This is joint work with Prof Ewa Orlowska, National Insitute of Telecommunications, Warsaw. In this talk we show that the fundamental notions of formal concept analysis, namely contexts and concepts, can be studied within the framework of discrete dualities. For contexts we define a class of context algebras and establish a discrete duality which includes a representation of a context algebra in terms of relational structures (or frames) that provide a semantics of the context logic associated with the context algebras. For the family of concepts of a context, together with operations of meet, join and negations, we define a class of concept lattices with negations and establish a discrete duality in terms of a non-topological relational structure. In conclusion we discuss the specification and verification within our framework of properties of formal concepts, of attribute dependencies and of implications.