[Om] logic1 CD revision?

Paul Libbrecht paul at activemath.org
Thu Aug 17 15:22:32 CEST 2006

I would be looking forward for issue-report or attempts at correction on 
the issue tracker:


Jacques Carette wrote:
> "the" logic???  Do you know how many two-valued boolean logics there are?
> You might mean "classical two-valued, first-order Boolean 
> propositional logic".
> And while I am looking at it:
> 1) doesn't anyone see anything wrong with the FMP for 'equivalent'?  
> It seems to use a circular definition.
> 2) the FMP (and CMP) for 'not' does not characterize 'not' as this FMP 
> is also satisfied by the identity.  The informal description is 
> actually a better 'definition'.
> 3) in the same vein, the FMP for 'or', 'and' are not sufficient to 
> uniquely define them either, as well as all being consequences of 
> excluded-middle.  So _all_ the FMPs in this CD turn out to be 
> restatements of excluded-middle!
> 4) those FMPs use the forall quantifier, which is defined in quant1 
> which depends on logic1.
> Jacques
> W Naylor wrote:
>> Clare is of course correct here. Would it be sufficient to change the 
>> top level Description element to say:
>> This CD defines the operations of the two valued Boolean logic.
>> Bill
>> On Tue, 15 Aug 2006, Clare So wrote:
>>> Dear OpenMathers,
>>> I would like to suggest that logic1 CD may need a revision.  The 
>>> description
>>> of it does not say whether the functions are for two-value logic or 
>>> not.  In
>>> some systems, three-value logic is used.  It would be better if we 
>>> state the
>>> meanings of each OMS as explicit as possible.
>>> Clare

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