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RE: [mathonweb] reminder: meetings this week

From: Pedersen, John <jpederse@wiley.com>
Date: Mon, 10 Sep 2018 21:03:32 +0000
To: Volker Sorge <volker.sorge@gmail.com>
CC: Neil Soiffer <soiffer@alum.mit.edu>, Peter Krautzberger <peter@krautzource.com>, mathonweb <public-mathonwebpages@w3.org>
Message-ID: <BN7PR02MB5265A5735723999143862794C1050@BN7PR02MB5265.namprd02.prod.outlook.com>
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):

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.)


On Mon, 10 Sep 2018 at 21:20, Pedersen, John <jpederse@wiley.com<mailto: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<mailto:volker.sorge@gmail.com>>
Sent: Monday, September 10, 2018 3:51 PM
To: Neil Soiffer <soiffer@alum.mit.edu<mailto:soiffer@alum.mit.edu>>
Cc: Peter Krautzberger <peter@krautzource.com<mailto:peter@krautzource.com>>; mathonweb <public-mathonwebpages@w3.org<mailto: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<mailto: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).


On Mon, Sep 10, 2018 at 10:55 AM, Volker Sorge <volker.sorge@gmail.com<mailto: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.

On Mon, 10 Sep 2018 at 18:33, Neil Soiffer <soiffer@alum.mit.edu<mailto: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 ;-).



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On Mon, Sep 10, 2018 at 12:36 AM, Peter Krautzberger <peter@krautzource.com<mailto: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


Received on Monday, 10 September 2018 21:03:57 UTC

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