Probabilistic Argumentation. An Equational Approach
  There is a generic way to add any new feature to a system. It involves 1)
identifying the basic units which build up the system and 2) introducing the
new feature to each of these basic units.
  In the case where the system is argumentation and the feature is
probabilistic we have the following. The basic units are: a. the nature of the
arguments involved; b. the membership relation in the set S of arguments; c.
the attack relation; and d. the choice of extensions.
  Generically to add a new aspect (probabilistic, or fuzzy, or temporal, etc)
to an argumentation network <S,R> can be done by adding this feature to each
component a-d. This is a brute-force method and may yield a non-intuitive or
meaningful result.
  A better way is to meaningfully translate the object system into another
target system which does have the aspect required and then let the target
system endow the aspect on the initial system. In our case we translate
argumentation into classical propositional logic and get probabilistic
argumentation from the translation.
  Of course what we get depends on how we translate.
  In fact, in this paper we introduce probabilistic semantics to abstract
argumentation theory based on the equational approach to argumentation
networks. We then compare our semantics with existing proposals in the
literature including the approaches by M. Thimm and by A. Hunter. Our
methodology in general is discussed in the conclusion.
