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Re: [ontolog-forum] n-ary vs binary

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Mitch Harris" <maharri@xxxxxxxxx>
Date: Tue, 10 Feb 2009 17:45:18 -0500
Message-id: <C39BABBD8517EC4D9E0E6975F9195B8E014092A5@xxxxxxxxxxxxxxxxxxxxx>
PH, JS, et al.:    (01)

> Semantically, 'give' has three participants.  One or two may be
> omitted in a grammatical English sentence if they are obvious
> from the context.  But they exist, whether or not the speaker
> or listener knows who or what they are.    (02)

To get back to a single relation that is stipulated rather than follow the
many (interesting) lexical/semantic paths surrounding donation, let's stick
with 'give' having all three parameters.    (03)

Let me make what I think is the appropriate summary (yes many of the
following are arguable, and have already been argued, but there it is):    (04)

Given the ternary relation "Gives(A, B, C)"  (which happens to mean that A
gave B to C) we can easily encode it as three binary relations: assign a
unique x, then Gives1(x, A), Gives2(x, B), Gives3(x, C) is derivable from
the ternary relation and one can reverse the derivation.    (05)

Converting everything to binary has its benefits: homogeneous
representation, most concepts are already binary (except maybe database
tables).    (06)

However, despite its simplicity, this equivalence/derivation is not well
known, and even when known it is counterintuitive to use (as humans usually
write these things).    (07)

Could the n-ary/binary debate be settled by allowing binary to be the
machine language and n-ary be the higher level human written language?    (08)

Mitchell A. Harris
Research Faculty (Instructor in Computer Science)
Department of Radiology
Massachusetts General Hospital/Harvard Medical School    (09)

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