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The paper shows how Combinatory Categorial Grammar (CCG) can be adapted to take advantage of the extra resource-sensitivity provided by the Categorial Type Logic framework. The resulting reformulation, Multi-Modal CCG, supports lexically specified control over the applicability of combinatory rules, permitting a universal rule component and shedding the need for language-specific restrictions on rules. We discuss some of the linguistic motivation for these changes, define the Multi-Modal CCG system and demonstrate how it works on some basic examples. We furthermore outline some possible extensions and address computational aspects of Multi-Modal CCG.