For an arbitrary triadic relation whether it happens to be a sign relation or not, there are six dyadic relations obtained by projecting on one of the planes of the -space The six dyadic projections of a triadic relation are defined and notated as shown in Table 2.
By way of unpacking the set-theoretic notation, here is what the first definition says in ordinary language.
The dyadic relation resulting from the projection of on the -plane is written briefly as or written more fully as and is defined as the set of all ordered pairs in the cartesian product for which there exists an ordered triple in for some element in the set
In the case where is a sign relation, which it becomes by satisfying one of the definitions of a sign relation, some of the dyadic aspects of can be recognized as formalizing aspects of sign meaning which have received their share of attention from students of signs over the centuries, and thus they can be associated with traditional concepts and terminology. Of course, traditions may vary as to the precise formation and usage of such concepts and terms. Other aspects of meaning have not received their fair share of attention, and thus remain anonymous on the contemporary scene of sign studies.
- Charles S. Peirce (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73. Online.
- Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52. Archive. Journal. Online (doc) (pdf).