This paper tackles the fundamental questions arising when
looking at argumentation frameworks as interacting components, characterized by
an Input/Output behavior, rather than as isolated monolithical entities. This modeling stance arises
naturally in some application contexts, like multi-agent systems, but, more
importantly, has a crucial impact on several general application-independent
issues, like argumentation dynamics, argument summarization and explanation,
incremental computation, and inter-formalism translation. Pursuing this
research direction, the paper introduces a general modeling approach and
provides a comprehensive set of theoretical results putting the intuitive
notion of Input/Output behavior of argumentation
frameworks on a solid formal ground. This is achieved by combining three main
ingredients. First, several novel notions are introduced at the representation
level, notably those of argumentation framework with input, of argumentation
multipole, and of replacement of multipoles within a traditional argumentation
framework. Second, several relevant features of argumentation semantics are
identified and formally characterized. In particular, the canonical local
function provides an input-aware semantics characterization and a suite of
decomposability properties are introduced, concerning the correspondences
between semantics outcomes at global and local level. The third ingredient
glues the former ones, as it consists of the investigation of some
semantics-dependent properties of the newly introduced entities, namely S-equivalence
of multipoles, S-legitimacy and S-safeness of replacements, and transparency of
a semantics with respect to replacements. Altogether they provide the basis and
draw the limits of sound interchangeability of multipoles within traditional
frameworks. The paper develops an extensive analysis of all the concepts listed
above, covering seven well-known literature semantics and taking into account
various, more or less constrained, ways of partitioning an argumentation
framework. Diverse examples, taken from the literature, are used to illustrate
the application of the results obtained and, finally, an extensive discussion
of the related literature is provided.