FAIW, here is a list of questions and
comments regarding the first part of the module 'Mereotopology' of the SUMO
(not including Varzi & Casati's hole story). I'd appreciate any comments,
feel free to reply to me personally.
This really accounts for a first
thorough pass over this material and aims mainly at making sure I'm not
tripping too badly before going further. Thanks for bringing me kindly back to
reason as needed. Another preliminary remark, I tried to play the game and to
worry, at the level of my humble understanding, about the quality of this
module within the context of the SUMO; in other words, trying to comment
without arguing too much over the material of the base and structural modules.
After the preliminaries, it was easier to go through the file and make
comments and suggestions as they occur. I hope that this won't be too tedious
to read and might be somewhat constructive at least as a starter for a few
rounds of discussion.
Preliminary comments regarding &%part:
Something needs to be done with &%part, there are serious problems,
even if trying to cope with the top level 'concepts' of the SUMO. The central
problematic thing is the domain of this relation, currently
&%SelfConnectedObject. IMHO, this is absurd enough but, even worse, the
SUMO is not consistent with respect to this choice.
Is the rationale
that disconnected objects do not form an object? Are not part of an object? It
seems that they form &%Collections, I confess I have a hard time with
this. Collections have members that are informally described as parts but, god
forbid, collections are not mereological sums of their members, rather some
sort-of intensional sort of set theoretical weirdos. Anyway, no need to be
controversial here.
One of the first things to do is to decide which
of &%part's argument constraints or of &%MereologicalSumFn's and
others need to be modified. So, either generalize to (domain part 1 [and 2]
Object) or alternatively restrain the domain of the mereological operators,
which currently do not require self connected objects. The first solution
would have important consequences for SUMO regarding its mereology. The second
solution is unfortunate (the only correct way I could find to qualify this).
The current nonsense comes from the fact that you could form the sum of two
members of a collection while neither of these members would be 'parts' of
this sum! Or am I missing something?
I suggest the first solution of
course and moreover to then question the notion of &%member and think
about what kind of species &%Object is lacking of. I seem to remember
ranting about this awhile ago, I'll pass on this for this time around.
However, let me add that, imho, the use of &%Collections conceived as
disconnected objects would be sounder if &%member were a sub-relation of
&%part, same thing for &%subCollection, assuming the broadening of the
domain of &%part in each argument place.
Still about
&%part, for the &%LinguisticObject guys… there are a few axioms
related to linguistic stuff that are using &%part, see
&%SymbolicString, &%Morpheme and &%Word for instance. Those aren't
well formed (or are they?) given the domain of &%part (which doesn't
subsume &%ContentBearingObject if I'm not mistaken). Three possible
solutions to this, maybe more, maybe with combination: i) generalize the use
of &%part (I would tend to prefer that anyway, although I'm not sure about
the particular of the linguistic stuff), ii) subsume &%Morpheme and others
under self connected object (I don't know what kind of sense that makes for
the various specialization of &%ContentBearingObject), iii) use another
relation where part was intended (to me this almost sounds like a gratuitous
step toward i) though). What d'y'all say?
As I read you, you have found the following problems with
the mereotopological component of the SUMO:
1. Given the current arg type restrictions on 'part'
and 'MereologicalSumFn', it is possible to form mereosums from two
'Objects' and yet not to have those 'Objects' be 'parts' of the meresum.
This is, as you point out, extremely
counterintuitive.
2. The use of 'part' with instances of
'LinguisticExpression' should not be allowed given the current arg type
restrictions on 'part'.
3. There is currently no relationship between 'part' and
'member', even though these are very closely related
predicates.
As you suggest, we can resolve these
three problems by generalizing the arg type restrictions on 'part' to
'Object' and by making 'member' a subrelation of 'part'. Both of these
suggestions sound good to me. If no one objects, I'll incorporate
them into the SUMO.
From now on, to follow
these comments, I suggest holding a print out of the part of the file on
mereotopology up to Varzi and Casati's stuff.
1. The document
mentions papers from Smith and from Guarino. Any paper in particular ? Which?
I'd be interested in this precision.
Fair enough. I'll try to track down the
references.
2. About &%connects. Shouldn't
the domain of the first argument be &%SelfConnectedObject? Maybe that's
just a need for clarifying the notion of &%SelfConnectedObject or maybe
the relation &%connects itself. It looks like some configurations are
allowed as examples by the present definition that seem not to have been
intended.
