|
- as
you say, a tuple is a sequence of things (a tuple is member of a product
of sets), so, yes, ordered with possible repetition. The number of things in the
tuple is n (the length of the sequence). So you can also call a tuple an n-tuple
(the number explicitly specified). And then the adjective to describe it is
n-ary (there are n places). The provenance: binary, ternary, quaternary,...,
n-ary. double, triple, quadruple,...n-tuple.
- as
to tuples fitting in to natural language, I'm not sure I see the trouble, just
describe the position of each element in the relation. I'll leave it to others
to elaborate if that is oversimplified.
--
Mitchell A. Harris,
PhD
Research Faculty (Instructor in Computer Science)
Department of
Radiology
Massachusetts General Hospital/Harvard Medical
School
Pat C, Others
Appealing, but sometimes we have "A relationship (Tuples)" tuples meaning
in my context a set of ordered things, are these n-arys?
How would tuples fit in Natural Language Syntax?
--
Thanks.
Ravi
(Dr. Ravi Sharma)
313 204 1740 Mobile
On Wed, Feb 11, 2009 at 7:47 AM, Patrick Cassidy <pat@xxxxxxxxx>
wrote:
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
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.
------------------------------------------------------------
IHMC
(850)434 8903
or (650)494 3973
40 South Alcaniz St. (850)202 4416
office
Pensacola
(850)202 4440 fax
FL 32502
(850)291 0667
mobile
_________________________________________________________________
Message
Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config
Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe:
mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared
Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To
Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (01)
|