I prefer the n-ary forms, because it allows one to say:
{PatC gave Book23 to Mary1256 on Date20090214Z-5}
This happens to be congenial to my
English-native-language way of reading, making comprehension faster than with a
set of binary relations.
Appropriate axioms can create the necessary and
sufficient relation of this assertion to each of the binary assertions, if they
are needed for some inference engine.
But I also feel that people should be able to use
any mode of _expression_ they want, and that there should be axioms that can
translate among the different modes.
PatC
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx
From:
ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
Sent: Wednesday, February 11, 2009 1:47 AM
To: maharri@xxxxxxxxx; [ontolog-forum]
Subject: Re: [ontolog-forum] n-ary vs binary
On Feb 10, 2009, at 4:45 PM, Mitch Harris wrote:
PH, JS, et al.:
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.
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.
Which begs the question. But let us proceed.
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):
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.
Not quite. There is no 'assignment' and no requirement of
uniqueness. The translation into case/role binary form simply refers to the existence
of the giving action. Also, the translation is usually stipulated so that the
original ternary (or whatever) relation becomes a predication establishing the
event as having the appropriate verbal type, in this case a giving. So one gets
the pattern:
(exists (x)( Foo(x) & FirsCaseName(x, A) &
SecondCaseName(x, B) & ThirdCaseName(x, C) )
where the appropriate case/role names depend on the
particuiar verb, but often have 'agent' as the first one.
Converting everything to binary has its benefits: homogeneous
representation, most concepts are already binary (except maybe database
tables).
The most important advantages are (1) the case/role names
identify the various arguments by name, making it easier to remember them (2)
the second form allows partial information to be recorded and used naturally,
and allows for arbitrary extensions, and (3) it also puts the actual event
described by the verb phrase into the universe of discourse, allowing other
properties and relations to be asserted about it. Finally (4) it means
that a relatively simple notation (such as RDF graph syntax, ie a labelled
directed graph) can be used to represent what seem on the surface to be much
more complicated facts. This is probably the origin of the idea that 'most'
relations are binary, which is actually much less obvious.
However, despite its simplicity, this equivalence/derivation is not well
known
It is very well known in AI/KR, ontology engineering, formal
logic and linguistics. Several widely used rule languages are based on it.
, and even when known it is counterintuitive to use (as
humans usually
write these things).
On the contrary, for rendering the meanings of simple
English action sentences, it is actually in many ways more intuitive; and it
supports important 'obvious' entailments. For example, if John gave a book to
Mary, then it follows that Mary was given a book by John.
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?
That is one way to proceed, but it ignores the intuitive and
human-engineering advantages of the case/role form, such as its being easier to
remember.
This whole topic is a storm in a teacup. Real ontology
engineering can all be done within binary languages such as RDF: this has been
known for decades. For some purposes, allowing higher adicity relationships is
advantageous, but even when they are possible, the classical case/role system
is still widely useful. It is easy, if a little tiresome, to mentally translate
back and forth between various surface conventions where needed, and also to
write preprocessors which present any logical form in almost any way that a
user feels comfortable with. Let everyone use their favorite notation, and we
can easily translate between them when necessary.
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