Our aim is to contribute to the extension of classical Formal Concept Analysis (FCA), allowing the management of unknown information. 
We present a new framework which allows us to work with this unknown information. In addition, we introduce a new algebraic framework. With this algebraic framework, we present the definition of partial formal context, that is, formal context with unknown information  and we introduce two Galois connection which allow us to capture different information from the Partial formal context: the information that might be true in any completion and the information that is true in the moment that we have but it can be not longer true if we have new information.