  In this report, we aim at the development of a decentralized abstraction
framework for multi-agent systems under coupled constraints, with the
possibility for a varying degree of decentralization. The methodology is based
on the analysis employed in our recent work, where decentralized abstractions
based exclusively on the information of each agent's neighbors were derived. In
the first part of this report, we define the notion each agent's m-neighbor
set, which constitutes a measure for the employed degree of decentralization.
Then, sufficient conditions are provided on the space and time discretization
that provides the abstract system's model, which guarantee the extraction of a
transition system with quantifiable transition possibilities.
