It would be more accurate to talk about "parts of speech" rather than
just referring to prepositions and verbs, as there are also subjects,
objects, indirect objects, adjectives, adverts, etc. and natural
languages classify and use these parts in many different ways. (01)
Mapping parts of speech to arities is only part of the issue here. (02)
The "problem" in many statements/situations is that one or more arities
are deemed to be implicit:
"Hillary gave Bill a warning" tells us something important about a
situation, but if - in this situation - Hillary and Bill are playing the
roles, respectively of:
- a girlfriend and a boyfriend;
- a First Lady and a US President;
- a wife and a husband;
- a Democrat contender and a former President;
the situations are very different, even when the subject and object are
the same in each situation. In these examples, the "arity" of time would
help distinguish 1, 2, and 4 but not between 2 and 3 or between 3 and 4. (03)
And that is "just" adding time and roles. Did she give the warning in
earshot of someone else? publicly? Is someone, via indirect speech,
making the uncorroborated claim that this situation occurred? In most
situations, other important aspects, or context, are "taken for granted"
or are added by particular observers or for particular purposes: We can
all add arities, "dimensions", further granularity, etc: the point is:
finding a mechanism that allows any user to reify and "talk about" any
particular arity, any occurrence of one, or any set thereof that is
useful:
- The problem with triples is the number of joins one needs to make in
order to create - and subsequently query, analyse, etc - a particular
tuple or infon.;
- The problem with n-ary tuples is the number of tuple types grows
exponentially with the number of arities used, making them more context
specific and less reusable. (04)
RDF uses pure triples, and require many joins;
Topic Maps goes one better and uses triples with, additionally, scope (0
to n times) assigned to the association arc and role(s) assigned to the
topic nodes connected by the arc; but still is inadequate to express
context - and although the arc type (association type) can be reified,
the scope cannot. (05)
Can CL really do this? It may be consistent in handling expressions (and
not assuming or prejudicing any specific number of arities) but it can
never claim to be complete. (06)
Peter (07)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F.
Sowa
Sent: 07 September 2007 21:33
To: [ontolog-forum]
Subject: Re: [ontolog-forum] quadruples talk (08)
Natural languages typically support 1, 2, or 3 arguments
for verbs and prepositions. Additional prepositions must
be added to support 4 or more arguments. (09)
0 arguments: (010)
[It] rains. (Dummy place holder, which is omitted
in many languages, such as Latin 'pluit'. (011)
1 argument: (012)
X sleeps, walks, exists, lives, dies. (013)
2 arguments: (014)
X has, sees, wants, knows Y (015)
X in, on, above, below, under Y (016)
3 arguments: (017)
Sue gave Bob a book. (018)
Jane painted the kitchen yellow. (019)
Bill called Jack a hero. (020)
X between Y and Z (021)
4 arguments: (022)
Sue sold Bob a book for ten dollars. (023)
Bob bought a book from Sue for ten dollars. (024)
6 arguments: (025)
Tom arrived at JFK from SFO at 9 pm via AA on Flight 18. (026)
Examples like the last illustrate two points: (027)
1. It is possible to use lots of dyadic relations, such as
'at', 'from', 'on, and 'via'. (028)
2. It is possible to reduce the number of dyadic relations
by grouping all six items into a single 6-tuple -- that's
the preferred solution in relational databases. (029)
Common Logic is intended to support all the major notations
for logic, and it is designed to accept input from any form,
and it can reorganize the result for output in any other form. (030)
John Sowa (031)
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