We develop data retrieval algorithms for crowd-sensing applications that reduce the underlying network bandwidth consumption or any additive cost metric by exploiting logical dependencies among data items, while maintaining the level of service to the client applications. Crowd sensing applications refer to those where local measurements are performed by humans or devices in their possession for subsequent aggregation and sharing purposes. In this paper, we focus on resource-limited crowd sensing, such as disaster response and recovery scenarios. The key challenge in those scenarios is to cope with resource constraints. Unlike the traditional application design, where measurements are sent to a central aggregator, in resource limited scenarios, data will typically reside at the source until requested to prevent needless transmission. Many applications exhibit dependencies among data items. For example, parts of a city might tend to get flooded together because of a correlated low elevation, and some roads might become useless for evacuation if a bridge they lead to fails. Such dependencies can be encoded as logic expressions that obviate retrieval of some data items based on values of others. Our algorithm takes logical data dependencies into consideration such that application queries are answered at the central aggregation node, while network bandwidth usage is minimized. The algorithms consider multiple concurrent queries and accommodate retrieval latency constraints. Simulation results show that our algorithm outperforms several baselines by significant margins, maintaining the level of service perceived by applications in the presence of resource-constraints.