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Re: [mathonweb] reminder: meetings this week

From: Neil Soiffer <soiffer@alum.mit.edu>
Date: Mon, 10 Sep 2018 15:19:43 -0700
Message-ID: <CAESRWkAgs+039QW-p9KD3G3nB3mg5Fy2TYKANWHXfG55VXbjog@mail.gmail.com>
To: Volker Sorge <volker.sorge@gmail.com>
Cc: "Pedersen, John - Hoboken" <jpederse@wiley.com>, Peter Krautzberger <peter@krautzource.com>, mathonweb <public-mathonwebpages@w3.org>
I'm sure there is a clever logical formula involving N, J, V, &, |, =>, >
that ends with  ... => & > |. I'm also sure it would be entirely unparsable
by any system :-)

    Neil


On Mon, Sep 10, 2018 at 2:36 PM, Volker Sorge <volker.sorge@gmail.com>
wrote:

> 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
>> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail>
>>
>>
>>
>> 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 22:20:08 UTC

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