On Thu, September 6, 2012 09:28, William Frank wrote:
> On Thu, Sep 6, 2012 at 1:08 AM, doug foxvog <doug@xxxxxxxxxx> wrote: (01)
...
>> If i gave the example:
>> (and
>> (between 10 5 11)
>> (between 10 11 9) )
>> this mapping would not apply.
>>
>> *Yes, Of course not. One of Andris van Ressenn's many points is that
> positional notations have an undesireable implicit semantics, in which
> position plays a hidden role as indicator of the role in the relation.
> Thus, when you make the roles explicit, and make separate assertions
> about each role played, you get a set of assertions, as all sets should be,
> that are order independent. (02)
If several roles in a positional notation are equivalent, as in an unordered
betweenness, separately defining each as a role can be problematic. (03)
>> > and there is an instance of this relation, b, such that in that
>> instance (04)
>> > 5 is the below integer in b
>> > 11 is the above integer in b.
>> > 10 is the between integer in b, (05)
>> > ? (06)
>> Yes, this gloss is a valid way for expressing in 4 triples what i
>> expressed in one quad. (07)
>> Actually, none of these are triples. They are all binary relations. (08)
?
Binary relations ARE triples: a relation and its two arguments. (09)
> [defining] the betweeness relation.
> ...
> Then, with all of this set up, we assert the existence of b, an instance
> of the type B. (010)
Triple #1: b <is an instance of> B (011)
> and we need the addition of the three independent assertions of what roles
> what integers play in b. (012)
Triples #2, 3, & 4: <arg1/2/3> <has specific B role in> b (013)
>> If i gave an example without a pre-existing default ordering
>> relation, e.g. with spatial betweeness, i'm not sure how you
>> would identify two different roles for arguments 2 and 3: (014)
> Well, first of all,
>
> if you don't SAY what kind of betweeness you are talking about, there is
> simply MORE that the reader must discern with his mind, what kind of
> betweeness you had in mind. (015)
Different rules on the between predicate could apply to different types
of arguments 1, 2, and 3. (016)
> Second,
> all betweenenss relations are based on SOME partial order or spacing, (017)
One can specify a total ordering of all terms in the ontology (say
alphabetically). Using this, one could arbitrarily generate an
ordering for two argument positions whose order is immaterial.
FWIW, this is what Cyc does. (018)
...
>> (between GoldenGateBridge SanFranciscoBay PacificOcean) (019)
> but you can now construct your own examples following the standard
>pattern for reducing n-nary relations to a set of binary relations
> among roles in a higher order logic. (020)
> For example, there is a geographical betweeness relation GB, with respect
> to locations on the globe, with three roles yada yada (021)
> but here, we might want to define what everyone intuits, (022)
> that the defintion of SB is that (023)
> a plays the bottom role in SB
> b plays the middle role in SB
> c plays he top role in SB (024)
> if and only if (025)
> the great circle distance between a and c is greater that the distance
> between a and b and the distance betwen b and c, and the great circle
> displacement of b from the great circle between a and c is less that the
> the distance between a and c. (026)
I note that this is IFF and that a and c are treated equivalently in the
definition. That means that any thing that plays the bottom role in SB
also plays the top role and vice versa. (027)
You could save the IFF by including the proviso: "and the URI of a is
greater than the URI of b". 8)# (028)
> Betweenness could be non-spatial as well: (029)
> Absolutely, betweeness depends on a partial order relationship of any
> kind. For example, is the child of. between in a line for musical
> chairs, (030)
Musical chairs is played in a (rough) circle. With 3 children and the
direction of travel not changing:
(between A B C)
(between B C A)
(between C A B)
(not (between A C B))
(not (between B A C))
(not (between C B A)) (031)
> between in class rankiing at harvard law. you name it. (032)
>> (between ModeratePoliticalPhilosophy ConservativePoliticalPhilosophy
>> ProgressivePoliticalPhilosophy) (033)
>> Again, assigning two different roles to arguments 2 and 3
>> is problematic. (034)
> I do not see why. Needs a slow, careful, thinking cap. That cap has to
> help one discern what the underling partial order is, and the further
> underlying metric on which that order is based, and Bob's your uncle. (035)
> Here, we have a degree of difference between views. Fits the bridge
> example quite well. (036)
> But more generally, an n-ary relation instance is always expressable as n
> independent role assertions. (037)
I think you mean "n+1". (038)
I'll agree with "often", but not "always". (039)
> [example of an n-ary relation assertion about an event modeled by
> n+1 assertions] (040)
> George gave the book to Mary. (041)
This is a ternary assertion. (042)
> There is an instance g of the giving action G. and (043)
Binary assertion #1. (044)
> In g, George played the role of giver, (045)
Binary assertion #2. (046)
> the book played the role of given,, (047)
Binary assertion #3. (048)
> and Mary played the role of reciever., (049)
Binary assertion #4. (050)
-- doug foxvog (051)
> Now, just because one CAN reduce n-aries to binaries, this does not mean
> it is a good thing to do, except to acheive a specific purpose. The lack
> of attention to purposes
> seems to me to be the biggest problem with "modern"
> logical education. Leads to unsaid assumptions. (052)
> -- doug foxvog
>>
>> > On Wed, Sep 5, 2012 at 8:47 AM, Andries van Renssen <
>> > andries.vanrenssen@xxxxxxxxxxx> wrote:
>> >
>> >> Doug and Kingsley,
>> >>
>> >> In any relation (of any arity) the related things play roles of
>> >> different
>> >> kinds that are specific for the kind of relation.
