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Re: [mathonweb] reminder: meetings this week

From: Volker Sorge <volker.sorge@gmail.com>
Date: Mon, 10 Sep 2018 22:36:42 +0100
Message-ID: <CAE5-06QiDH6bW011ckBqiQ8dRJvn86Ph3FBD3nRaa4bW7-XhcQ@mail.gmail.com>
To: "Pedersen, John - Hoboken" <jpederse@wiley.com>
Cc: Neil Soiffer <soiffer@alum.mit.edu>, Peter Krautzberger <peter@krautzource.com>, mathonweb <public-mathonwebpages@w3.org>
I agree, it is probably just a typo. In particular since ATP systems like
prover9 use & before |.
I pinged Geoff to clarify.

As for the classics (available here
https://www.scribd.com/document/2519503/Frege-Gottlob-Begriffsschrift): I
would still interpret §7 pages 11-13 as not defining a precedence order on
"and" and "or". They are both derived as equivalent concepts via negation
and material implication.

But in all fairness. Neil, John, you are probably both right and "and"
before "or" is the accepted precedence order.
Don't listen to a nitpicker like me. Sorry, for causing all the confusion.

Best,
Volker

PS: But for whoever is interested, there is a really good critique of
Frege's system by Pavel Tichý.







On Mon, 10 Sep 2018 at 22:03, Pedersen, John <jpederse@wiley.com> wrote:

> Frege is certainly quite classical!  I wonder if the Sutcliffe page may
> just just be a typo: in the second bullet just above where it talks about
> the precedence order, it has P & Q listed before P | Q.  But you may have
> at least one supporter in
> https://en.wikipedia.org/wiki/Logical_connective#Order_of_precedence. It
> says near the end of that section that some have changed precedence order,
> but it’s for disjunction vs. implication and equivalence (which is also
> interesting -
> https://books.google.com/books?id=DDv8Ie_jBUQC&pg=PA263#v=onepage&q&f=false).
> But the penultimate sentence does say, although without any supporting
> citation, that  conjunction/disjunction precedence may be unspecified. In
> any case, I would certainly agree that it’s best for students (and
> everyone) to use parentheses for conjuction/disjunction to make everyone’s
> understanding clear.
>
>
>
>
>
> *From:* Volker Sorge <volker.sorge@gmail.com>
> *Sent:* Monday, September 10, 2018 4:33 PM
> *To:* Pedersen, John <jpederse@wiley.com>
> *Cc:* Neil Soiffer <soiffer@alum.mit.edu>; Peter Krautzberger <
> peter@krautzource.com>; mathonweb <public-mathonwebpages@w3.org>
> *Subject:* Re: [mathonweb] reminder: meetings this week
>
>
>
> I might be wrong then. All I can find quickly is Geoff Sutcliffe's page
> (some way down):
>
>
> http://www.cs.miami.edu/home/geoff/Courses/COMP6210-10M/Content/Propositional.shtml
>
> I also seem to recall from reading Frege that he does not define an order.
> But it's been a while since I've read Begriffsschrift.
>
> Anyway, I generally teach my students to better check the definitions
> before assuming an order on those two connectives with any author. (And I
> require them to use parentheses.)
>
>
>
> Best,
>
> Volker
>
>
>
> On Mon, 10 Sep 2018 at 21:20, Pedersen, John <jpederse@wiley.com> wrote:
>
> Although it’s been a while, I did teach undergraduate and graduate-level
> logic and algebra for a number of years and I have the same understanding
> as Neil that in propositional, first, and higher-level logics, conjunction
> has priority over disjunction. There are numerous classic texts where this
> is given as the rule. Can you point to any text or other source where the
> order is stated to be different?
>
>
>
> *From:* Volker Sorge <volker.sorge@gmail.com>
> *Sent:* Monday, September 10, 2018 3:51 PM
> *To:* Neil Soiffer <soiffer@alum.mit.edu>
> *Cc:* Peter Krautzberger <peter@krautzource.com>; mathonweb <
> public-mathonwebpages@w3.org>
> *Subject:* Re: [mathonweb] reminder: meetings this week
>
>
>
> I am confused; I don't understand your point. I was explicitly referring
> to classical logic.
>
> Of course you can define a precedence order. Programming languages often
> do following Boolean algebra habits, so do often authors of logic text
> books. But even then the order between and/or can depend on the author.
>
>
>
>
>
>
>
> On Mon, 10 Sep 2018 at 19:10, Neil Soiffer <soiffer@alum.mit.edu> wrote:
>
> I disagree about there not being an accepted precedence for *and* vs *or*.
> The precedence in programming languages that I know all have *and *with a
> higher precedence than *or*. In MathML, the default operator table does
> so also. The other notation used for logical and/or is  ·/+ (as in a ·b + c
> or ab+c) and these again use the convention that the "times" operator has a
> higher precedence than "plus" for and/or.
>
>
>
> It may be that some books/articles do it the other way around, but I'd
> like to see some examples proving me wrong. Or if they are considered equal
> precedence, again, I'd like to see some examples where this is true (as
> opposed to just using parens to make it clearer).
>
>
>
>     Neil
>
>
>
>
>
> On Mon, Sep 10, 2018 at 10:55 AM, Volker Sorge <volker.sorge@gmail.com>
> wrote:
>
> There is no precedence order for logical and/or ∧/∨.
>
> Precedence in classical logic is: negation over conjunction/disjunction
> over (material) implication over equivalence.
>
> You always need to disambiguate order of and/or.
>
> Volker
>
>
>
> On Mon, 10 Sep 2018 at 18:33, Neil Soiffer <soiffer@alum.mit.edu> wrote:
>
> Apologies for missing the meeting today -- I don't seem to have the
> meetings properly entered into my calendar and due to the time difference,
> I don't see Peter's reminders until after I start work.
>
>
>
> I have a question about what someone wrote on the Wiki:
>
>      a∧b∨c it is not clear the order precedence. Usually ∧ has precedence
> over ∨, but not always.
>
>
>
> Can someone clarify (on the wiki) *when* it the normal precedence doesn't
> hold. What surprised me when I first looked into notations and precedence
> (20 years ago -- yikes!) was that although a symbols might have many
> different meanings, the precedence relationships it has didn't seem to
> change. I attributed that to people trying to avoid confusion when using
> familiar notation for new functionality. Having '∨' have a different
> precedence relative to '∧' in some cases seems very strange to me. But
> mathematicians do strange things at times (especially logicians ;-).
>
>
>
>     Neil
>
>
>
>
>
>
> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail>
>
> Virus-free. www.avg.com
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>
>
>
> On Mon, Sep 10, 2018 at 12:36 AM, Peter Krautzberger <
> peter@krautzource.com> wrote:
>
> Hi everyone,
>
>
>
> Just a quick reminder for the CG meetings this week.
>
>
>
> - a11y TF, Monday, Sept 10, 11am Eastern
>
> - css TF, Monday, Sept 10, 12pm Eastern
>
> - no CG meeting this week
>
>
>
> Best,
>
> Peter.
>
>
>
>
>
>
Received on Monday, 10 September 2018 21:37:18 UTC

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