We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cut-free proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on a two-letter alphabet.
['Harish Devarajan', 'Dominic J. D. Hughes', 'Gordon D. Plotkin', 'Vaughan R. Pratt']
Full completeness of the multiplicative linear logic of Chu spaces