Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al., allow for the composition of justification systems. This notion of nesting thus enables the modular definition of semantics of rule-based languages, and increases the representational capacities of justification theory. As we show in this paper, the original characterization of semantics for nested justification systems leads to the loss of information relevant for explanations. In view of this problem, we provide an alternative characterization of their semantics and show that it is equivalent to the original one. Furthermore, we show how nested justification systems allow representing fixpoint definitions.

We propose a class of random scale-free spatial networks with nested community structures called SHEM and analyze Reed–Frost epidemics with community related independent transmissions. We show that in a specific example of the SHEM the epidemic threshold may be trivial or not as a function of the relation among community sizes, distribution of the number of communities, and transmission rates.

The MARK III FAA (Flexible Automatic Assembly) cell was designed to minimise the risk factors associated with FAA. This FAA cell is stepwise upgradeable and adopts the sub-batch principle and reversed material flow solutions. It allows for the assembly of products with an annual volume normally too low to justify automation. The MARK III FAA cell was implemented with the FACE programming and control system, a PC-based, modular programming and control platform for FAA cells. It enables the management of unpredictable order schemes and leads to very low programming costs.