a list after finding two trues
09:30:04 <hppavilion[1]> Right. Somewhere in there I went from pure math to Haskell.
09:41:40 <hppavilion[1]> though that no longer strictly counts as a three-level logic solution since the count function takes two different types of input.
09:42:32 <hppavilion[1]> I'm not referencing any specific mathematical definitions there; just vibes.
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13:59:18 <esolangs> [[U+00BF]] N https://esolangs.org/w/index.php?oldid=124340 * None1 * (+16) Redirected page to [[]]
14:08:44 <esolangs> [[]] https://esolangs.org/w/index.php?diff=124341&oldid=124113 * None1 * (+785) /* Hello, World! */ Added python interpreter
14:16:00 <esolangs> [[]] M https://esolangs.org/w/index.php?diff=124342&oldid=124341 * None1 * (-2) /* External Resources */
14:20:47 <esolangs> [[User:None1/InDev]] https://esolangs.org/w/index.php?diff=124343&oldid=124262 * None1 * (-2772)
14:22:02 <esolangs> [[Readable]] N https://esolangs.org/w/index.php?oldid=124344 * None1 * (+2813) Created page with "'''Readable''' is a language invented by [[User:None1]] and inspired by [[Unreadable]]. Unlike its name, programs in this language are ''very'' unreadable because it uses the characters <code></code> (U+2212) and <code>-</code> (U+002D), which looks exactly the same in s
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14:24:35 <esolangs> [[User:None1]] M https://esolangs.org/w/index.php?diff=124347&oldid=124346 * None1 * (+0) /* My Esolangs */
14:33:38 <esolangs> [[Bracket]] https://esolangs.org/w/index.php?diff=124348&oldid=124328 * PaxtonPenguin * (+7)
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18:43:39 <esolangs> [[Esolang:Sandbox/Sandbin]] N https://esolangs.org/w/index.php?oldid=124360 * PaxtonPenguin * (+18) Created page with "Lets start anew"
18:44:48 <esolangs> [[Work to Survive!]] N https://esolangs.org/w/index.php?oldid=124361 * ILoveCursedCode * (+4305) Created page with "'''Work to Survive!''' is a type of esolang (as well as a language standard) that forces the user to waste CPU cycles to "work" in order not to get the main process killed. == Specifications (Work to Survive! 1.0) == The user can work in '''Work to Sur
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