This paper provides a computable quantitative measure which accounts for the difficulty in human processing of sentences: why is a sentence harder to parse than another one? Why is some reading of a sentence easier than another one? We take for granted psycholinguistic results on human processing complexity like the ones by Gibson. We define a new metric which uses Categorial Proof Nets to correctly model Gibson's account in his Dependency Locality Theory. The proposed metric correctly predicts some performance phenomena such as structures with embedded pronouns, garden paths, unacceptable center embeddings, preference for lower attachment and passive paraphrases acceptability. Our proposal gets closer to the modern computational psycholinguistic theories, while it opens the door to include semantic complexity, because of the straightforward syntax-semantics interface in categorial grammars.