Developing a matrix characterization for MELL

Abstract

We present a matrix characterization of logical validity in the multiplicitative exponential fragment of linear logic. It extends an earlier characterization of the multiplicative fragment by the exponentials and multiplicative constant. In the process of proving the matrix characterization correct and complete, a methodology for developing a matrix characterization from a sequent calculus by a series of intermediate calculi is demonstrated. Our characterization provides a foundation for matrix-based proof search procedures as well as for procedures which translate machine-found proofs back into the usual sequent calculus.