I am using the curly bracket notion that I happen to like (which
I have mentioned before), which merely reverses the order of the first two
argument of a parenthesis-delimited relation, to permit an English-sentence-like
form. The curly brackets can be automatically converted to the parentheses
by a simple utility, if you are using a reasoner that can only interpret
parenthetic sentences. The relation is “gave’ and the parenthesis
equivalent is
(gave PatC Book23 to Mary1256 on Date20090214Z-5).
This is actually a 6-ary relation, but the fillers for the 3rd
and 5th arguments can be restricted to “to” and “on”
respectively; the only logical implications derivable from this relation (in
this example) depend on those fillers being present. It is
possible to be more flexible; the 5th argument might also be “at”,
in that case requiring a time point rather than date for the 6th
argument. Any other fillers would not have any logical
implications, and would be declared ill-formed by the input consistency
checker, having arguments of the wrong type. If one wanted to be able to
leave out arguments, the relation would have to be of more than one possible arity.
We could also allow:
{PatC gave Book23 to Mary1256 on Date20090214Z-5 asa BirthdayPresent in (the
LivingRoom)}
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 2:47 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] n-ary vs binary
On Feb 11, 2009, at 6:47 AM, Patrick Cassidy wrote:
I prefer the n-ary forms, because it allows one to say:
{PatC gave Book23 to Mary1256 on Date20090214Z-5}
Not in any version of logical syntax I know you can't.
What is the 4-ary relation here?
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.
On Feb 10, 2009, at 4:45 PM, Mitch
Harris wrote:
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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