This paper reports on first attempts to develop a contextual logic of ordinal data. The investigations are based on a mathematical theory of ordinal contexts which has been developed within Formal Concept Analysis. From ordinal contexts, binary power context families are derived as semantic basis of a contextual logic of ordinal data. They are used to characterize compound attributes extensionally. In this way, the contextual logic becomes a relational logic within the framework of the Peircean Algebraic Logic, as reconstructed by R. W. Burch. The considerations of this papers are discussed through an example of ordinal data investigated toward a meaningful representation in ordered vector spaces.