Non-deterministic Multiple-valued Structures
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The ordinary concept  of a multiple-valued
matrix is generalized by introducing
non-deterministic matrices (Nmatrices), in which
non-deterministic computations of truth-values are
allowed. It is shown that
some important logics for reasoning under uncertainty
can be characterized by finite Nmatrices, although they
have only infinite characteristic ordinary (deterministic)  matrices.
on the other hand a strong connection is established between
the admissibility of the cut rule in canonical Gentzen-type propositional
systems, non-triviality of such systems,
and the existence of sound and complete non-deterministic
two-valued semantics for them.