. This paper provides a unified approach for matrix characterizations for propositional substructural logics, whereby the focus is laid on a uniform representation of different validity concepts in matrices. Starting from a restricted validity concept for matrices called basic-validity, where a matrix is considered as valid if each literal is connected exactly once, we use rewrite rules to obtain a wider class of validity concepts. Here a matrix is considered as valid if it can be transformed to a basic-valid matrix by using the appropriate rewrite-rules. For each validity concept we give corresponding algebraic semantics. 1 Introduction In the last years there has been an undeniable growing interest in the computer science community concerning non-classical logics. This is on the one side caused by the development of new logics like Girards linear logic . On the other side there are application-domains, for example planning tasks where ordinary first-order logic turns out..