Non-interference is a popular way to enforce confidentiality of sensitive data. However, declassification of sensitive information is often needed in realistic applications but breaks non-interference. We present Anosy, an approximate knowledge synthesizer for quantitative declassification policies. Anosy uses refinement types to automatically construct machine checked over- and under-approximations of attacker knowledge for boolean queries on multi-integer secrets. It also provides an AnosyT monad to track the at- tacker knowledge over multiple declassification queries and checks for violations against user-specified policies in information flow control applications. We implement a prototype of Anosy and show that it is precise and permissive: up to 14 declassification queries are permitted before a policy violation occurs using the powerset of intervals domain.