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This paper discusses the semantic content of syntactic dependencies. We assume that syntactic dependencies play a central role in the process of semantic interpretation. They are defined as selective functions on word denotations. Among their properties, special attention will be paid to their ability to make interpretation co-compositional and incremental. To describe the semantic properties of dependencies, the paper will be focused on two particular linguistic tasks: word sense disambiguation and attachment resolution. The second task will be performed using a strategy based on automatic acquisition from corpora.