In classical formal concept analysis, attribute logic refers to the study of implications that hold between the attributes of a formal context. In some scenarios, attributes may be logically interdependent a priori by definition, particularly when they are defined by logical formulae. This paper examines various settings in which attributes are logically defined and explores the resulting effects on attribute logic and on the structure of the concept lattice. We also investigate under which conditions the implicational theory of a context with logically defined attributes is as informative as the underlying context itself for deciding the validity of logical formulae.