>> >> The semantics of the kind of relation depends on the roles that the
>> >> related
>> >> things play in the relation.
>> >> An explicit specification of roles is required to define the
>> semantics.
>> >> This
>> >> is independent of the sequence of arguments in an expression.
>> >> If you don't make those roles explicit, then you have find an
>> >> alternative,
>> >> such as the sequence of the arguments (as in <is between on path>).
>> >> Their
>> >> sequence becomes a pseudo specification of the kinds of roles in the
>> >> definition of the meaning of the relation.
>> >> Furthermore, the inverse expression has a different sequence of
>> >> arguments,
>> >> and is also a valid expression of the same fact.
>> >> Therefore, semantically it is purer to explicitly specify the kinds
>> of
>> >> roles.
>> >>
>> >> Therefore, a basic semantic structure for the expressions of facts
>> could
>> >> be:
>> >> * kind of relation - kind of role - related thing
>> >> For an n-ary relation you need n such expressions.
>> >>
>> >> The form
>> >> * related thing - kind of relation - related thing
>> >> is just a short cut for a pair of such expressions, in which the
>> kinds
>> >> of
>> >> roles are assumed to be known from the definition of the kinds of
>> >> relation.
>> >> This short cut is only suitable for binary relations and needs a
>> >> mechanism
>> >> to determine which role is played by the left hand thing and right
>> hand
>> >> thing respectively.
>> >>
>> >> A semantic model of the definition of a kind of relation requires
>> even
>> >> more
>> >> detailed relations.
>> >> Such a model requires the specification of which kinds of roles are
>> >> required
>> >> by which kind of relation and which kinds of things may play such a
>> >> role.
>> >> This implies expressions such as:
>> >> * kind of relation - required played - kind of role
>> >> * kind of role - required player - kind of thing
>> >>
>> >> Note that the individual relations and roles are not yet explicit in
>> >> these
>> >> expressions. The basic semantic structures that I developed includes
>> >> also
>> >> the individual roles and relations and allows for the short cut
>> >> expressions
>> >> (see http://www.gellish.net/topics/semantic-modelling.html).
>> >>
>> >> Each of these triples requires the expression of auxiliary facts,
>> such
>> >> as
>> >> their intention (illocutionary force), author, dates, context, etc.
>> >> In my view it is therefore not a question whether facts can be
>> expressed
>> >> in
>> >> triples, but whether triples are a suitable structure when we in
>> >> practice
>> >> always model in collections of triples.
>> >>
>> >> The Gellish Data Table is a universal structure for all these kinds
>> of
>> >> expressions, including the expression of auxiliary facts. That table
>> is
>> >> an
>> >> alternative to RDF (with some creativity it can be converted into
>> >> collections of triples if you like). It is described in the document
>> >> "Definition of Universal Semantic Databases and Data Exchange
>> Messages"
>> >> on
>> >> http://www.gellish.net/downloads/category/2-english.html.
>> >>
>> >> Andries
>> >>
>> >>
>> >> -----Oorspronkelijk bericht-----
>> >> Van: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>> >> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] Namens doug foxvog
>> >> Verzonden: woensdag 5 september 2012 6:02
>> >> Aan: [ontolog-forum]
>> >> Onderwerp: Re: [ontolog-forum] Accommodating legacy software
>> >>
>> >> On Tue, September 4, 2012 17:02, Kingsley Idehen wrote:
>> >> > On 9/4/12 3:41 PM, doug foxvog wrote:
>> >> >> On Tue, September 4, 2012 12:34, Kingsley Idehen wrote:
>> >> ...
>> >>
>> >> >>> I believe Data denotes Subject Observation.
>> >> >>> I believe all observations are comprised of:
>> >> >>> 1. a subject
>> >> >>> 2. subject attributes
>> >> >>> 3. subject attribute values.
>> >>
>> >> ...
>> >> >> One common type of observation is that A is between B and C.
>> >> >> How would you express this with a single triple? 8)#
>> >>
>> >> > I would state that A is between B. A is Between C. Then I would
>> define
>> >> > the semantics of the 'Between' predicate .
>> >>
>> >> !??
>> >> Let's explore this:
>> >> (and
>> >> (between 10 5 11)
>> >> (between 10 4 11)
>> >> (between 10 6 11)
>> >> (between 10 7 11))
>> >> Using the KI translator this becomes:
>> >> AND
>> >> 10 is between 5
>> >> 10 is between 11
>> >> 10 is between 4
>> >> 10 is between 11
>> >> 10 is between 6
>> >> 10 is between 11
>> >> 10 is between 7
>> >> 10 is between 11.
>> >>
>> >> What semantics does the between predicate have?
>> >>
>> >> How about the quaternary predicate, isBetweenOnPath?
>> >> Can you express the following with triples:
>> >>
>> >> (and
>> >> (isBetweenOnPath WashingtonDC Maryland Virginia I95)
>> >> (not (isBetweenOnPath WashingtonDC Maryland Virginia I495)))
>> >>
>> >>
>> >> -- doug foxvog
>> >> ...
>> >> >
>> >> > Kingsley
>> >> >>
>> >> >> -- doug foxvog
>> >>
>> >>
>> >>
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> (053)
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