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Prerequisites can play a crucial role in users' decision-making yet recommendation systems have not fully utilized such contextual background knowledge. Traditional recommendation systems (RS) mostly enrich user-item interactions where the context consists of static user profiles and item descriptions, ignoring the contextual logic and constraints that underlie them. For example, an RS may recommend an item on the condition that the user has interacted with another item as its prerequisite. Modeling prerequisite context from conceptual side information can overcome this weakness. We propose Prerequisite Driven Recommendation (PDR), a generic context-aware framework where prerequisite context is explicitly modeled to facilitate recommendation. We first design a Prerequisite Knowledge Linking (PKL) algorithm, to curate datasets facilitating PDR research. Employing it, we build a 75k+ high-quality prerequisite concept dataset which spans three domains. We then contribute PDRS, a neural instantiation of PDR. By jointly optimizing both the prerequisite learning and recommendation tasks through multi-layer perceptrons, we find PDRS consistently outperforms baseline models in all three domains, by an average margin of 7.41%. Importantly, PDRS performs especially well in cold-start scenarios with improvements of up to 17.65%.