A Semantic Proof of Polytime Soundness of Light Affine Logic

Abstract

We define realizability semantics for Light Affine Logic ( $\mathsf{LAL}$) which has the property that denotations of functions are polynomial time computable by construction of the model. This gives a new proof of polytime-soundness of $\mathsf{LAL}$which is considerably simpler than the standard proof based on proof nets and is entirely semantical in nature. The model construction uses a new instance of a resource monoid; a general method for interpreting systems based on Linear Logic introduced earlier by the authors.