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 transformer to track the attacker knowledge over multiple declassification queries, and checks for violations against the user-specified policies on information flow control applications. We implemented a prototype of ANOSY and showed that it is precise and permissive: up to 14 declassification queries were permitted before policy violation using the powersets of interval domain.