  In traditional justification logic, evidence terms have the syntactic form of
polynomials, but they are not equipped with the corresponding algebraic
structure. We present a novel semantic approach to justification logic that
models evidence by a semiring. Hence justification terms can be interpreted as
polynomial functions on that semiring. This provides an adequate semantics for
evidence terms and clarifies the role of variables in justification logic.
Moreover, the algebraic structure makes it possible to compute with evidence.
Depending on the chosen semiring this can be used to model trust,
probabilities, cost, etc. Last but not least the semiring approach seems
promising for obtaining a realization procedure for modal fixed point logics.
