Property information
Derivation as a relation between instances. The temporal relation of derivation is more complex. Transformation, on the instance level, is just the relation of identity: each adult is identical to some child existing at some earlier time. Derivation on the instance-level is a relation holding between non-identicals. More precisely, it holds between distinct material continuants when one succeeds the other across a temporal divide in such a way that at least a biologically significant portion of the matter of the earlier continuant is inherited by the later. Thus we will have axioms to the effect that from c derives_from c1 we can infer that c and c1 are not identical and that there is some instant of time t such that c1 exists only prior to and c only subsequent to t. We will also be able to infer that the spatial region occupied by c as it begins to exist at t overlaps with the spatial region occupied by c1 as it ceases to exist in the same instant.
Derivation on the instance level (*derives_from*) holds between distinct material continuants when one succeeds the other across a temporal divide in such a way that at least a biologically significant portion of the matter of the earlier continuant is inherited by the later. We say that one class C derives_from class C' if instances of C are connected to instances of C' via some chain of instance-level derivation relations. Example: osteocyte derives_from osteoblast. Formally: C derives_immediately_from C' if and only if: given any c and any t, if c instantiates C at time t, then there is some c' and some t', such that c' instantiates C' at t' and t' earlier-than t and c *derives_from* c'. C derives_from C' if and only if: there is an chain of immediate derivation relations connecting C to C'.