Off the top of my head, I might suggest a look at the class theory in SUMO, which explicitly allows for self-membership:
(documentation Class EnglishLanguage "classes differ from sets in three important respects. First, classes are not assumed to be extensional. That is, distinct classes might well have exactly the same instances.
MW: This is different for us. We go for extensional classes, which can work because of the 4D paradigm we use – we discussed that not so long ago. I suspect that even though it is not stated here, SUMO classes can change their membership over time, which we also do not need.
Second, classes typically have an associated `condition' that determines the instances of the class.
So, for example, the condition `human' determines the class of humans.
MW: Yes, often the case for us, but not necessarily. Arbitrary collections are also allowed.
Note that some classes might satisfy their own condition (e.g., the class ofabstract things is abstract) and hence be instances of themselves.
MW: Which we also have.
Third, the instances of a class may occur only once within the class, i.e. a class cannot contain duplicate instances.")
MW: Yes I’m familiar with bags that this is excluding.
MW: So it looks like we should just say that classes are extensional and more or less leave it at that.
Tel: +44 560 302 3685
Mobile: +44 750 3385279
This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177.
Registered office: 2 Brookside, Meadow Way, Letchworth Garden City, Hertfordshire, SG6 3JE.