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A number of complexity classes, most notably PTIME, have been characterised by sub-systems of linear logic. In this paper we show that the functions computable in logarithmic space can also be characterised by a restricted version of linear logic. We introduce Stratified Bounded Affine Logic (SBAL), a restricted version of Bounded Linear Logic, in which not only the modality ! but also the universal quantifier is bounded by a resource polynomial. We show that the proofs of certain sequents indoi:10.1109/lics.2007.45 dblp:conf/lics/Schopp07 fatcat:rblt4b5qsrgy3kaqtftonbex5u