Stupid logic symbols

[tahnan]

All right. Is there anyone out there who can actually tell me the proper uses in logic of Unicode symbols 22A2 and 22A6 through 22AB, which is to say:

1. ⊢, "Right tack"
2. ⊦, "Assertion"
3. ⊧, "Models"
4. ⊨, "True"
5. ⊩, "Forces"
6. ⊪, "Triple Vertical Bar Right Turnstile"
7. ⊫, "Double Vertical Bar Double Right Turnstile"

?

Alonzo Church's Introduction to Mathematical Logic doesn't seem to use any of them but "assertion"; Boolos and Jeffrey's Computability and Logic doesn't index its symbols; the names are too generic to easily websearch, except by adding the latter two and then you just get Unicode pages...

And which, if any, have something to do with entailment? Semantic entailment? I swear, I'm just going to use my own darned symbols.

Comments

[aneequs.livejournal.com]

I'd use 3 or 4, I don't know what the difference is between them, though.

How to track down mathematical symbols

[dtm]

1. Find out how to make the symbols in LaTeX. (search that file for the string "Vdash"; almost all of those symbols are around there)
   
2. Google for the LaTeX symbol name and filetype:tex.
   
3. Try to comprehend the results.

Re: How to track down mathematical symbols

[dtm]

Actually, a googling for entailment filetype:tex by itself yields some results that at a distance seem promising. If you need any LaTeX files converted to decent pdf files, let me know - I've got a pretty complete LaTeX environment here.

Re: How to track down mathematical symbols

[tahnan.livejournal.com]

Of course, one problem with this is that the symbols are used by (a) logicians, (b) linguists, and (c) computer scientists, and I'm not 100% sure that usage is consistent among the three.

[jydog1.livejournal.com]

I think I went through one of the 'Triple vertical bar right turnstiles' the other day when i was trying to catch the A-train . . .

Sorry.

[jenaflynn.livejournal.com]

I saw those symbols, and I immediately saw them for being parts of Ansi art, from the old BBS days. And then I realized how wrong I was.

[luckylefty.livejournal.com]

The logic text I used, by Kleene I think, used something somewhere in between 1 and 2 to mean "The thing on the right is provable from the stuff on the left", and something like 3 to mean "the statement on the right is true in the model on the left". The two symbols were the same size and shape except for the one-versus-two horizontals, so I suppose that 2, since it's the one parallel to 3, is the one you want, at least in Kleene's use of the symbols.