  The modeling of cascade processes in multi-agent systems in the form of
complex networks has in recent years become an important topic of study due to
its many applications: the adoption of commercial products, spread of disease,
the diffusion of an idea, etc. In this paper, we begin by identifying a
desiderata of seven properties that a framework for modeling such processes
should satisfy: the ability to represent attributes of both nodes and edges, an
explicit representation of time, the ability to represent non-Markovian
temporal relationships, representation of uncertain information, the ability to
represent competing cascades, allowance of non-monotonic diffusion, and
computational tractability. We then present the MANCaLog language, a formalism
based on logic programming that satisfies all these desiderata, and focus on
algorithms for finding minimal models (from which the outcome of cascades can
be obtained) as well as how this formalism can be applied in real world
scenarios. We are not aware of any other formalism in the literature that meets
all of the above requirements.
