This paper deals with approaches to approximate reduction in inconsistent formal decision contexts. Congruence relations on the object power set are first introduced in a formal context. Then relationships between congruence relations and the corresponding concept lattices are discussed. Based on the congruence relations, notions of lower approximate and upper approximate attribute reduct are then developed in inconsistent formal decision contexts. Finally, discernibility matrices and discernibility functions associated with the proposed attribute reduction are defined, from which we can calculate all attribute reducts.