Reasoning in Systems with Elements that Randomly Switch Characteristics
  We examine the issue of stability of probability in reasoning about complex
systems with uncertainty in structure. Normally, propositions are viewed as
probability functions on an abstract random graph where it is implicitly
assumed that the nodes of the graph have stable properties. But what if some of
the nodes change their characteristics? This is a situation that cannot be
covered by abstractions of either static or dynamic sets when these changes
take place at regular intervals. We propose the use of sets with elements that
change, and modular forms are proposed to account for one type of such change.
An expression for the dependence of the mean on the probability of the
switching elements has been determined. The system is also analyzed from the
perspective of decision between different hypotheses. Such sets are likely to
be of use in complex system queries and in analysis of surveys.
