6.3 Entity and Absurdity
In every type hierarchy, the following two types always exist:
The universal type is the type that is a supertype of every other type in the type hierarchy. Therefore, it says nothing about anything. Thus the label "Entity" can be used to refer to anything at all in the type hierarchy, since "Entity" is a supertype of everything else.
The absurd type is the type that is a subtype of every other type in the type hierarchy. Nothing is lower than "Absurdity" in the type hierarchy, and nothing exists which is an instance of "Absurdity".
Relationships among types
Everything is a subtype of Entity. In particular, Absurdity is a proper subtype of Entity:
Entity > Absurdity
. Also, if "Bird" were in our type hierarchy, then it would be true that
Absurdity < Bird
and also that
Bird < Entity
Usefulness of the universal type
Especially the type Entity is useful, in that it can be used to represent any entity. For example the following graph,
relation Poss(*x,*y) is [Animate: ?x]->(Has)->[Entity: ?y]
could be used to define the relation "Poss" or "possession". It says that "An animate thing has an entity", without specifying which kind of entity. The symbols '?x' and '?y' are place-holders for whatever is in the concepts that belong to the Poss relation. In fact, we have just seen an instance of a lambda expression, which will be defined later on.
Reason for the Absurdity type
The reason why there has to be an Absurdity element is that it makes for certain theoretical conveniences, which are deeply rooted in lattice theory and in partial order theory. We do not need to concern ourselves with the details in this course. We just accept that it is common practice to have an Absurdity element.
If you want to know a little bit more about partial orders (not required), click here.
An important concept related to the subtype relation ≤ is that of inheritance. We discuss this concept next.
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Next: 6.4 Inheritance