Written Arabic is a especially ambiguous due to the lack of diacritisation of texts, and this makes the translation harder for automatic systems that do not take into account the context of phrases. Here, we use a standard Phrase-Based Statistical Machine Translation architecture to build an Arabic-to-English translation system, but we extend it by incorporating a local discriminative phrase selection model which addresses this semantic ambiguity. Local classifiers are trained using both linguistic information and context to translate a phrase, and this significantly increases the accuracy in phrase selection with respect to the most frequent translation traditionally considered. These classifiers are integrated into the translation system so that the global task gets benefits from the discriminative learning. As a result, we obtain improvements in the full translation of Arabic documents at the lexical, syntactic and semantic levels as measured by an heterogeneous set of automatic metrics.