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Re: [ontolog-forum] Fwd: MOVED: Re: [ontology-summit] Hackathon: BACnet

To: "Steven Ericsson-Zenith" <steven@xxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>, Hassan Aït-Kaci <hak@xxxxxxx>
From: sowa@xxxxxxxxxxx
Date: Tue, 26 Mar 2013 06:28:44 -0400 (EDT)
Message-id: <5acd6fb6d30db678918d1ff575d7d915.squirrel@xxxxxxxxxxxxxxxxxxxx>


> I'm not sure that I Peirce would accept the functional notation as
> triadic, but - as you say - he would prefer a a diagram/graph...

The basic arithmetic operators -- add, subtract, and multiply -- take two inputs and generate one output.  That is certainly triadic.

You can reduce the triads to dyads by Currying, but those dyads only represent intermediate results.  You still get triadic connections in the complete diagrams.

Divide taks two inputs (dividend and divisor) and generates two outputs (quotient and remainder).  But it can be represented by two triads -- one that takes the two inputs and generates the quotient, and the other that takes the same inputs and generates the remainder.

If you use a purely relational notation (as Peirce did for his algebra of 1885 or his existential graphs of 1897), all those functions must be represented by triadic relations.

As another example, look at Prolog.  It represents the basic arithmetic operators by triadic relations.


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