I wondered the same! It seems to have to do with Girard's idea that linear logic involves 'additive' and 'multiplicative' 'universes' (all words in quotes beca

I wondered the same! It seems to have to do with Girard's idea that linear logic involves 'additive' and 'multiplicative' 'universes' (all words in quotes because I've only skimmed to try to get an idea—even the editors of TCS apparently found the paper unreferee-able). See logical p. 3 (physical p. 4) of http://iml.univ-mrs.fr/~girard/linear.pdf http://iml.univ-mrs.fr/~girard/linear.pdf . (How exponentials fit into the picture I don't know.) Then drdeca (https://news.ycombinator.com/item?id=14684219 https://news.ycombinator.com/item?id=14684219) 's explanation of why affine logic is so called seems plausible, but I haven't looked into it.