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This paper reports on the phenomenon that may be called "derivative meaning," where the basic semantic conventions for certain graphical representation systems give rise to additional informational relations between features of representations and features of the represented. We will discuss several examples of graphical systems, such as the systems of scatter plots, data maps, and tabular representations, whose informational potentials heavily depend on this phenomenon. We will then give an analysis of the way a new meaning relation is derived from basic semantic conventions, and specify the exact conditions for a representation system to support this phenomenon.