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Logic matrix

These diagrams are equivalent representations of the 2-ary boolean functions. What are the symbols used in the top left diagram?

(Source: wikicommons user mate2code)

QuietThud
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    I'm fairly certain that the symbols in the upper left diagram are not standard in the field of symbolic logic. – Trevor Wilson Mar 21 '13 at 01:52
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    I'm not even going to follow your link, but I predict it's an illustration created by user "Lipedia". He (or she) is somewhat infamous for creating extremely confusing and unclear (though sometimes visually beautiful) "visualizations" of a range of discrete math topics. There's a good chance he invented some of this symbolism himself and nobody else uses it. – hmakholm left over Monica Mar 21 '13 at 01:55
  • @TrevorWilson Me too. But why have they been included in this compiled image? It's been driving me crazy. – QuietThud Mar 21 '13 at 01:55
  • @HenningMakholm The user is mate2code. Confusing visualizations are one thing, but I don't see how they would be even hypothetically useful in this case. If mate is a troll, he is a good one. – QuietThud Mar 21 '13 at 01:59
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    It looks like Lipedia's account is now called Mate2code. I don't think he's a troll; he's way too prolific and lavishes too much loving care on his illustrations for that. But he also has a real problem with understanding which kind of diagrams will be any use for a reader. – hmakholm left over Monica Mar 21 '13 at 02:01
  • @Henning: You’re right; at least Lipedia redirects to mate2code. (And that’s a really impressive collection of graphics.) Oh, and it says that no pages link to this particular picture. – Brian M. Scott Mar 21 '13 at 02:01
  • Found another image using these symbols, perhaps he is trying to institute them: http://upload.wikimedia.org/wikipedia/commons/4/45/16x16_matrix_like_octeract_Hasse_diagram.svg. It is well known that a logician is not successful until he has created his own notation and forced other people to use it. – QuietThud Mar 21 '13 at 02:08
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    It appears to be what he calls Nibble Shorthands, which represent nibbles, I guess. You could probably ask him how he came up with them and why their shapes make sense, I would bet he has a beautiful answer. – Alfonso Fernandez Mar 21 '13 at 02:14
  • @AlfonsoFernandez Thanks! Just what I needed. – QuietThud Mar 21 '13 at 02:19
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    @AlfonsoFernandez: That's as close to an answer as we'll ever get, I think. (I tend to use the symbols 0123456789ABCDEF to represent nibbles, but I'm just a freak, I suppose). – hmakholm left over Monica Mar 21 '13 at 02:20
  • @Alfonso Your comment is probably as complete an answer as is likely to be given; could you promote it to an answer? – Lord_Farin May 17 '13 at 18:19
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    @Lord_Farin Done. – Alfonso Fernandez May 17 '13 at 21:34

1 Answers1

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Based on a comment by Henning Makholm and a short link trace I conducted, these are nonstandard symbols invented by Wikimedia user mate2code (formerly Lipedia).

mate2code calls them nibble shorthands, and they simply represent all possible nibbles (four digit binary strings, more commonly represented by the numbers $0$ to $15$ or by the hexadecimal digits 0 to F), in an order which can be seen here (by interpreting the red dots under each symbol as $1$'s and the white dots as $0$'s).

Note: The links may be volatile, as they refer to Wikimedia user pages.

Alfonso Fernandez
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