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A Semantic Proof of Polytime Soundness of Light Affine Logic

By Ugo Dal Lago and Martin Hofmann


Abstract. We define a denotational semantics for Light Affine Logic (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 LAL which is considerably simpler than the standard proof based on proof nets and also is entirely semantical in nature. The model construction uses a new instance of a resource monoid; a general method for interpreting variations of linear logic with complexity restrictions introduced earlier by the authors.

Year: 2011
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