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We develop a matrix characterization of logical validity in MELL, the multiplicative fragment of propositional linear logic with exponentials and constants. To prove the correctness and completeness of our characterization, we use a purely proof theoretical justification rather than semantical arguments. Our characterization is based on concepts similar to matrix characterizations proposed by Wallen for other non-classical logics. It provides a foundation for developing proof search proceduresdoi:10.1023/b:jars.0000029976.22387.ac fatcat:iw2ki256vjf6xfocfayaxwytgi