# A Matrix Characterization for Multiplicative Exponential Linear Logic

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## Abstract

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 nonclassical logics. It provides a foundation for developing proof search procedures for *MELL* by adopting techniques that are based on these concepts and also makes it possible to adopt algorithms that translate the machine-found proofs back into the usual sequent calculus for *MELL*.

linear logic automated deduction connection method

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