  This work is divided between two main areas: in the theory of multialgebras,
we focus mostly on a new definition of what a freely generated object should be
in their category, and on how this category is equivalent to another with
partially ordered algebras as objects; we then use nondeterministic semantics,
specially those we have named restricted Nmatrices, on paraconsistent logics
and some systems dealing with a new presentation of the natural concept of
incompatibility, which generalizes inconsistency.