Let OBJ2 and OBJ3 be two non connected pieces of ceramic on
Mr. Bell's workbench (here, I guess it suffices to say that OBJ2 does not
touch OBJ3). Let OBJ1 be the mereological sum of two layers of glue such that
LG1 (respectively LG2) is spread over OBJ2 (respectively OBJ3) at time t by
Mr. Bell. Let's not argue over glue's physical properties, unless that really
is something decisive I'm missing, just take the layer of glue as two
&%(SelfConnected?)Objects. At t, &%connects does not hold of LG1 and
LG2, that is OBJ1 is not self connected. At time t+s, Mr. Bell assembles OBJ2
and OBJ3, thus fixing Odette's saucer. LG1 and LG2 are connected (say,
&%meetsSpatially holds). It seems to me that the current definition allows
&%connects to hold of OBJ1, OBJ2 and OBJ3 in this order at both time t and
t+s. What's puzzling being that it could hold at t.
I agree that this is counterintuitive and that the best way of
resolving the problem is to narrow the arg type restrictions on 'connects' to
'SelfConnectedObject'.
3.
Isn't
(=>
(partlyLocated ?OBJ ?REGION)
(overlapsSpatially ?OBJ
?REGION))
better replaced with,
(subrelation partlyLocated
overlapsSpatially)?
This seems better to me too. If no one
objects, I'll make the replacement in the SUMO source
file.
4. About &%overlapsPartially: this is symmetric, right? Then,
couldn't the current implication be simplified?
For instance,
(not
(and
(overlapsPartially ?OBJ1 ?OBJ2)
(part ?OBJ1
?OBJ2)))
Also, isn't this relation irreflexive?
Right, the predicate is both symmetric and irreflexive, and
I agree that the axiom can be simplified as you
indicate.
5. A question about
&%superficialPart. Why is it so that an appeal to the geometric complement
of an object should be taken as an intuitive recourse? Why isn't this notion
in the SUMO and why not formalizing the parenthetic criterion in the
documentation of &%superficialPart? It seems that an object has a single
geometric complement, is that correct? Is the 'geometric complement' something
potentially as general as an &%Object or more specifically a &%Region?
Or it could a &%Collection maybe? Of regions only?
I think the appeal to "geometric complement" is probably not
very helpful. I'll reformulate the documentation
string.
6. Isn't there a problem with the axiom for
&%surface:
(=>
(surface ?OBJ1 ?OBJ2)
(forall (?PART)
(and
(instance ?OBJ1 SelfConnetcedObject)
(=>
(superficialPart ?PART ?OBJ2)
(part ?OBJ3 ?OBJ1)))))?
Assume
(surface ?OBJ1 ?OBJ2). On one hand, a surface of an object is self connected,
(instance ?OBJ1 SelfConnectedObject). (Note that given the present setting,
this is trivial given the domain specification of the relation.) On the other
hand, any superficial part of an object is a part of this self connected
object, (forAll (?PART) (=> (superficialPart ?OBJ3 ?OBJ2) (part ?OBJ3
?OBJ1))).
I agree that the clause about 'SelfConnectedObject' is
redundant given what the arg type restrictions should be on 'surface'.
I'll add these restrictions and delete the clause in the source file. As
for the rest, note that you have not copied the axiom
correctly.
That just can't be, that is, unless
?OBJ2 has only 1 surface, i.e. only one maximally connected superficial part.
Take an hollow object such as a tennis ball. The geometric complement is
disconnected, that is an indication that there are at least two superficial
parts. There's an 'exterior' and an 'interior' surface in other words.
The
implication in the consequent of the present axiom could hold in case the
object has a certain property of 'density', maybe this can be indexed to the
number of maximally connected superficial parts (the present form of the axiom
is adequate if the object has no 'interior superficial part'). Note that
'interior superficial parts' are allowed, those are not '&%interiorParts'!
This could suggest introducing terms for relation for maximally
connected part, vocabulary for density or alternatively flesh out the
hierarchy of self connected objects according to their topology, and
accordingly, sub-relations of &%superficialPart, etc.
Well, I think an easier route would be just to allow that
hollow objects like tennis balls can have two disconnected surfaces, the inner
surface and the outer surface, and to change the documentation string of
'surface' so that readers aren't left with the incorrect impression that
all 'SelfConnectedObjects' have a single
surface.
I have to stop there, apologies
for the messy presentation, poor language and any confusion.
Thanks
for your time,
Pierre