Moreover, we introduce the notion of degree correlation for the case where only the statistical information of a power grid is known.
This raises the question whether the notion of belief can be reduced to the notion of degree of belief.
Consider the following two proposals for a link between the qualitative notion of belief and the quantitative notion of degree of belief.
On its face, a single notion of degree of confirmation does not apply in different contexts of inquiry.
In a recent paper we gave a notion of degree for a class of perturbations of nonlinear Fredholm maps of index zero between real infinite dimensional Banach spaces.
The notion of degree of confirmation that is applicable to a scientific theory, which ranges over several fields of inquiry, appears to differ from the confirmability of specific scientific hypotheses regarding results of an experiment in chemistry or biology.
It is worth mentioning that since the notion of degree makes sense only in the case of acyclic networks, special issues arise when networks contain cycles (see Antonelli (1997) for a treatment of inheritance on cyclic networks).
Furthermore, one reason for adopting standard ranking functions with a well-ordered domain is that the notion of degree of entrenchement makes only sense for natural (or ordinal) numbers, because one has to count the independent and minimally positively reliable information sources.
This dichotomy of the notion of degree in the non-flat situation is not evident in R k : it is masked by the fact that an equation of the type f ( x ) = y can be written as f ( x ) − y = 0. Anyhow, in the context of RFDEs (ODEs included), it is the degree of a vector field that plays a significative role.
Finally, we remark that our methods can be generalized beyond the simple notion of degree centrality to other more complicated centrality measures that also have functional significance.
