1. "A participation" is about as strange as "a connectedness": what language
is this?
2. What is the difference between "a participation" and "a kind of
participation"?

The notion of role type as explained by Steve Pepper (posted
2/19/2003 to the sc34wg3 list) reads in part:
***Quote from Steve Pepper***
In 13250, an association role (represented by an  element)
represents the involvement of a certain topic in a certain association.
It has a 'type' attribute which represents the class to which the role
belongs. There is thus a kind of type-instance relationship between the
role type and the (individual) role. A role type can be thought of as
the set of all similar involvements in associations. Thus "husband" (for
example) is a *role type*, not a *role*.
***End Quote from Steve Pepper***
In prose, 13250 mentions role type in the following paragraphs (ignoring
it in the syntax productions):
***ISO 13250 passages on role type***
The optional occurrence role type (type) attribute references a single
topic link. The subject of the
referenced topic link is a class of occurrence role of which the
occurrence role expressed by the
occurs element is an instance. The class-instance relationship
established between the subject of
the referenced topic link and the referencing occurs element could
alternatively be established by
making the occurs element an occurrence of the referenced topic link,
within the scope of an
occurrence role whose meaning is that the occurrence role is an instance
of the subject of the topic
link.
If the occurrence role type (type) attribute is specified, and if the
topic referenced by the type
attribute has a name characteristic that lies within a scope that is
appropriate to the topic map user's
context, the referenced topic's name characteristic is used to
characterize the occurrence role for the
user. Otherwise, the value of the occrl attribute (or, if the occrl
attribute is not specified, the generic
identifier) is used to characterize the occurrence role for the user.
....
The optional association role type (type) attribute references a single
topic link. The subject of the
referenced topic link is a class of association role of which the
association role expressed by the
assocrl element is an instance. The class-instance relationship thus
established between the subject
of the referenced topic link and the referencing assocrl element could
alternatively be established
by making the assocrl element an occurrence of the referenced topic
link, within the scope of an
occurrence role whose meaning is that the association role is an
instance of the subject of the topic
link.
NOTE 43 If the topic links whose subjects are association role types
specify identity attributes, and if the subjec
descriptor(s) referenced by those identity attributes describe the same
subject, the assocrl elements that are instances of those association
role types can be universally recognized as specifications of equivalent
association roles. Depending on the nature of such association roles,
the use of public subject descriptors to define association role types
may significantly facilitate the process of merging topic maps, even
when they emanate from disparate sources.
If the association role type (type) attribute is specified, and if the
topic referenced by the type
attribute has a name characteristic that lies within a scope that is
appropriate to the topic map user's
context, the referenced topic's name characteristic is used to
characterize the association role for the
user. Otherwise, the value of the anchrole attribute (or, if the
anchrole attribute is not specified, the
generic identifier) is used to characterize the association role for the
user.
***End 13250 passages***
At Steve Pepper's suggestion, I also consulted the latest draft of the
SAM, which reports:
***SAM passages on role type***
(3.9 Association role items)
An association role connects two pieces of information within an
association: the subject participating in the association, known as the
association role player, and the subject defining the nature of its
participation, known as the association role type.
Association role items represent association roles, and may have the
following properties:
....
2. [type]: A topic item. This is the topic item that represents the
association role type.
***End 3.9***
The other place I found role type was under open issues:
***SAM open issues***
Issue (assoc-role-player-type):
Must both [role playing topic] and [role type] have values?
***End SAM open issues***
The open issue in the SAM is as good a jumping off point as any.
The SAM issue illustrates the confusion that is caused by treating a
role as a class rather than an individual instance. But for that
conflation of role (as in John as the husband in an assertion) and the
class of being a husband, the suggested reading for role type, then the
open issue of the SAM would not have arisen. When those two ideas are
pushed together, it becomes a real practical question of why would
"husband" be repeated?
In RM terms, I read the attributes in 13250 as being assertions about
the role and hence, the idea of class being something that is asserted
about a role and not conflated with the role itself. With that reading,
the answer to the open issue resolves to Yes, [role playing topic] must
have a value, [role] must have a value and, if you wish to make an
assertion about the role, such as class, then [role-type] must have a value.
The problem of conflating instances and classes is not unknown. It is
termed the "assumption of inherent classification" in *Emancipating
Instances from the Tyranny of Classes in Information Modeling* by
Parsons and Wand, see
http://citeseer.nj.nec.com/parsons00emancipating.html for the full 56
page paper which I won't try to summarize here. It may also be of
interest to look at: *Coordinating Heterogeneous Work: Information and
Representation in Medical Care* by  Reddy, Dourish, Pratt, who favorably
cite the work of Parsons and Wand in designing information systems for
an actual heterogeneous environment, see
http://citeseer.nj.nec.com/reddy01coordinating.html for that paper.
The final problem with the suggested usage is that it results in fairly
awkward English. I would not describe myself as playing the role-type of
husband in an assertion about Carol (my wife) and myself. I would say
that I play the role of husband. If I want to make assertions about the
role of husband as a class, then I should make a separate assertion,
with which others could disagree, ignore, etc., that the role of husband
is a class.
Sorry to go on at such length but I felt I owed both Steve's, Pepper and
Newcomb, a fairly detailed explanation about why I am suggesting a
departure from what is apparently one reading of 13250.