Talk:Turnstile (symbol)

comment of Night Gyr 2006-11-15

Nice article, but it needs a source. Also could use a mention of its use in computer science to signify "derivable in a single step," or its meaning of "semantic validity" in formal logic. Mention of double turnstile and possibly a move to Turnstile (symbol) would be in order? Night Gyr (talk/Oy) 19:20, 15 November 2006 (UTC)

Thanks for the comments. The article is just a stub right now; I'll make sure it has sources before the stub tag is removed. I know that there are a lot of uses in computer science, but I am not familiar with all of them. I included just one so far. If someone from CS would like to add more uses, I would be grateful. Moving to Turnstile (symbol) would be OK with me. Semantic validity is a different symbol, $\models$ (corrected). I thought about including that in another section, eventually. CMummert 19:24, 15 November 2006 (UTC)

Ah, my logic prof always used the turnstile with the single vertical. Some clarification would probably be in order. Night Gyr (talk/Oy) 19:45, 15 November 2006 (UTC)

You're right; I typed the symbol $\Vdash$ instead of $\models$. The second one is the logical validity relation. CMummert 20:29, 15 November 2006 (UTC)

Ah right, it's syntactic validity that has the single horizontal. Night Gyr (talk/Oy) 20:30, 15 November 2006 (UTC)

Right. In all of its uses in math and CS, $\vdash$ always represents some sort of syntactic derivability. CMummert 20:39, 15 November 2006 (UTC)

Farthest to the left?

Can someone please include a description of how this symbol is read when it is the farthest left in a statement? See Generalization (logic) for examples of this usage.129.171.180.147 (talk) 09:45, 13 February 2008 (UTC)

That's the proof theory usage. It means the formula after it can be proved from the stuff before it—i.e. no premises are needed. Algebraist 23:24, 26 April 2008 (UTC)

Vdash and tack?

Any thoughts on adding a redirect from the nonexistant page Vdash and adding a link from the Tack page? When looking for the real name of the turnstile symbol, I knew both vdash and tack, but neither were helpful. Steve Checkoway (talk) 00:35, 17 July 2008 (UTC)

Unicode

What's the difference in usage between these two turnstiles in unicode: http://www.fileformat.info/info/unicode/char/22a2/index.htm http://www.fileformat.info/info/unicode/char/22a6/index.htm Adam.a.a.golding (talk) 00:31, 27 January 2011 (UTC)

Axioms

Quick question regarding "which is to say that the expression can be derived from the rules using an empty set of axioms": What is an empty set of axioms? I thought that the rules of inference are the axioms. — Preceding unsigned comment added by 2001:16B8:2B8C:3100:F453:836F:A6C7:1FE4 (talk) 03:31, 10 October 2018 (UTC)

So, in natural deduction, there are only rules, and few or no "axioms". This is in contrast to Hilbert-style systems, which has only one rule for deducing things, and everything else is an axiom. In some general sense, they are two different ways of talking about the same thing, so one could informally believe that "a rule is an axiom", but in some technical sense, rules and axioms are not the same thing. 67.198.37.16 (talk) 17:31, 18 December 2018 (UTC)

Connection to Heta

I haven't researched it further, but I just stumbled on the article on the Greek letter Heta, a variant of the Eta. Eta is pronounced roughly like the Latin letter e as far as I can tell. Is it just a coincidence that it evolved to be used for something that can mean entailed? It would fit quite nicely. --Divof (talk) 17:40, 20 February 2020 (UTC)

Pure coincidence, from what I can see. There are only so many shapes you can make with a few horizontal and vertical strokes. Paradoctor (talk) 17:54, 20 February 2020 (UTC)

Addition of use in Casio calculators

The turnstile symbol is used on the Casio fx-92 Collège 2D and fx-92+ Spéciale Collège calculators. I've always wondered what the button does on both of those calculators, and since I don't own one (seeing that I'm not French or Belgian), I decided to look it up in the manuals after having no luck when reading this page. I've added the symbol's usage onto the growing list of interpretations! jol1411 (James Livesey) 19:12, 24 December 2020 (UTC)