On Tue, March 26, 2013 23:23, Steven Ericsson-Zenith wrote:
> Dear Doug, (01)
> See my note to John, if that does not answer your questions then I'll be
> happy to respond at greater length. (02)
I did not ask any questions. I explained that logic can handle higher arity
relations than binary relations and that if needed, a higher arity
relation can
be encoded as a reified thing with multiple binary relations. (03)
> Let me simply note that merely having three parts does not a triad make in
> this case - you cannot express what Peirce calls a triadic relation with
> any number of binary relations. (04)
This forum has not been discussing Pierce's true triad. We've been
discussing encoding of ontologies. If someone wants to ontologize
philosophical concepts, they can take a shot at Piercian Triad. But
that is not what i have been discussing. (05)
> Peirce's entire point is that a triadic
> relation cannot be decomposed to sets of binary relations without
> destroying it - they are binary relations... (06)
Pierce's point is far more than that. (07)
But ontologically, when one translates from a ternary notation to a
binary one, something in addition to the new set of binary relations
and the original arguments DOES have to be represented. That
thing is typed and has properties. (08)
If we are modeling sentences about events, that additional something
can be the Davidsonian unitary event (as John and Ed have discussed
and i have alluded to). Or, as in the case of mathematical formulae,
it can be the reified formula. (09)
> It is not simply that it is
> expressed differently as John suggested earlier but something is actually
> gone. (010)
That something is modeled as an additional thing. If it is not assigned
a type that provides additional meaning, yes, something IS lost. (011)
> In the quote I cite for John in my earlier post, Peirce shows that to be
> exact you can expand the triad conceptually "upward" to a triadic tetrad
> but not downward to simple binary, dyadic, decomposition. (012)
Pierce, in translating a triad to a set of dyads, generated a new term
that has a type and various properties. (013)
That's what is needed in ontological modeling, also. (014)
But i find forcing natural triads into dyads (or higher arity relations into
sets of binary relations) to be overly complex and recommend against it. (015)
-- doug foxvog (016)
> Best regards,
> Steven
>
>
> --
> Dr. Steven Ericsson-Zenith
> Institute for Advanced Science & Engineering
> http://iase.info
>
>
> On Mar 26, 2013, at 12:50 PM, doug foxvog <doug@xxxxxxxxxx> wrote:
>
>> On Thu, March 21, 2013 01:52, Steven Ericsson-Zenith wrote:
>>
>>> It is unlikely that any "controlled English" can be processed into
>>> formal
>>> logic and maintain its original meaning, not least because of Peirce's
>>> "third."
>>
>>> Peirce's simple example is: "A gives B to C" which is impossible to
>>> capture in dyadic form.
>>
>> Neither "controlled English" nor logic ignore triads. Awkward languages
>> such as OWL only allow binary relations, which make expression of
>> triads complex, but not impossible, as John & Ed have noted.
>>
>> As they noted the event of giving can be reified and various relations
>> relative to the act can be related to it with binary relations. This
>> has
>> the advantage of not only allowing the encoding of the NL sentence,
>> but allows innumerable other properties of the event to be expressed,
>> which can not be done without a reified event (or reified sentence
>> representing the event).
>>
>> The mathematical operations John discusses can only be expressed
>> dyadically by reifying the sentence.
>>
>> But logic formalisms that allow ternary and higher relations are
>> available, so there should be no issue about converting a controlled
>> natural language to expressions in a logic language.
>>
>> -- doug foxvog
>>
>>
>>
>>> Regards,
>>> Steven
>>>
>>>
>>>
>>> On Mar 20, 2013, at 10:07 PM, "Barkmeyer, Edward J"
>>> <edward.barkmeyer@xxxxxxxx> wrote:
>>>
>>>> It does not define a controlled English that one could guarantee to
>>>> process into formal logic
>>>
>>>
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