An argumentation system for reasoning with conflict-minimal
  paraconsistent ALC
  The semantic web is an open and distributed environment in which it is hard
to guarantee consistency of knowledge and information. Under the standard
two-valued semantics everything is entailed if knowledge and information is
inconsistent. The semantics of the paraconsistent logic LP offers a solution.
However, if the available knowledge and information is consistent, the set of
conclusions entailed under the three-valued semantics of the paraconsistent
logic LP is smaller than the set of conclusions entailed under the two-valued
semantics. Preferring conflict-minimal three-valued interpretations eliminates
this difference.
  Preferring conflict-minimal interpretations introduces non-monotonicity. To
handle the non-monotonicity, this paper proposes an assumption-based
argumentation system. Assumptions needed to close branches of a semantic
tableaux form the arguments. Stable extensions of the set of derived arguments
correspond to conflict minimal interpretations and conclusions entailed by all
conflict-minimal interpretations are supported by arguments in all stable
extensions.
